hypothesis for a correlational study

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How to Write a Hypothesis for Correlation

How to Calculate a P-Value

A hypothesis is a testable statement about how something works in the natural world. While some hypotheses predict a causal relationship between two variables, other hypotheses predict a correlation between them. According to the Research Methods Knowledge Base, a correlation is a single number that describes the relationship between two variables. If you do not predict a causal relationship or cannot measure one objectively, state clearly in your hypothesis that you are merely predicting a correlation.

Research the topic in depth before forming a hypothesis. Without adequate knowledge about the subject matter, you will not be able to decide whether to write a hypothesis for correlation or causation. Read the findings of similar experiments before writing your own hypothesis.

Identify the independent variable and dependent variable. Your hypothesis will be concerned with what happens to the dependent variable when a change is made in the independent variable. In a correlation, the two variables undergo changes at the same time in a significant number of cases. However, this does not mean that the change in the independent variable causes the change in the dependent variable.

Construct an experiment to test your hypothesis. In a correlative experiment, you must be able to measure the exact relationship between two variables. This means you will need to find out how often a change occurs in both variables in terms of a specific percentage.

Establish the requirements of the experiment with regard to statistical significance. Instruct readers exactly how often the variables must correlate to reach a high enough level of statistical significance. This number will vary considerably depending on the field. In a highly technical scientific study, for instance, the variables may need to correlate 98 percent of the time; but in a sociological study, 90 percent correlation may suffice. Look at other studies in your particular field to determine the requirements for statistical significance.

State the null hypothesis. The null hypothesis gives an exact value that implies there is no correlation between the two variables. If the results show a percentage equal to or lower than the value of the null hypothesis, then the variables are not proven to correlate.

Record and summarize the results of your experiment. State whether or not the experiment met the minimum requirements of your hypothesis in terms of both percentage and significance.

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• University of New England; Steps in Hypothesis Testing for Correlation; 2000
• Research Methods Knowledge Base; Correlation; William M.K. Trochim; 2006
• Science Buddies; Hypothesis

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Brian Gabriel has been a writer and blogger since 2009, contributing to various online publications. He earned his Bachelor of Arts in history from Whitworth University.

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How to Determine the Sample Size in a Quantitative Research Study

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11.2: Correlation Hypothesis Test

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The correlation coefficient, \(r\), tells us about the strength and direction of the linear relationship between \(x\) and \(y\). However, the reliability of the linear model also depends on how many observed data points are in the sample. We need to look at both the value of the correlation coefficient \(r\) and the sample size \(n\), together. We perform a hypothesis test of the "significance of the correlation coefficient" to decide whether the linear relationship in the sample data is strong enough to use to model the relationship in the population.

The sample data are used to compute \(r\), the correlation coefficient for the sample. If we had data for the entire population, we could find the population correlation coefficient. But because we have only sample data, we cannot calculate the population correlation coefficient. The sample correlation coefficient, \(r\), is our estimate of the unknown population correlation coefficient.

• The symbol for the population correlation coefficient is \(\rho\), the Greek letter "rho."
• \(\rho =\) population correlation coefficient (unknown)
• \(r =\) sample correlation coefficient (known; calculated from sample data)

The hypothesis test lets us decide whether the value of the population correlation coefficient \(\rho\) is "close to zero" or "significantly different from zero". We decide this based on the sample correlation coefficient \(r\) and the sample size \(n\).

If the test concludes that the correlation coefficient is significantly different from zero, we say that the correlation coefficient is "significant."

• Conclusion: There is sufficient evidence to conclude that there is a significant linear relationship between \(x\) and \(y\) because the correlation coefficient is significantly different from zero.
• What the conclusion means: There is a significant linear relationship between \(x\) and \(y\). We can use the regression line to model the linear relationship between \(x\) and \(y\) in the population.

If the test concludes that the correlation coefficient is not significantly different from zero (it is close to zero), we say that correlation coefficient is "not significant".

• Conclusion: "There is insufficient evidence to conclude that there is a significant linear relationship between \(x\) and \(y\) because the correlation coefficient is not significantly different from zero."
• What the conclusion means: There is not a significant linear relationship between \(x\) and \(y\). Therefore, we CANNOT use the regression line to model a linear relationship between \(x\) and \(y\) in the population.
• If \(r\) is significant and the scatter plot shows a linear trend, the line can be used to predict the value of \(y\) for values of \(x\) that are within the domain of observed \(x\) values.
• If \(r\) is not significant OR if the scatter plot does not show a linear trend, the line should not be used for prediction.
• If \(r\) is significant and if the scatter plot shows a linear trend, the line may NOT be appropriate or reliable for prediction OUTSIDE the domain of observed \(x\) values in the data.

PERFORMING THE HYPOTHESIS TEST

• Null Hypothesis: \(H_{0}: \rho = 0\)
• Alternate Hypothesis: \(H_{a}: \rho \neq 0\)

WHAT THE HYPOTHESES MEAN IN WORDS:

• Null Hypothesis \(H_{0}\) : The population correlation coefficient IS NOT significantly different from zero. There IS NOT a significant linear relationship(correlation) between \(x\) and \(y\) in the population.
• Alternate Hypothesis \(H_{a}\) : The population correlation coefficient IS significantly DIFFERENT FROM zero. There IS A SIGNIFICANT LINEAR RELATIONSHIP (correlation) between \(x\) and \(y\) in the population.

DRAWING A CONCLUSION:There are two methods of making the decision. The two methods are equivalent and give the same result.

• Method 1: Using the \(p\text{-value}\)
• Method 2: Using a table of critical values

In this chapter of this textbook, we will always use a significance level of 5%, \(\alpha = 0.05\)

Using the \(p\text{-value}\) method, you could choose any appropriate significance level you want; you are not limited to using \(\alpha = 0.05\). But the table of critical values provided in this textbook assumes that we are using a significance level of 5%, \(\alpha = 0.05\). (If we wanted to use a different significance level than 5% with the critical value method, we would need different tables of critical values that are not provided in this textbook.)

METHOD 1: Using a \(p\text{-value}\) to make a decision

Using the ti83, 83+, 84, 84+ calculator.

To calculate the \(p\text{-value}\) using LinRegTTEST:

On the LinRegTTEST input screen, on the line prompt for \(\beta\) or \(\rho\), highlight "\(\neq 0\)"

The output screen shows the \(p\text{-value}\) on the line that reads "\(p =\)".

(Most computer statistical software can calculate the \(p\text{-value}\).)

If the \(p\text{-value}\) is less than the significance level ( \(\alpha = 0.05\) ):

• Decision: Reject the null hypothesis.
• Conclusion: "There is sufficient evidence to conclude that there is a significant linear relationship between \(x\) and \(y\) because the correlation coefficient is significantly different from zero."

If the \(p\text{-value}\) is NOT less than the significance level ( \(\alpha = 0.05\) )

• Decision: DO NOT REJECT the null hypothesis.
• Conclusion: "There is insufficient evidence to conclude that there is a significant linear relationship between \(x\) and \(y\) because the correlation coefficient is NOT significantly different from zero."

Calculation Notes:

• You will use technology to calculate the \(p\text{-value}\). The following describes the calculations to compute the test statistics and the \(p\text{-value}\):
• The \(p\text{-value}\) is calculated using a \(t\)-distribution with \(n - 2\) degrees of freedom.
• The formula for the test statistic is \(t = \frac{r\sqrt{n-2}}{\sqrt{1-r^{2}}}\). The value of the test statistic, \(t\), is shown in the computer or calculator output along with the \(p\text{-value}\). The test statistic \(t\) has the same sign as the correlation coefficient \(r\).
• The \(p\text{-value}\) is the combined area in both tails.

An alternative way to calculate the \(p\text{-value}\) ( \(p\) ) given by LinRegTTest is the command 2*tcdf(abs(t),10^99, n-2) in 2nd DISTR.

THIRD-EXAM vs FINAL-EXAM EXAMPLE: \(p\text{-value}\) method

• Consider the third exam/final exam example.
• The line of best fit is: \(\hat{y} = -173.51 + 4.83x\) with \(r = 0.6631\) and there are \(n = 11\) data points.
• Can the regression line be used for prediction? Given a third exam score ( \(x\) value), can we use the line to predict the final exam score (predicted \(y\) value)?
• \(H_{0}: \rho = 0\)
• \(H_{a}: \rho \neq 0\)
• \(\alpha = 0.05\)
• The \(p\text{-value}\) is 0.026 (from LinRegTTest on your calculator or from computer software).
• The \(p\text{-value}\), 0.026, is less than the significance level of \(\alpha = 0.05\).
• Decision: Reject the Null Hypothesis \(H_{0}\)
• Conclusion: There is sufficient evidence to conclude that there is a significant linear relationship between the third exam score (\(x\)) and the final exam score (\(y\)) because the correlation coefficient is significantly different from zero.

Because \(r\) is significant and the scatter plot shows a linear trend, the regression line can be used to predict final exam scores.

METHOD 2: Using a table of Critical Values to make a decision

The 95% Critical Values of the Sample Correlation Coefficient Table can be used to give you a good idea of whether the computed value of \(r\) is significant or not . Compare \(r\) to the appropriate critical value in the table. If \(r\) is not between the positive and negative critical values, then the correlation coefficient is significant. If \(r\) is significant, then you may want to use the line for prediction.

Example \(\PageIndex{1}\)

Suppose you computed \(r = 0.801\) using \(n = 10\) data points. \(df = n - 2 = 10 - 2 = 8\). The critical values associated with \(df = 8\) are \(-0.632\) and \(+0.632\). If \(r <\) negative critical value or \(r >\) positive critical value, then \(r\) is significant. Since \(r = 0.801\) and \(0.801 > 0.632\), \(r\) is significant and the line may be used for prediction. If you view this example on a number line, it will help you.

Exercise \(\PageIndex{1}\)

For a given line of best fit, you computed that \(r = 0.6501\) using \(n = 12\) data points and the critical value is 0.576. Can the line be used for prediction? Why or why not?

If the scatter plot looks linear then, yes, the line can be used for prediction, because \(r >\) the positive critical value.

Example \(\PageIndex{2}\)

Suppose you computed \(r = –0.624\) with 14 data points. \(df = 14 – 2 = 12\). The critical values are \(-0.532\) and \(0.532\). Since \(-0.624 < -0.532\), \(r\) is significant and the line can be used for prediction

Exercise \(\PageIndex{2}\)

For a given line of best fit, you compute that \(r = 0.5204\) using \(n = 9\) data points, and the critical value is \(0.666\). Can the line be used for prediction? Why or why not?

No, the line cannot be used for prediction, because \(r <\) the positive critical value.

Example \(\PageIndex{3}\)

Suppose you computed \(r = 0.776\) and \(n = 6\). \(df = 6 - 2 = 4\). The critical values are \(-0.811\) and \(0.811\). Since \(-0.811 < 0.776 < 0.811\), \(r\) is not significant, and the line should not be used for prediction.

Exercise \(\PageIndex{3}\)

For a given line of best fit, you compute that \(r = -0.7204\) using \(n = 8\) data points, and the critical value is \(= 0.707\). Can the line be used for prediction? Why or why not?

Yes, the line can be used for prediction, because \(r <\) the negative critical value.

THIRD-EXAM vs FINAL-EXAM EXAMPLE: critical value method

Consider the third exam/final exam example. The line of best fit is: \(\hat{y} = -173.51 + 4.83x\) with \(r = 0.6631\) and there are \(n = 11\) data points. Can the regression line be used for prediction? Given a third-exam score ( \(x\) value), can we use the line to predict the final exam score (predicted \(y\) value)?

• Use the "95% Critical Value" table for \(r\) with \(df = n - 2 = 11 - 2 = 9\).
• The critical values are \(-0.602\) and \(+0.602\)
• Since \(0.6631 > 0.602\), \(r\) is significant.
• Conclusion:There is sufficient evidence to conclude that there is a significant linear relationship between the third exam score (\(x\)) and the final exam score (\(y\)) because the correlation coefficient is significantly different from zero.

Example \(\PageIndex{4}\)

Suppose you computed the following correlation coefficients. Using the table at the end of the chapter, determine if \(r\) is significant and the line of best fit associated with each r can be used to predict a \(y\) value. If it helps, draw a number line.

• \(r = –0.567\) and the sample size, \(n\), is \(19\). The \(df = n - 2 = 17\). The critical value is \(-0.456\). \(-0.567 < -0.456\) so \(r\) is significant.
• \(r = 0.708\) and the sample size, \(n\), is \(9\). The \(df = n - 2 = 7\). The critical value is \(0.666\). \(0.708 > 0.666\) so \(r\) is significant.
• \(r = 0.134\) and the sample size, \(n\), is \(14\). The \(df = 14 - 2 = 12\). The critical value is \(0.532\). \(0.134\) is between \(-0.532\) and \(0.532\) so \(r\) is not significant.
• \(r = 0\) and the sample size, \(n\), is five. No matter what the \(dfs\) are, \(r = 0\) is between the two critical values so \(r\) is not significant.

Exercise \(\PageIndex{4}\)

For a given line of best fit, you compute that \(r = 0\) using \(n = 100\) data points. Can the line be used for prediction? Why or why not?

No, the line cannot be used for prediction no matter what the sample size is.

Assumptions in Testing the Significance of the Correlation Coefficient

Testing the significance of the correlation coefficient requires that certain assumptions about the data are satisfied. The premise of this test is that the data are a sample of observed points taken from a larger population. We have not examined the entire population because it is not possible or feasible to do so. We are examining the sample to draw a conclusion about whether the linear relationship that we see between \(x\) and \(y\) in the sample data provides strong enough evidence so that we can conclude that there is a linear relationship between \(x\) and \(y\) in the population.

The regression line equation that we calculate from the sample data gives the best-fit line for our particular sample. We want to use this best-fit line for the sample as an estimate of the best-fit line for the population. Examining the scatter plot and testing the significance of the correlation coefficient helps us determine if it is appropriate to do this.

The assumptions underlying the test of significance are:

• There is a linear relationship in the population that models the average value of \(y\) for varying values of \(x\). In other words, the expected value of \(y\) for each particular value lies on a straight line in the population. (We do not know the equation for the line for the population. Our regression line from the sample is our best estimate of this line in the population.)
• The \(y\) values for any particular \(x\) value are normally distributed about the line. This implies that there are more \(y\) values scattered closer to the line than are scattered farther away. Assumption (1) implies that these normal distributions are centered on the line: the means of these normal distributions of \(y\) values lie on the line.
• The standard deviations of the population \(y\) values about the line are equal for each value of \(x\). In other words, each of these normal distributions of \(y\) values has the same shape and spread about the line.
• The residual errors are mutually independent (no pattern).
• The data are produced from a well-designed, random sample or randomized experiment.

Linear regression is a procedure for fitting a straight line of the form \(\hat{y} = a + bx\) to data. The conditions for regression are:

• Linear In the population, there is a linear relationship that models the average value of \(y\) for different values of \(x\).
• Independent The residuals are assumed to be independent.
• Normal The \(y\) values are distributed normally for any value of \(x\).
• Equal variance The standard deviation of the \(y\) values is equal for each \(x\) value.
• Random The data are produced from a well-designed random sample or randomized experiment.

The slope \(b\) and intercept \(a\) of the least-squares line estimate the slope \(\beta\) and intercept \(\alpha\) of the population (true) regression line. To estimate the population standard deviation of \(y\), \(\sigma\), use the standard deviation of the residuals, \(s\). \(s = \sqrt{\frac{SEE}{n-2}}\). The variable \(\rho\) (rho) is the population correlation coefficient. To test the null hypothesis \(H_{0}: \rho =\) hypothesized value , use a linear regression t-test. The most common null hypothesis is \(H_{0}: \rho = 0\) which indicates there is no linear relationship between \(x\) and \(y\) in the population. The TI-83, 83+, 84, 84+ calculator function LinRegTTest can perform this test (STATS TESTS LinRegTTest).

Formula Review

Least Squares Line or Line of Best Fit:

\[\hat{y} = a + bx\]

\[a = y\text{-intercept}\]

\[b = \text{slope}\]

Standard deviation of the residuals:

\[s = \sqrt{\frac{SSE}{n-2}}\]

\[SSE = \text{sum of squared errors}\]

\[n = \text{the number of data points}\]

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• Correlational Research | Guide, Design & Examples

Correlational Research | Guide, Design & Examples

Published on 5 May 2022 by Pritha Bhandari . Revised on 5 December 2022.

A correlational research design investigates relationships between variables without the researcher controlling or manipulating any of them.

A correlation reflects the strength and/or direction of the relationship between two (or more) variables. The direction of a correlation can be either positive or negative.

Table of contents

Correlational vs experimental research, when to use correlational research, how to collect correlational data, how to analyse correlational data, correlation and causation, frequently asked questions about correlational research.

Correlational and experimental research both use quantitative methods to investigate relationships between variables. But there are important differences in how data is collected and the types of conclusions you can draw.

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Correlational research is ideal for gathering data quickly from natural settings. That helps you generalise your findings to real-life situations in an externally valid way.

There are a few situations where correlational research is an appropriate choice.

To investigate non-causal relationships

You want to find out if there is an association between two variables, but you don’t expect to find a causal relationship between them.

Correlational research can provide insights into complex real-world relationships, helping researchers develop theories and make predictions.

To explore causal relationships between variables

You think there is a causal relationship between two variables, but it is impractical, unethical, or too costly to conduct experimental research that manipulates one of the variables.

Correlational research can provide initial indications or additional support for theories about causal relationships.

To test new measurement tools

You have developed a new instrument for measuring your variable, and you need to test its reliability or validity .

Correlational research can be used to assess whether a tool consistently or accurately captures the concept it aims to measure.

There are many different methods you can use in correlational research. In the social and behavioural sciences, the most common data collection methods for this type of research include surveys, observations, and secondary data.

It’s important to carefully choose and plan your methods to ensure the reliability and validity of your results. You should carefully select a representative sample so that your data reflects the population you’re interested in without bias .

In survey research , you can use questionnaires to measure your variables of interest. You can conduct surveys online, by post, by phone, or in person.

Surveys are a quick, flexible way to collect standardised data from many participants, but it’s important to ensure that your questions are worded in an unbiased way and capture relevant insights.

Naturalistic observation

Naturalistic observation is a type of field research where you gather data about a behaviour or phenomenon in its natural environment.

This method often involves recording, counting, describing, and categorising actions and events. Naturalistic observation can include both qualitative and quantitative elements, but to assess correlation, you collect data that can be analysed quantitatively (e.g., frequencies, durations, scales, and amounts).

Naturalistic observation lets you easily generalise your results to real-world contexts, and you can study experiences that aren’t replicable in lab settings. But data analysis can be time-consuming and unpredictable, and researcher bias may skew the interpretations.

Secondary data

Instead of collecting original data, you can also use data that has already been collected for a different purpose, such as official records, polls, or previous studies.

Using secondary data is inexpensive and fast, because data collection is complete. However, the data may be unreliable, incomplete, or not entirely relevant, and you have no control over the reliability or validity of the data collection procedures.

After collecting data, you can statistically analyse the relationship between variables using correlation or regression analyses, or both. You can also visualise the relationships between variables with a scatterplot.

Different types of correlation coefficients and regression analyses are appropriate for your data based on their levels of measurement and distributions .

Correlation analysis

Using a correlation analysis, you can summarise the relationship between variables into a correlation coefficient : a single number that describes the strength and direction of the relationship between variables. With this number, you’ll quantify the degree of the relationship between variables.

The Pearson product-moment correlation coefficient, also known as Pearson’s r , is commonly used for assessing a linear relationship between two quantitative variables.

Correlation coefficients are usually found for two variables at a time, but you can use a multiple correlation coefficient for three or more variables.

Regression analysis

With a regression analysis , you can predict how much a change in one variable will be associated with a change in the other variable. The result is a regression equation that describes the line on a graph of your variables.

You can use this equation to predict the value of one variable based on the given value(s) of the other variable(s). It’s best to perform a regression analysis after testing for a correlation between your variables.

It’s important to remember that correlation does not imply causation . Just because you find a correlation between two things doesn’t mean you can conclude one of them causes the other, for a few reasons.

Directionality problem

If two variables are correlated, it could be because one of them is a cause and the other is an effect. But the correlational research design doesn’t allow you to infer which is which. To err on the side of caution, researchers don’t conclude causality from correlational studies.

Third variable problem

A confounding variable is a third variable that influences other variables to make them seem causally related even though they are not. Instead, there are separate causal links between the confounder and each variable.

In correlational research, there’s limited or no researcher control over extraneous variables . Even if you statistically control for some potential confounders, there may still be other hidden variables that disguise the relationship between your study variables.

Although a correlational study can’t demonstrate causation on its own, it can help you develop a causal hypothesis that’s tested in controlled experiments.

A correlation reflects the strength and/or direction of the association between two or more variables.

• A positive correlation means that both variables change in the same direction.
• A negative correlation means that the variables change in opposite directions.
• A zero correlation means there’s no relationship between the variables.

A correlational research design investigates relationships between two variables (or more) without the researcher controlling or manipulating any of them. It’s a non-experimental type of quantitative research .

Controlled experiments establish causality, whereas correlational studies only show associations between variables.

• In an experimental design , you manipulate an independent variable and measure its effect on a dependent variable. Other variables are controlled so they can’t impact the results.
• In a correlational design , you measure variables without manipulating any of them. You can test whether your variables change together, but you can’t be sure that one variable caused a change in another.

In general, correlational research is high in external validity while experimental research is high in internal validity .

A correlation is usually tested for two variables at a time, but you can test correlations between three or more variables.

A correlation coefficient is a single number that describes the strength and direction of the relationship between your variables.

Different types of correlation coefficients might be appropriate for your data based on their levels of measurement and distributions . The Pearson product-moment correlation coefficient (Pearson’s r ) is commonly used to assess a linear relationship between two quantitative variables.

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6.2 Correlational Research

Learning objectives.

• Define correlational research and give several examples.
• Explain why a researcher might choose to conduct correlational research rather than experimental research or another type of non-experimental research.
• Interpret the strength and direction of different correlation coefficients.
• Explain why correlation does not imply causation.

What Is Correlational Research?

Correlational research is a type of non-experimental research in which the researcher measures two variables and assesses the statistical relationship (i.e., the correlation) between them with little or no effort to control extraneous variables. There are many reasons that researchers interested in statistical relationships between variables would choose to conduct a correlational study rather than an experiment. The first is that they do not believe that the statistical relationship is a causal one or are not interested in causal relationships. Recall two goals of science are to describe and to predict and the correlational research strategy allows researchers to achieve both of these goals. Specifically, this strategy can be used to describe the strength and direction of the relationship between two variables and if there is a relationship between the variables then the researchers can use scores on one variable to predict scores on the other (using a statistical technique called regression).

Another reason that researchers would choose to use a correlational study rather than an experiment is that the statistical relationship of interest is thought to be causal, but the researcher  cannot  manipulate the independent variable because it is impossible, impractical, or unethical. For example, while I might be interested in the relationship between the frequency people use cannabis and their memory abilities I cannot ethically manipulate the frequency that people use cannabis. As such, I must rely on the correlational research strategy; I must simply measure the frequency that people use cannabis and measure their memory abilities using a standardized test of memory and then determine whether the frequency people use cannabis use is statistically related to memory test performance. 

Correlation is also used to establish the reliability and validity of measurements. For example, a researcher might evaluate the validity of a brief extraversion test by administering it to a large group of participants along with a longer extraversion test that has already been shown to be valid. This researcher might then check to see whether participants’ scores on the brief test are strongly correlated with their scores on the longer one. Neither test score is thought to cause the other, so there is no independent variable to manipulate. In fact, the terms  independent variable  and dependent variabl e  do not apply to this kind of research.

Another strength of correlational research is that it is often higher in external validity than experimental research. Recall there is typically a trade-off between internal validity and external validity. As greater controls are added to experiments, internal validity is increased but often at the expense of external validity. In contrast, correlational studies typically have low internal validity because nothing is manipulated or control but they often have high external validity. Since nothing is manipulated or controlled by the experimenter the results are more likely to reflect relationships that exist in the real world.

Finally, extending upon this trade-off between internal and external validity, correlational research can help to provide converging evidence for a theory. If a theory is supported by a true experiment that is high in internal validity as well as by a correlational study that is high in external validity then the researchers can have more confidence in the validity of their theory. As a concrete example, correlational studies establishing that there is a relationship between watching violent television and aggressive behavior have been complemented by experimental studies confirming that the relationship is a causal one (Bushman & Huesmann, 2001) [1] .  These converging results provide strong evidence that there is a real relationship (indeed a causal relationship) between watching violent television and aggressive behavior.

Data Collection in Correlational Research

Again, the defining feature of correlational research is that neither variable is manipulated. It does not matter how or where the variables are measured. A researcher could have participants come to a laboratory to complete a computerized backward digit span task and a computerized risky decision-making task and then assess the relationship between participants’ scores on the two tasks. Or a researcher could go to a shopping mall to ask people about their attitudes toward the environment and their shopping habits and then assess the relationship between these two variables. Both of these studies would be correlational because no independent variable is manipulated. 

Correlations Between Quantitative Variables

Correlations between quantitative variables are often presented using scatterplots . Figure 6.3 shows some hypothetical data on the relationship between the amount of stress people are under and the number of physical symptoms they have. Each point in the scatterplot represents one person’s score on both variables. For example, the circled point in Figure 6.3 represents a person whose stress score was 10 and who had three physical symptoms. Taking all the points into account, one can see that people under more stress tend to have more physical symptoms. This is a good example of a positive relationship , in which higher scores on one variable tend to be associated with higher scores on the other. A  negative relationship  is one in which higher scores on one variable tend to be associated with lower scores on the other. There is a negative relationship between stress and immune system functioning, for example, because higher stress is associated with lower immune system functioning.

Figure 6.3 Scatterplot Showing a Hypothetical Positive Relationship Between Stress and Number of Physical Symptoms. The circled point represents a person whose stress score was 10 and who had three physical symptoms. Pearson’s r for these data is +.51.

The strength of a correlation between quantitative variables is typically measured using a statistic called  Pearson’s Correlation Coefficient (or Pearson’s  r ) . As Figure 6.4 shows, Pearson’s r ranges from −1.00 (the strongest possible negative relationship) to +1.00 (the strongest possible positive relationship). A value of 0 means there is no relationship between the two variables. When Pearson’s  r  is 0, the points on a scatterplot form a shapeless “cloud.” As its value moves toward −1.00 or +1.00, the points come closer and closer to falling on a single straight line. Correlation coefficients near ±.10 are considered small, values near ± .30 are considered medium, and values near ±.50 are considered large. Notice that the sign of Pearson’s  r  is unrelated to its strength. Pearson’s  r  values of +.30 and −.30, for example, are equally strong; it is just that one represents a moderate positive relationship and the other a moderate negative relationship. With the exception of reliability coefficients, most correlations that we find in Psychology are small or moderate in size. The website http://rpsychologist.com/d3/correlation/ , created by Kristoffer Magnusson, provides an excellent interactive visualization of correlations that permits you to adjust the strength and direction of a correlation while witnessing the corresponding changes to the scatterplot.

Figure 6.4 Range of Pearson’s r, From −1.00 (Strongest Possible Negative Relationship), Through 0 (No Relationship), to +1.00 (Strongest Possible Positive Relationship)

There are two common situations in which the value of Pearson’s  r  can be misleading. Pearson’s  r  is a good measure only for linear relationships, in which the points are best approximated by a straight line. It is not a good measure for nonlinear relationships, in which the points are better approximated by a curved line. Figure 6.5, for example, shows a hypothetical relationship between the amount of sleep people get per night and their level of depression. In this example, the line that best approximates the points is a curve—a kind of upside-down “U”—because people who get about eight hours of sleep tend to be the least depressed. Those who get too little sleep and those who get too much sleep tend to be more depressed. Even though Figure 6.5 shows a fairly strong relationship between depression and sleep, Pearson’s  r  would be close to zero because the points in the scatterplot are not well fit by a single straight line. This means that it is important to make a scatterplot and confirm that a relationship is approximately linear before using Pearson’s  r . Nonlinear relationships are fairly common in psychology, but measuring their strength is beyond the scope of this book.

Figure 6.5 Hypothetical Nonlinear Relationship Between Sleep and Depression

The other common situations in which the value of Pearson’s  r  can be misleading is when one or both of the variables have a limited range in the sample relative to the population. This problem is referred to as  restriction of range . Assume, for example, that there is a strong negative correlation between people’s age and their enjoyment of hip hop music as shown by the scatterplot in Figure 6.6. Pearson’s  r  here is −.77. However, if we were to collect data only from 18- to 24-year-olds—represented by the shaded area of Figure 6.6—then the relationship would seem to be quite weak. In fact, Pearson’s  r  for this restricted range of ages is 0. It is a good idea, therefore, to design studies to avoid restriction of range. For example, if age is one of your primary variables, then you can plan to collect data from people of a wide range of ages. Because restriction of range is not always anticipated or easily avoidable, however, it is good practice to examine your data for possible restriction of range and to interpret Pearson’s  r  in light of it. (There are also statistical methods to correct Pearson’s  r  for restriction of range, but they are beyond the scope of this book).

Figure 6.6 Hypothetical Data Showing How a Strong Overall Correlation Can Appear to Be Weak When One Variable Has a Restricted Range.The overall correlation here is −.77, but the correlation for the 18- to 24-year-olds (in the blue box) is 0.

Correlation Does Not Imply Causation

You have probably heard repeatedly that “Correlation does not imply causation.” An amusing example of this comes from a 2012 study that showed a positive correlation (Pearson’s r = 0.79) between the per capita chocolate consumption of a nation and the number of Nobel prizes awarded to citizens of that nation [2] . It seems clear, however, that this does not mean that eating chocolate causes people to win Nobel prizes, and it would not make sense to try to increase the number of Nobel prizes won by recommending that parents feed their children more chocolate.

There are two reasons that correlation does not imply causation. The first is called the  directionality problem . Two variables,  X  and  Y , can be statistically related because X  causes  Y  or because  Y  causes  X . Consider, for example, a study showing that whether or not people exercise is statistically related to how happy they are—such that people who exercise are happier on average than people who do not. This statistical relationship is consistent with the idea that exercising causes happiness, but it is also consistent with the idea that happiness causes exercise. Perhaps being happy gives people more energy or leads them to seek opportunities to socialize with others by going to the gym. The second reason that correlation does not imply causation is called the  third-variable problem . Two variables,  X  and  Y , can be statistically related not because  X  causes  Y , or because  Y  causes  X , but because some third variable,  Z , causes both  X  and  Y . For example, the fact that nations that have won more Nobel prizes tend to have higher chocolate consumption probably reflects geography in that European countries tend to have higher rates of per capita chocolate consumption and invest more in education and technology (once again, per capita) than many other countries in the world. Similarly, the statistical relationship between exercise and happiness could mean that some third variable, such as physical health, causes both of the others. Being physically healthy could cause people to exercise and cause them to be happier. Correlations that are a result of a third-variable are often referred to as  spurious correlations.

Some excellent and funny examples of spurious correlations can be found at http://www.tylervigen.com  (Figure 6.7  provides one such example).

“Lots of Candy Could Lead to Violence”

Although researchers in psychology know that correlation does not imply causation, many journalists do not. One website about correlation and causation, http://jonathan.mueller.faculty.noctrl.edu/100/correlation_or_causation.htm , links to dozens of media reports about real biomedical and psychological research. Many of the headlines suggest that a causal relationship has been demonstrated when a careful reading of the articles shows that it has not because of the directionality and third-variable problems.

One such article is about a study showing that children who ate candy every day were more likely than other children to be arrested for a violent offense later in life. But could candy really “lead to” violence, as the headline suggests? What alternative explanations can you think of for this statistical relationship? How could the headline be rewritten so that it is not misleading?

As you have learned by reading this book, there are various ways that researchers address the directionality and third-variable problems. The most effective is to conduct an experiment. For example, instead of simply measuring how much people exercise, a researcher could bring people into a laboratory and randomly assign half of them to run on a treadmill for 15 minutes and the rest to sit on a couch for 15 minutes. Although this seems like a minor change to the research design, it is extremely important. Now if the exercisers end up in more positive moods than those who did not exercise, it cannot be because their moods affected how much they exercised (because it was the researcher who determined how much they exercised). Likewise, it cannot be because some third variable (e.g., physical health) affected both how much they exercised and what mood they were in (because, again, it was the researcher who determined how much they exercised). Thus experiments eliminate the directionality and third-variable problems and allow researchers to draw firm conclusions about causal relationships.

Key Takeaways

• Correlational research involves measuring two variables and assessing the relationship between them, with no manipulation of an independent variable.
• Correlation does not imply causation. A statistical relationship between two variables,  X  and  Y , does not necessarily mean that  X  causes  Y . It is also possible that  Y  causes  X , or that a third variable,  Z , causes both  X  and  Y .
• While correlational research cannot be used to establish causal relationships between variables, correlational research does allow researchers to achieve many other important objectives (establishing reliability and validity, providing converging evidence, describing relationships and making predictions)
• Correlation coefficients can range from -1 to +1. The sign indicates the direction of the relationship between the variables and the numerical value indicates the strength of the relationship.
• A cognitive psychologist compares the ability of people to recall words that they were instructed to “read” with their ability to recall words that they were instructed to “imagine.”
• A manager studies the correlation between new employees’ college grade point averages and their first-year performance reports.
• An automotive engineer installs different stick shifts in a new car prototype, each time asking several people to rate how comfortable the stick shift feels.
• A food scientist studies the relationship between the temperature inside people’s refrigerators and the amount of bacteria on their food.
• A social psychologist tells some research participants that they need to hurry over to the next building to complete a study. She tells others that they can take their time. Then she observes whether they stop to help a research assistant who is pretending to be hurt.

2. Practice: For each of the following statistical relationships, decide whether the directionality problem is present and think of at least one plausible third variable.

• People who eat more lobster tend to live longer.
• People who exercise more tend to weigh less.
• College students who drink more alcohol tend to have poorer grades.
• Bushman, B. J., & Huesmann, L. R. (2001). Effects of televised violence on aggression. In D. Singer & J. Singer (Eds.), Handbook of children and the media (pp. 223–254). Thousand Oaks, CA: Sage. ↵
• Messerli, F. H. (2012). Chocolate consumption, cognitive function, and Nobel laureates. New England Journal of Medicine, 367 , 1562-1564. ↵

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7.2 Correlational Research

Learning objectives.

• Define correlational research and give several examples.
• Explain why a researcher might choose to conduct correlational research rather than experimental research or another type of nonexperimental research.

What Is Correlational Research?

Correlational research is a type of nonexperimental research in which the researcher measures two variables and assesses the statistical relationship (i.e., the correlation) between them with little or no effort to control extraneous variables. There are essentially two reasons that researchers interested in statistical relationships between variables would choose to conduct a correlational study rather than an experiment. The first is that they do not believe that the statistical relationship is a causal one. For example, a researcher might evaluate the validity of a brief extraversion test by administering it to a large group of participants along with a longer extraversion test that has already been shown to be valid. This researcher might then check to see whether participants’ scores on the brief test are strongly correlated with their scores on the longer one. Neither test score is thought to cause the other, so there is no independent variable to manipulate. In fact, the terms independent variable and dependent variable do not apply to this kind of research.

The other reason that researchers would choose to use a correlational study rather than an experiment is that the statistical relationship of interest is thought to be causal, but the researcher cannot manipulate the independent variable because it is impossible, impractical, or unethical. For example, Allen Kanner and his colleagues thought that the number of “daily hassles” (e.g., rude salespeople, heavy traffic) that people experience affects the number of physical and psychological symptoms they have (Kanner, Coyne, Schaefer, & Lazarus, 1981). But because they could not manipulate the number of daily hassles their participants experienced, they had to settle for measuring the number of daily hassles—along with the number of symptoms—using self-report questionnaires. Although the strong positive relationship they found between these two variables is consistent with their idea that hassles cause symptoms, it is also consistent with the idea that symptoms cause hassles or that some third variable (e.g., neuroticism) causes both.

A common misconception among beginning researchers is that correlational research must involve two quantitative variables, such as scores on two extraversion tests or the number of hassles and number of symptoms people have experienced. However, the defining feature of correlational research is that the two variables are measured—neither one is manipulated—and this is true regardless of whether the variables are quantitative or categorical. Imagine, for example, that a researcher administers the Rosenberg Self-Esteem Scale to 50 American college students and 50 Japanese college students. Although this “feels” like a between-subjects experiment, it is a correlational study because the researcher did not manipulate the students’ nationalities. The same is true of the study by Cacioppo and Petty comparing college faculty and factory workers in terms of their need for cognition. It is a correlational study because the researchers did not manipulate the participants’ occupations.

Figure 7.2 “Results of a Hypothetical Study on Whether People Who Make Daily To-Do Lists Experience Less Stress Than People Who Do Not Make Such Lists” shows data from a hypothetical study on the relationship between whether people make a daily list of things to do (a “to-do list”) and stress. Notice that it is unclear whether this is an experiment or a correlational study because it is unclear whether the independent variable was manipulated. If the researcher randomly assigned some participants to make daily to-do lists and others not to, then it is an experiment. If the researcher simply asked participants whether they made daily to-do lists, then it is a correlational study. The distinction is important because if the study was an experiment, then it could be concluded that making the daily to-do lists reduced participants’ stress. But if it was a correlational study, it could only be concluded that these variables are statistically related. Perhaps being stressed has a negative effect on people’s ability to plan ahead (the directionality problem). Or perhaps people who are more conscientious are more likely to make to-do lists and less likely to be stressed (the third-variable problem). The crucial point is that what defines a study as experimental or correlational is not the variables being studied, nor whether the variables are quantitative or categorical, nor the type of graph or statistics used to analyze the data. It is how the study is conducted.

Figure 7.2 Results of a Hypothetical Study on Whether People Who Make Daily To-Do Lists Experience Less Stress Than People Who Do Not Make Such Lists

Data Collection in Correlational Research

Again, the defining feature of correlational research is that neither variable is manipulated. It does not matter how or where the variables are measured. A researcher could have participants come to a laboratory to complete a computerized backward digit span task and a computerized risky decision-making task and then assess the relationship between participants’ scores on the two tasks. Or a researcher could go to a shopping mall to ask people about their attitudes toward the environment and their shopping habits and then assess the relationship between these two variables. Both of these studies would be correlational because no independent variable is manipulated. However, because some approaches to data collection are strongly associated with correlational research, it makes sense to discuss them here. The two we will focus on are naturalistic observation and archival data. A third, survey research, is discussed in its own chapter.

Naturalistic Observation

Naturalistic observation is an approach to data collection that involves observing people’s behavior in the environment in which it typically occurs. Thus naturalistic observation is a type of field research (as opposed to a type of laboratory research). It could involve observing shoppers in a grocery store, children on a school playground, or psychiatric inpatients in their wards. Researchers engaged in naturalistic observation usually make their observations as unobtrusively as possible so that participants are often not aware that they are being studied. Ethically, this is considered to be acceptable if the participants remain anonymous and the behavior occurs in a public setting where people would not normally have an expectation of privacy. Grocery shoppers putting items into their shopping carts, for example, are engaged in public behavior that is easily observable by store employees and other shoppers. For this reason, most researchers would consider it ethically acceptable to observe them for a study. On the other hand, one of the arguments against the ethicality of the naturalistic observation of “bathroom behavior” discussed earlier in the book is that people have a reasonable expectation of privacy even in a public restroom and that this expectation was violated.

Researchers Robert Levine and Ara Norenzayan used naturalistic observation to study differences in the “pace of life” across countries (Levine & Norenzayan, 1999). One of their measures involved observing pedestrians in a large city to see how long it took them to walk 60 feet. They found that people in some countries walked reliably faster than people in other countries. For example, people in the United States and Japan covered 60 feet in about 12 seconds on average, while people in Brazil and Romania took close to 17 seconds.

Because naturalistic observation takes place in the complex and even chaotic “real world,” there are two closely related issues that researchers must deal with before collecting data. The first is sampling. When, where, and under what conditions will the observations be made, and who exactly will be observed? Levine and Norenzayan described their sampling process as follows:

Male and female walking speed over a distance of 60 feet was measured in at least two locations in main downtown areas in each city. Measurements were taken during main business hours on clear summer days. All locations were flat, unobstructed, had broad sidewalks, and were sufficiently uncrowded to allow pedestrians to move at potentially maximum speeds. To control for the effects of socializing, only pedestrians walking alone were used. Children, individuals with obvious physical handicaps, and window-shoppers were not timed. Thirty-five men and 35 women were timed in most cities. (p. 186)

Precise specification of the sampling process in this way makes data collection manageable for the observers, and it also provides some control over important extraneous variables. For example, by making their observations on clear summer days in all countries, Levine and Norenzayan controlled for effects of the weather on people’s walking speeds.

The second issue is measurement. What specific behaviors will be observed? In Levine and Norenzayan’s study, measurement was relatively straightforward. They simply measured out a 60-foot distance along a city sidewalk and then used a stopwatch to time participants as they walked over that distance. Often, however, the behaviors of interest are not so obvious or objective. For example, researchers Robert Kraut and Robert Johnston wanted to study bowlers’ reactions to their shots, both when they were facing the pins and then when they turned toward their companions (Kraut & Johnston, 1979). But what “reactions” should they observe? Based on previous research and their own pilot testing, Kraut and Johnston created a list of reactions that included “closed smile,” “open smile,” “laugh,” “neutral face,” “look down,” “look away,” and “face cover” (covering one’s face with one’s hands). The observers committed this list to memory and then practiced by coding the reactions of bowlers who had been videotaped. During the actual study, the observers spoke into an audio recorder, describing the reactions they observed. Among the most interesting results of this study was that bowlers rarely smiled while they still faced the pins. They were much more likely to smile after they turned toward their companions, suggesting that smiling is not purely an expression of happiness but also a form of social communication.

Naturalistic observation has revealed that bowlers tend to smile when they turn away from the pins and toward their companions, suggesting that smiling is not purely an expression of happiness but also a form of social communication.

sieneke toering – bowling big lebowski style – CC BY-NC-ND 2.0.

When the observations require a judgment on the part of the observers—as in Kraut and Johnston’s study—this process is often described as coding . Coding generally requires clearly defining a set of target behaviors. The observers then categorize participants individually in terms of which behavior they have engaged in and the number of times they engaged in each behavior. The observers might even record the duration of each behavior. The target behaviors must be defined in such a way that different observers code them in the same way. This is the issue of interrater reliability. Researchers are expected to demonstrate the interrater reliability of their coding procedure by having multiple raters code the same behaviors independently and then showing that the different observers are in close agreement. Kraut and Johnston, for example, video recorded a subset of their participants’ reactions and had two observers independently code them. The two observers showed that they agreed on the reactions that were exhibited 97% of the time, indicating good interrater reliability.

Archival Data

Another approach to correlational research is the use of archival data , which are data that have already been collected for some other purpose. An example is a study by Brett Pelham and his colleagues on “implicit egotism”—the tendency for people to prefer people, places, and things that are similar to themselves (Pelham, Carvallo, & Jones, 2005). In one study, they examined Social Security records to show that women with the names Virginia, Georgia, Louise, and Florence were especially likely to have moved to the states of Virginia, Georgia, Louisiana, and Florida, respectively.

As with naturalistic observation, measurement can be more or less straightforward when working with archival data. For example, counting the number of people named Virginia who live in various states based on Social Security records is relatively straightforward. But consider a study by Christopher Peterson and his colleagues on the relationship between optimism and health using data that had been collected many years before for a study on adult development (Peterson, Seligman, & Vaillant, 1988). In the 1940s, healthy male college students had completed an open-ended questionnaire about difficult wartime experiences. In the late 1980s, Peterson and his colleagues reviewed the men’s questionnaire responses to obtain a measure of explanatory style—their habitual ways of explaining bad events that happen to them. More pessimistic people tend to blame themselves and expect long-term negative consequences that affect many aspects of their lives, while more optimistic people tend to blame outside forces and expect limited negative consequences. To obtain a measure of explanatory style for each participant, the researchers used a procedure in which all negative events mentioned in the questionnaire responses, and any causal explanations for them, were identified and written on index cards. These were given to a separate group of raters who rated each explanation in terms of three separate dimensions of optimism-pessimism. These ratings were then averaged to produce an explanatory style score for each participant. The researchers then assessed the statistical relationship between the men’s explanatory style as college students and archival measures of their health at approximately 60 years of age. The primary result was that the more optimistic the men were as college students, the healthier they were as older men. Pearson’s r was +.25.

This is an example of content analysis —a family of systematic approaches to measurement using complex archival data. Just as naturalistic observation requires specifying the behaviors of interest and then noting them as they occur, content analysis requires specifying keywords, phrases, or ideas and then finding all occurrences of them in the data. These occurrences can then be counted, timed (e.g., the amount of time devoted to entertainment topics on the nightly news show), or analyzed in a variety of other ways.

Key Takeaways

• Correlational research involves measuring two variables and assessing the relationship between them, with no manipulation of an independent variable.
• Correlational research is not defined by where or how the data are collected. However, some approaches to data collection are strongly associated with correlational research. These include naturalistic observation (in which researchers observe people’s behavior in the context in which it normally occurs) and the use of archival data that were already collected for some other purpose.

Discussion: For each of the following, decide whether it is most likely that the study described is experimental or correlational and explain why.

• An educational researcher compares the academic performance of students from the “rich” side of town with that of students from the “poor” side of town.
• A cognitive psychologist compares the ability of people to recall words that they were instructed to “read” with their ability to recall words that they were instructed to “imagine.”
• A manager studies the correlation between new employees’ college grade point averages and their first-year performance reports.
• An automotive engineer installs different stick shifts in a new car prototype, each time asking several people to rate how comfortable the stick shift feels.
• A food scientist studies the relationship between the temperature inside people’s refrigerators and the amount of bacteria on their food.
• A social psychologist tells some research participants that they need to hurry over to the next building to complete a study. She tells others that they can take their time. Then she observes whether they stop to help a research assistant who is pretending to be hurt.

Kanner, A. D., Coyne, J. C., Schaefer, C., & Lazarus, R. S. (1981). Comparison of two modes of stress measurement: Daily hassles and uplifts versus major life events. Journal of Behavioral Medicine, 4 , 1–39.

Kraut, R. E., & Johnston, R. E. (1979). Social and emotional messages of smiling: An ethological approach. Journal of Personality and Social Psychology, 37 , 1539–1553.

Levine, R. V., & Norenzayan, A. (1999). The pace of life in 31 countries. Journal of Cross-Cultural Psychology, 30 , 178–205.

Pelham, B. W., Carvallo, M., & Jones, J. T. (2005). Implicit egotism. Current Directions in Psychological Science, 14 , 106–110.

Peterson, C., Seligman, M. E. P., & Vaillant, G. E. (1988). Pessimistic explanatory style is a risk factor for physical illness: A thirty-five year longitudinal study. Journal of Personality and Social Psychology, 55 , 23–27.

Research Methods in Psychology Copyright © 2016 by University of Minnesota is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License , except where otherwise noted.

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Non-Experimental Research

29 Correlational Research

Learning objectives.

• Define correlational research and give several examples.
• Explain why a researcher might choose to conduct correlational research rather than experimental research or another type of non-experimental research.
• Interpret the strength and direction of different correlation coefficients.
• Explain why correlation does not imply causation.

What Is Correlational Research?

Correlational research is a type of non-experimental research in which the researcher measures two variables (binary or continuous) and assesses the statistical relationship (i.e., the correlation) between them with little or no effort to control extraneous variables. There are many reasons that researchers interested in statistical relationships between variables would choose to conduct a correlational study rather than an experiment. The first is that they do not believe that the statistical relationship is a causal one or are not interested in causal relationships. Recall two goals of science are to describe and to predict and the correlational research strategy allows researchers to achieve both of these goals. Specifically, this strategy can be used to describe the strength and direction of the relationship between two variables and if there is a relationship between the variables then the researchers can use scores on one variable to predict scores on the other (using a statistical technique called regression, which is discussed further in the section on Complex Correlation in this chapter).

Another reason that researchers would choose to use a correlational study rather than an experiment is that the statistical relationship of interest is thought to be causal, but the researcher  cannot manipulate the independent variable because it is impossible, impractical, or unethical. For example, while a researcher might be interested in the relationship between the frequency people use cannabis and their memory abilities they cannot ethically manipulate the frequency that people use cannabis. As such, they must rely on the correlational research strategy; they must simply measure the frequency that people use cannabis and measure their memory abilities using a standardized test of memory and then determine whether the frequency people use cannabis is statistically related to memory test performance. 

Correlation is also used to establish the reliability and validity of measurements. For example, a researcher might evaluate the validity of a brief extraversion test by administering it to a large group of participants along with a longer extraversion test that has already been shown to be valid. This researcher might then check to see whether participants’ scores on the brief test are strongly correlated with their scores on the longer one. Neither test score is thought to cause the other, so there is no independent variable to manipulate. In fact, the terms  independent variable  and dependent variabl e  do not apply to this kind of research.

Another strength of correlational research is that it is often higher in external validity than experimental research. Recall there is typically a trade-off between internal validity and external validity. As greater controls are added to experiments, internal validity is increased but often at the expense of external validity as artificial conditions are introduced that do not exist in reality. In contrast, correlational studies typically have low internal validity because nothing is manipulated or controlled but they often have high external validity. Since nothing is manipulated or controlled by the experimenter the results are more likely to reflect relationships that exist in the real world.

Finally, extending upon this trade-off between internal and external validity, correlational research can help to provide converging evidence for a theory. If a theory is supported by a true experiment that is high in internal validity as well as by a correlational study that is high in external validity then the researchers can have more confidence in the validity of their theory. As a concrete example, correlational studies establishing that there is a relationship between watching violent television and aggressive behavior have been complemented by experimental studies confirming that the relationship is a causal one (Bushman & Huesmann, 2001) [1] .

Does Correlational Research Always Involve Quantitative Variables?

A common misconception among beginning researchers is that correlational research must involve two quantitative variables, such as scores on two extraversion tests or the number of daily hassles and number of symptoms people have experienced. However, the defining feature of correlational research is that the two variables are measured—neither one is manipulated—and this is true regardless of whether the variables are quantitative or categorical. Imagine, for example, that a researcher administers the Rosenberg Self-Esteem Scale to 50 American college students and 50 Japanese college students. Although this “feels” like a between-subjects experiment, it is a correlational study because the researcher did not manipulate the students’ nationalities. The same is true of the study by Cacioppo and Petty comparing college faculty and factory workers in terms of their need for cognition. It is a correlational study because the researchers did not manipulate the participants’ occupations.

Figure 6.2 shows data from a hypothetical study on the relationship between whether people make a daily list of things to do (a “to-do list”) and stress. Notice that it is unclear whether this is an experiment or a correlational study because it is unclear whether the independent variable was manipulated. If the researcher randomly assigned some participants to make daily to-do lists and others not to, then it is an experiment. If the researcher simply asked participants whether they made daily to-do lists, then it is a correlational study. The distinction is important because if the study was an experiment, then it could be concluded that making the daily to-do lists reduced participants’ stress. But if it was a correlational study, it could only be concluded that these variables are statistically related. Perhaps being stressed has a negative effect on people’s ability to plan ahead (the directionality problem). Or perhaps people who are more conscientious are more likely to make to-do lists and less likely to be stressed (the third-variable problem). The crucial point is that what defines a study as experimental or correlational is not the variables being studied, nor whether the variables are quantitative or categorical, nor the type of graph or statistics used to analyze the data. What defines a study is how the study is conducted.

Data Collection in Correlational Research

Again, the defining feature of correlational research is that neither variable is manipulated. It does not matter how or where the variables are measured. A researcher could have participants come to a laboratory to complete a computerized backward digit span task and a computerized risky decision-making task and then assess the relationship between participants’ scores on the two tasks. Or a researcher could go to a shopping mall to ask people about their attitudes toward the environment and their shopping habits and then assess the relationship between these two variables. Both of these studies would be correlational because no independent variable is manipulated. 

Correlations Between Quantitative Variables

Correlations between quantitative variables are often presented using scatterplots . Figure 6.3 shows some hypothetical data on the relationship between the amount of stress people are under and the number of physical symptoms they have. Each point in the scatterplot represents one person’s score on both variables. For example, the circled point in Figure 6.3 represents a person whose stress score was 10 and who had three physical symptoms. Taking all the points into account, one can see that people under more stress tend to have more physical symptoms. This is a good example of a positive relationship , in which higher scores on one variable tend to be associated with higher scores on the other. In other words, they move in the same direction, either both up or both down. A negative relationship is one in which higher scores on one variable tend to be associated with lower scores on the other. In other words, they move in opposite directions. There is a negative relationship between stress and immune system functioning, for example, because higher stress is associated with lower immune system functioning.

The strength of a correlation between quantitative variables is typically measured using a statistic called  Pearson’s Correlation Coefficient (or Pearson's  r ) . As Figure 6.4 shows, Pearson’s r ranges from −1.00 (the strongest possible negative relationship) to +1.00 (the strongest possible positive relationship). A value of 0 means there is no relationship between the two variables. When Pearson’s  r  is 0, the points on a scatterplot form a shapeless “cloud.” As its value moves toward −1.00 or +1.00, the points come closer and closer to falling on a single straight line. Correlation coefficients near ±.10 are considered small, values near ± .30 are considered medium, and values near ±.50 are considered large. Notice that the sign of Pearson’s  r  is unrelated to its strength. Pearson’s  r  values of +.30 and −.30, for example, are equally strong; it is just that one represents a moderate positive relationship and the other a moderate negative relationship. With the exception of reliability coefficients, most correlations that we find in Psychology are small or moderate in size. The website http://rpsychologist.com/d3/correlation/ , created by Kristoffer Magnusson, provides an excellent interactive visualization of correlations that permits you to adjust the strength and direction of a correlation while witnessing the corresponding changes to the scatterplot.

There are two common situations in which the value of Pearson’s  r  can be misleading. Pearson’s  r  is a good measure only for linear relationships, in which the points are best approximated by a straight line. It is not a good measure for nonlinear relationships, in which the points are better approximated by a curved line. Figure 6.5, for example, shows a hypothetical relationship between the amount of sleep people get per night and their level of depression. In this example, the line that best approximates the points is a curve—a kind of upside-down “U”—because people who get about eight hours of sleep tend to be the least depressed. Those who get too little sleep and those who get too much sleep tend to be more depressed. Even though Figure 6.5 shows a fairly strong relationship between depression and sleep, Pearson’s  r  would be close to zero because the points in the scatterplot are not well fit by a single straight line. This means that it is important to make a scatterplot and confirm that a relationship is approximately linear before using Pearson’s  r . Nonlinear relationships are fairly common in psychology, but measuring their strength is beyond the scope of this book.

The other common situations in which the value of Pearson’s  r  can be misleading is when one or both of the variables have a limited range in the sample relative to the population. This problem is referred to as  restriction of range . Assume, for example, that there is a strong negative correlation between people’s age and their enjoyment of hip hop music as shown by the scatterplot in Figure 6.6. Pearson’s  r  here is −.77. However, if we were to collect data only from 18- to 24-year-olds—represented by the shaded area of Figure 6.6—then the relationship would seem to be quite weak. In fact, Pearson’s  r  for this restricted range of ages is 0. It is a good idea, therefore, to design studies to avoid restriction of range. For example, if age is one of your primary variables, then you can plan to collect data from people of a wide range of ages. Because restriction of range is not always anticipated or easily avoidable, however, it is good practice to examine your data for possible restriction of range and to interpret Pearson’s  r  in light of it. (There are also statistical methods to correct Pearson’s  r  for restriction of range, but they are beyond the scope of this book).

Correlation Does Not Imply Causation

You have probably heard repeatedly that “Correlation does not imply causation.” An amusing example of this comes from a 2012 study that showed a positive correlation (Pearson’s r = 0.79) between the per capita chocolate consumption of a nation and the number of Nobel prizes awarded to citizens of that nation [2] . It seems clear, however, that this does not mean that eating chocolate causes people to win Nobel prizes, and it would not make sense to try to increase the number of Nobel prizes won by recommending that parents feed their children more chocolate.

There are two reasons that correlation does not imply causation. The first is called the  directionality problem . Two variables,  X  and  Y , can be statistically related because X  causes  Y  or because  Y  causes  X . Consider, for example, a study showing that whether or not people exercise is statistically related to how happy they are—such that people who exercise are happier on average than people who do not. This statistical relationship is consistent with the idea that exercising causes happiness, but it is also consistent with the idea that happiness causes exercise. Perhaps being happy gives people more energy or leads them to seek opportunities to socialize with others by going to the gym. The second reason that correlation does not imply causation is called the  third-variable problem . Two variables,  X  and  Y , can be statistically related not because  X  causes  Y , or because  Y  causes  X , but because some third variable,  Z , causes both  X  and  Y . For example, the fact that nations that have won more Nobel prizes tend to have higher chocolate consumption probably reflects geography in that European countries tend to have higher rates of per capita chocolate consumption and invest more in education and technology (once again, per capita) than many other countries in the world. Similarly, the statistical relationship between exercise and happiness could mean that some third variable, such as physical health, causes both of the others. Being physically healthy could cause people to exercise and cause them to be happier. Correlations that are a result of a third-variable are often referred to as  spurious correlations .

Some excellent and amusing examples of spurious correlations can be found at http://www.tylervigen.com  (Figure 6.7  provides one such example).

“Lots of Candy Could Lead to Violence”

Although researchers in psychology know that correlation does not imply causation, many journalists do not. One website about correlation and causation, http://jonathan.mueller.faculty.noctrl.edu/100/correlation_or_causation.htm , links to dozens of media reports about real biomedical and psychological research. Many of the headlines suggest that a causal relationship has been demonstrated when a careful reading of the articles shows that it has not because of the directionality and third-variable problems.

One such article is about a study showing that children who ate candy every day were more likely than other children to be arrested for a violent offense later in life. But could candy really “lead to” violence, as the headline suggests? What alternative explanations can you think of for this statistical relationship? How could the headline be rewritten so that it is not misleading?

As you have learned by reading this book, there are various ways that researchers address the directionality and third-variable problems. The most effective is to conduct an experiment. For example, instead of simply measuring how much people exercise, a researcher could bring people into a laboratory and randomly assign half of them to run on a treadmill for 15 minutes and the rest to sit on a couch for 15 minutes. Although this seems like a minor change to the research design, it is extremely important. Now if the exercisers end up in more positive moods than those who did not exercise, it cannot be because their moods affected how much they exercised (because it was the researcher who used random assignment to determine how much they exercised). Likewise, it cannot be because some third variable (e.g., physical health) affected both how much they exercised and what mood they were in. Thus experiments eliminate the directionality and third-variable problems and allow researchers to draw firm conclusions about causal relationships.

Media Attributions

• Nicholas Cage and Pool Drownings  © Tyler Viegen is licensed under a  CC BY (Attribution)  license
• Bushman, B. J., & Huesmann, L. R. (2001). Effects of televised violence on aggression. In D. Singer & J. Singer (Eds.), Handbook of children and the media (pp. 223–254). Thousand Oaks, CA: Sage. ↵
• Messerli, F. H. (2012). Chocolate consumption, cognitive function, and Nobel laureates. New England Journal of Medicine, 367 , 1562-1564. ↵

A graph that presents correlations between two quantitative variables, one on the x-axis and one on the y-axis. Scores are plotted at the intersection of the values on each axis.

A relationship in which higher scores on one variable tend to be associated with higher scores on the other.

A relationship in which higher scores on one variable tend to be associated with lower scores on the other.

A statistic that measures the strength of a correlation between quantitative variables.

When one or both variables have a limited range in the sample relative to the population, making the value of the correlation coefficient misleading.

The problem where two variables, X  and  Y , are statistically related either because X  causes  Y, or because  Y  causes  X , and thus the causal direction of the effect cannot be known.

Two variables, X and Y, can be statistically related not because X causes Y, or because Y causes X, but because some third variable, Z, causes both X and Y.

Correlations that are a result not of the two variables being measured, but rather because of a third, unmeasured, variable that affects both of the measured variables.

Research Methods in Psychology Copyright © 2019 by Rajiv S. Jhangiani, I-Chant A. Chiang, Carrie Cuttler, & Dana C. Leighton is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License , except where otherwise noted.

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5.10: Correlational Research

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Learning Objectives

• Explain what a correlation coefficient tells us about the relationship between variables
• Describe why correlation does not mean causation

Did you know that as sales in ice cream increase, so does the overall rate of crime? Is it possible that indulging in your favorite flavor of ice cream could send you on a crime spree? Or, after committing crime do you think you might decide to treat yourself to a cone? There is no question that a relationship exists between ice cream and crime (e.g., Harper, 2013), but it would be pretty foolish to decide that one thing actually caused the other to occur.

It is much more likely that both ice cream sales and crime rates are related to the temperature outside. When the temperature is warm, there are lots of people out of their houses, interacting with each other, getting annoyed with one another, and sometimes committing crimes. Also, when it is warm outside, we are more likely to seek a cool treat like ice cream. How do we determine if there is indeed a relationship between two things? And when there is a relationship, how can we discern whether it is attributable to coincidence or causation?

Correlational Research

Correlation means that there is a relationship between two or more variables (such as ice cream consumption and crime), but this relationship does not necessarily imply cause and effect. When two variables are correlated, it simply means that as one variable changes, so does the other. We can measure correlation by calculating a statistic known as a correlation coefficient. A correlation coefficient is a number from -1 to +1 that indicates the strength and direction of the relationship between variables. The correlation coefficient is usually represented by the letter r .

The number portion of the correlation coefficient indicates the strength of the relationship. The closer the number is to 1 (be it negative or positive), the more strongly related the variables are, and the more predictable changes in one variable will be as the other variable changes. The closer the number is to zero, the weaker the relationship, and the less predictable the relationships between the variables becomes. For instance, a correlation coefficient of 0.9 indicates a far stronger relationship than a correlation coefficient of 0.3. If the variables are not related to one another at all, the correlation coefficient is 0. The example above about ice cream and crime is an example of two variables that we might expect to have no relationship to each other.

The sign—positive or negative—of the correlation coefficient indicates the direction of the relationship (Figure 1). A positive correlation means that the variables move in the same direction. Put another way, it means that as one variable increases so does the other, and conversely, when one variable decreases so does the other. A negative correlation means that the variables move in opposite directions. If two variables are negatively correlated, a decrease in one variable is associated with an increase in the other and vice versa.

The example of ice cream and crime rates is a positive correlation because both variables increase when temperatures are warmer. Other examples of positive correlations are the relationship between an individual’s height and weight or the relationship between a person’s age and number of wrinkles. One might expect a negative correlation to exist between someone’s tiredness during the day and the number of hours they slept the previous night: the amount of sleep decreases as the feelings of tiredness increase. In a real-world example of negative correlation, student researchers at the University of Minnesota found a weak negative correlation ( r = -0.29) between the average number of days per week that students got fewer than 5 hours of sleep and their GPA (Lowry, Dean, & Manders, 2010). Keep in mind that a negative correlation is not the same as no correlation. For example, we would probably find no correlation between hours of sleep and shoe size.

As mentioned earlier, correlations have predictive value. Imagine that you are on the admissions committee of a major university. You are faced with a huge number of applications, but you are able to accommodate only a small percentage of the applicant pool. How might you decide who should be admitted? You might try to correlate your current students’ college GPA with their scores on standardized tests like the SAT or ACT. By observing which correlations were strongest for your current students, you could use this information to predict relative success of those students who have applied for admission into the university.

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Correlation Does Not Indicate Causation

Correlational research is useful because it allows us to discover the strength and direction of relationships that exist between two variables. However, correlation is limited because establishing the existence of a relationship tells us little about cause and effect . While variables are sometimes correlated because one does cause the other, it could also be that some other factor, a confounding variable , is actually causing the systematic movement in our variables of interest. In the ice cream/crime rate example mentioned earlier, temperature is a confounding variable that could account for the relationship between the two variables.

Even when we cannot point to clear confounding variables, we should not assume that a correlation between two variables implies that one variable causes changes in another. This can be frustrating when a cause-and-effect relationship seems clear and intuitive. Think back to our discussion of the research done by the American Cancer Society and how their research projects were some of the first demonstrations of the link between smoking and cancer. It seems reasonable to assume that smoking causes cancer, but if we were limited to correlational research , we would be overstepping our bounds by making this assumption.

Unfortunately, people mistakenly make claims of causation as a function of correlations all the time. Such claims are especially common in advertisements and news stories. For example, recent research found that people who eat cereal on a regular basis achieve healthier weights than those who rarely eat cereal (Frantzen, Treviño, Echon, Garcia-Dominic, & DiMarco, 2013; Barton et al., 2005). Guess how the cereal companies report this finding. Does eating cereal really cause an individual to maintain a healthy weight, or are there other possible explanations, such as, someone at a healthy weight is more likely to regularly eat a healthy breakfast than someone who is obese or someone who avoids meals in an attempt to diet (Figure 2)? While correlational research is invaluable in identifying relationships among variables, a major limitation is the inability to establish causality. Psychologists want to make statements about cause and effect, but the only way to do that is to conduct an experiment to answer a research question. The next section describes how scientific experiments incorporate methods that eliminate, or control for, alternative explanations, which allow researchers to explore how changes in one variable cause changes in another variable.

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Watch this clip from Freakonomics for an example of how correlation does  not  indicate causation.

You can view the transcript for “Correlation vs. Causality: Freakonomics Movie” here (opens in new window) .

Illusory Correlations

The temptation to make erroneous cause-and-effect statements based on correlational research is not the only way we tend to misinterpret data. We also tend to make the mistake of illusory correlations, especially with unsystematic observations. Illusory correlations , or false correlations, occur when people believe that relationships exist between two things when no such relationship exists. One well-known illusory correlation is the supposed effect that the moon’s phases have on human behavior. Many people passionately assert that human behavior is affected by the phase of the moon, and specifically, that people act strangely when the moon is full (Figure 3).

There is no denying that the moon exerts a powerful influence on our planet. The ebb and flow of the ocean’s tides are tightly tied to the gravitational forces of the moon. Many people believe, therefore, that it is logical that we are affected by the moon as well. After all, our bodies are largely made up of water. A meta-analysis of nearly 40 studies consistently demonstrated, however, that the relationship between the moon and our behavior does not exist (Rotton & Kelly, 1985). While we may pay more attention to odd behavior during the full phase of the moon, the rates of odd behavior remain constant throughout the lunar cycle.

Why are we so apt to believe in illusory correlations like this? Often we read or hear about them and simply accept the information as valid. Or, we have a hunch about how something works and then look for evidence to support that hunch, ignoring evidence that would tell us our hunch is false; this is known as confirmation bias . Other times, we find illusory correlations based on the information that comes most easily to mind, even if that information is severely limited. And while we may feel confident that we can use these relationships to better understand and predict the world around us, illusory correlations can have significant drawbacks. For example, research suggests that illusory correlations—in which certain behaviors are inaccurately attributed to certain groups—are involved in the formation of prejudicial attitudes that can ultimately lead to discriminatory behavior (Fiedler, 2004).

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Think It Over

We all have a tendency to make illusory correlations from time to time. Try to think of an illusory correlation that is held by you, a family member, or a close friend. How do you think this illusory correlation came about and what can be done in the future to combat them?

cause-and-effect relationship:  changes in one variable cause the changes in the other variable; can be determined only through an experimental research design

confirmation bias:  tendency to ignore evidence that disproves ideas or beliefs

confounding variable:  unanticipated outside factor that affects both variables of interest, often giving the false impression that changes in one variable causes changes in the other variable, when, in actuality, the outside factor causes changes in both variables

correlation:  relationship between two or more variables; when two variables are correlated, one variable changes as the other does

correlation coefficient:  number from -1 to +1, indicating the strength and direction of the relationship between variables, and usually represented by r

illusory correlation:  seeing relationships between two things when in reality no such relationship exists

negative correlation:  two variables change in different directions, with one becoming larger as the other becomes smaller; a negative correlation is not the same thing as no correlation

positive correlation:  two variables change in the same direction, both becoming either larger or smaller

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• Correlation vs. Causality: Freakonomics Movie. Located at : https://www.youtube.com/watch?v=lbODqslc4Tg . License : Other . License Terms : Standard YouTube License

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Correlation Studies in Psychology Research

Determining the relationship between two or more variables.

Kendra Cherry, MS, is a psychosocial rehabilitation specialist, psychology educator, and author of the "Everything Psychology Book."

Emily is a board-certified science editor who has worked with top digital publishing brands like Voices for Biodiversity, Study.com, GoodTherapy, Vox, and Verywell.

Verywell / Brianna Gilmartin

• Characteristics

Potential Pitfalls

Frequently asked questions.

A correlational study is a type of research design that looks at the relationships between two or more variables. Correlational studies are non-experimental, which means that the experimenter does not manipulate or control any of the variables.

A correlation refers to a relationship between two variables. Correlations can be strong or weak and positive or negative. Sometimes, there is no correlation.

There are three possible outcomes of a correlation study: a positive correlation, a negative correlation, or no correlation. Researchers can present the results using a numerical value called the correlation coefficient, a measure of the correlation strength. It can range from –1.00 (negative) to +1.00 (positive). A correlation coefficient of 0 indicates no correlation.

• Positive correlations : Both variables increase or decrease at the same time. A correlation coefficient close to +1.00 indicates a strong positive correlation.
• Negative correlations : As the amount of one variable increases, the other decreases (and vice versa). A correlation coefficient close to -1.00 indicates a strong negative correlation.
• No correlation : There is no relationship between the two variables. A correlation coefficient of 0 indicates no correlation.

Characteristics of a Correlational Study

Correlational studies are often used in psychology, as well as other fields like medicine. Correlational research is a preliminary way to gather information about a topic. The method is also useful if researchers are unable to perform an experiment.

Researchers use correlations to see if a relationship between two or more variables exists, but the variables themselves are not under the control of the researchers.

While correlational research can demonstrate a relationship between variables, it cannot prove that changing one variable will change another. In other words, correlational studies cannot prove cause-and-effect relationships.

When you encounter research that refers to a "link" or an "association" between two things, they are most likely talking about a correlational study.

Types of Correlational Research

There are three types of correlational research: naturalistic observation, the survey method, and archival research. Each type has its own purpose, as well as its pros and cons.

Naturalistic Observation

The naturalistic observation method involves observing and recording variables of interest in a natural setting without interference or manipulation.  

Can inspire ideas for further research

Option if lab experiment not available

Variables are viewed in natural setting

Can be time-consuming and expensive

Extraneous variables can't be controlled

No scientific control of variables

Subjects might behave differently if aware of being observed

This method is well-suited to studies where researchers want to see how variables behave in their natural setting or state.   Inspiration can then be drawn from the observations to inform future avenues of research.

In some cases, it might be the only method available to researchers; for example, if lab experimentation would be precluded by access, resources, or ethics. It might be preferable to not being able to conduct research at all, but the method can be costly and usually takes a lot of time.  

Naturalistic observation presents several challenges for researchers. For one, it does not allow them to control or influence the variables in any way nor can they change any possible external variables.

However, this does not mean that researchers will get reliable data from watching the variables, or that the information they gather will be free from bias.

For example, study subjects might act differently if they know that they are being watched. The researchers might not be aware that the behavior that they are observing is not necessarily the subject's natural state (i.e., how they would act if they did not know they were being watched).

Researchers also need to be aware of their biases, which can affect the observation and interpretation of a subject's behavior.  

Surveys and questionnaires are some of the most common methods used for psychological research. The survey method involves having a  random sample  of participants complete a survey, test, or questionnaire related to the variables of interest.   Random sampling is vital to the generalizability of a survey's results.

Cheap, easy, and fast

Can collect large amounts of data in a short amount of time

Results can be affected by poor survey questions

Results can be affected by unrepresentative sample

Outcomes can be affected by participants

If researchers need to gather a large amount of data in a short period of time, a survey is likely to be the fastest, easiest, and cheapest option.  

It's also a flexible method because it lets researchers create data-gathering tools that will help ensure they get the information they need (survey responses) from all the sources they want to use (a random sample of participants taking the survey).

Survey data might be cost-efficient and easy to get, but it has its downsides. For one, the data is not always reliable—particularly if the survey questions are poorly written or the overall design or delivery is weak.   Data is also affected by specific faults, such as unrepresented or underrepresented samples .

The use of surveys relies on participants to provide useful data. Researchers need to be aware of the specific factors related to the people taking the survey that will affect its outcome.

For example, some people might struggle to understand the questions. A person might answer a particular way to try to please the researchers or to try to control how the researchers perceive them (such as trying to make themselves "look better").

Sometimes, respondents might not even realize that their answers are incorrect or misleading because of mistaken memories .

Archival Research

Many areas of psychological research benefit from analyzing studies that were conducted long ago by other researchers, as well as reviewing historical records and case studies.

For example, in an experiment known as  "The Irritable Heart ," researchers used digitalized records containing information on American Civil War veterans to learn more about post-traumatic stress disorder (PTSD).

Large amount of data

Can be less expensive

Researchers cannot change participant behavior

Can be unreliable

Information might be missing

No control over data collection methods

Using records, databases, and libraries that are publicly accessible or accessible through their institution can help researchers who might not have a lot of money to support their research efforts.

Free and low-cost resources are available to researchers at all levels through academic institutions, museums, and data repositories around the world.

Another potential benefit is that these sources often provide an enormous amount of data that was collected over a very long period of time, which can give researchers a way to view trends, relationships, and outcomes related to their research.

While the inability to change variables can be a disadvantage of some methods, it can be a benefit of archival research. That said, using historical records or information that was collected a long time ago also presents challenges. For one, important information might be missing or incomplete and some aspects of older studies might not be useful to researchers in a modern context.

A primary issue with archival research is reliability. When reviewing old research, little information might be available about who conducted the research, how a study was designed, who participated in the research, as well as how data was collected and interpreted.

Researchers can also be presented with ethical quandaries—for example, should modern researchers use data from studies that were conducted unethically or with questionable ethics?

You've probably heard the phrase, "correlation does not equal causation." This means that while correlational research can suggest that there is a relationship between two variables, it cannot prove that one variable will change another.

For example, researchers might perform a correlational study that suggests there is a relationship between academic success and a person's self-esteem. However, the study cannot show that academic success changes a person's self-esteem.

To determine why the relationship exists, researchers would need to consider and experiment with other variables, such as the subject's social relationships, cognitive abilities, personality, and socioeconomic status.

The difference between a correlational study and an experimental study involves the manipulation of variables. Researchers do not manipulate variables in a correlational study, but they do control and systematically vary the independent variables in an experimental study. Correlational studies allow researchers to detect the presence and strength of a relationship between variables, while experimental studies allow researchers to look for cause and effect relationships.

If the study involves the systematic manipulation of the levels of a variable, it is an experimental study. If researchers are measuring what is already present without actually changing the variables, then is a correlational study.

The variables in a correlational study are what the researcher measures. Once measured, researchers can then use statistical analysis to determine the existence, strength, and direction of the relationship. However, while correlational studies can say that variable X and variable Y have a relationship, it does not mean that X causes Y.

The goal of correlational research is often to look for relationships, describe these relationships, and then make predictions. Such research can also often serve as a jumping off point for future experimental research. 

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Schneider FW. Applied Social Psychology . 2nd ed. SAGE; 2012:50-53.

Curtis EA, Comiskey C, Dempsey O. Importance and use of correlational research .  Nurse Researcher . 2016;23(6):20-25. doi:10.7748/nr.2016.e1382

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Pizarro J, Silver RC, Prause J. Physical and mental health costs of traumatic war experiences among civil war veterans .  Arch Gen Psychiatry . 2006;63(2):193. doi:10.1001/archpsyc.63.2.193

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Lau F. Chapter 12 Methods for Correlational Studies . In: Lau F, Kuziemsky C, eds. Handbook of eHealth Evaluation: An Evidence-based Approach . University of Victoria.

Akoglu H. User's guide to correlation coefficients .  Turk J Emerg Med . 2018;18(3):91-93. doi:10.1016/j.tjem.2018.08.001

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By Kendra Cherry, MSEd Kendra Cherry, MS, is a psychosocial rehabilitation specialist, psychology educator, and author of the "Everything Psychology Book."

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• How to Write a Strong Hypothesis | Steps & Examples

How to Write a Strong Hypothesis | Steps & Examples

Published on May 6, 2022 by Shona McCombes . Revised on November 20, 2023.

A hypothesis is a statement that can be tested by scientific research. If you want to test a relationship between two or more variables, you need to write hypotheses before you start your experiment or data collection .

Example: Hypothesis

Daily apple consumption leads to fewer doctor’s visits.

Table of contents

What is a hypothesis, developing a hypothesis (with example), hypothesis examples, other interesting articles, frequently asked questions about writing hypotheses.

A hypothesis states your predictions about what your research will find. It is a tentative answer to your research question that has not yet been tested. For some research projects, you might have to write several hypotheses that address different aspects of your research question.

A hypothesis is not just a guess – it should be based on existing theories and knowledge. It also has to be testable, which means you can support or refute it through scientific research methods (such as experiments, observations and statistical analysis of data).

Variables in hypotheses

Hypotheses propose a relationship between two or more types of variables .

• An independent variable is something the researcher changes or controls.
• A dependent variable is something the researcher observes and measures.

If there are any control variables , extraneous variables , or confounding variables , be sure to jot those down as you go to minimize the chances that research bias  will affect your results.

In this example, the independent variable is exposure to the sun – the assumed cause . The dependent variable is the level of happiness – the assumed effect .

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Step 1. ask a question.

Writing a hypothesis begins with a research question that you want to answer. The question should be focused, specific, and researchable within the constraints of your project.

Step 2. Do some preliminary research

Your initial answer to the question should be based on what is already known about the topic. Look for theories and previous studies to help you form educated assumptions about what your research will find.

At this stage, you might construct a conceptual framework to ensure that you’re embarking on a relevant topic . This can also help you identify which variables you will study and what you think the relationships are between them. Sometimes, you’ll have to operationalize more complex constructs.

Step 3. Formulate your hypothesis

Now you should have some idea of what you expect to find. Write your initial answer to the question in a clear, concise sentence.

4. Refine your hypothesis

You need to make sure your hypothesis is specific and testable. There are various ways of phrasing a hypothesis, but all the terms you use should have clear definitions, and the hypothesis should contain:

• The relevant variables
• The specific group being studied
• The predicted outcome of the experiment or analysis

5. Phrase your hypothesis in three ways

To identify the variables, you can write a simple prediction in  if…then form. The first part of the sentence states the independent variable and the second part states the dependent variable.

In academic research, hypotheses are more commonly phrased in terms of correlations or effects, where you directly state the predicted relationship between variables.

If you are comparing two groups, the hypothesis can state what difference you expect to find between them.

6. Write a null hypothesis

If your research involves statistical hypothesis testing , you will also have to write a null hypothesis . The null hypothesis is the default position that there is no association between the variables. The null hypothesis is written as H 0 , while the alternative hypothesis is H 1 or H a .

• H 0 : The number of lectures attended by first-year students has no effect on their final exam scores.
• H 1 : The number of lectures attended by first-year students has a positive effect on their final exam scores.

If you want to know more about the research process , methodology , research bias , or statistics , make sure to check out some of our other articles with explanations and examples.

• Sampling methods
• Simple random sampling
• Stratified sampling
• Cluster sampling
• Likert scales
• Reproducibility

 Statistics

• Null hypothesis
• Statistical power
• Probability distribution
• Effect size
• Poisson distribution

Research bias

• Optimism bias
• Cognitive bias
• Implicit bias
• Hawthorne effect
• Anchoring bias
• Explicit bias

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A hypothesis is not just a guess — it should be based on existing theories and knowledge. It also has to be testable, which means you can support or refute it through scientific research methods (such as experiments, observations and statistical analysis of data).

Null and alternative hypotheses are used in statistical hypothesis testing . The null hypothesis of a test always predicts no effect or no relationship between variables, while the alternative hypothesis states your research prediction of an effect or relationship.

Hypothesis testing is a formal procedure for investigating our ideas about the world using statistics. It is used by scientists to test specific predictions, called hypotheses , by calculating how likely it is that a pattern or relationship between variables could have arisen by chance.

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Correlation in Psychology: Meaning, Types, Examples & coefficient

Saul Mcleod, PhD

Editor-in-Chief for Simply Psychology

BSc (Hons) Psychology, MRes, PhD, University of Manchester

Saul Mcleod, PhD., is a qualified psychology teacher with over 18 years of experience in further and higher education. He has been published in peer-reviewed journals, including the Journal of Clinical Psychology.

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Olivia Guy-Evans, MSc

Associate Editor for Simply Psychology

BSc (Hons) Psychology, MSc Psychology of Education

Olivia Guy-Evans is a writer and associate editor for Simply Psychology. She has previously worked in healthcare and educational sectors.

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Correlation means association – more precisely, it measures the extent to which two variables are related. There are three possible results of a correlational study: a positive correlation, a negative correlation, and no correlation.

• A positive correlation is a relationship between two variables in which both variables move in the same direction. Therefore, one variable increases as the other variable increases, or one variable decreases while the other decreases. An example of a positive correlation would be height and weight. Taller people tend to be heavier.

• A negative correlation is a relationship between two variables in which an increase in one variable is associated with a decrease in the other. An example of a negative correlation would be the height above sea level and temperature. As you climb the mountain (increase in height), it gets colder (decrease in temperature).

• A zero correlation exists when there is no relationship between two variables. For example, there is no relationship between the amount of tea drunk and the level of intelligence.

Scatter Plots

A correlation can be expressed visually. This is done by drawing a scatter plot (also known as a scattergram, scatter graph, scatter chart, or scatter diagram).

A scatter plot is a graphical display that shows the relationships or associations between two numerical variables (or co-variables), which are represented as points (or dots) for each pair of scores.

A scatter plot indicates the strength and direction of the correlation between the co-variables.

When you draw a scatter plot, it doesn’t matter which variable goes on the x-axis and which goes on the y-axis.

Remember, in correlations, we always deal with paired scores, so the values of the two variables taken together will be used to make the diagram.

Decide which variable goes on each axis and then simply put a cross at the point where the two values coincide.

Uses of Correlations

• If there is a relationship between two variables, we can make predictions about one from another.
• Concurrent validity (correlation between a new measure and an established measure).

Reliability

• Test-retest reliability (are measures consistent?).
• Inter-rater reliability (are observers consistent?).

Theory verification

• Predictive validity.

Correlation Coefficients

Instead of drawing a scatter plot, a correlation can be expressed numerically as a coefficient, ranging from -1 to +1. When working with continuous variables, the correlation coefficient to use is Pearson’s r.

The correlation coefficient ( r ) indicates the extent to which the pairs of numbers for these two variables lie on a straight line. Values over zero indicate a positive correlation, while values under zero indicate a negative correlation.

A correlation of –1 indicates a perfect negative correlation, meaning that as one variable goes up, the other goes down. A correlation of +1 indicates a perfect positive correlation, meaning that as one variable goes up, the other goes up.

There is no rule for determining what correlation size is considered strong, moderate, or weak. The interpretation of the coefficient depends on the topic of study.

When studying things that are difficult to measure, we should expect the correlation coefficients to be lower (e.g., above 0.4 to be relatively strong). When we are studying things that are easier to measure, such as socioeconomic status, we expect higher correlations (e.g., above 0.75 to be relatively strong).)

In these kinds of studies, we rarely see correlations above 0.6. For this kind of data, we generally consider correlations above 0.4 to be relatively strong; correlations between 0.2 and 0.4 are moderate, and those below 0.2 are considered weak.

When we are studying things that are more easily countable, we expect higher correlations. For example, with demographic data, we generally consider correlations above 0.75 to be relatively strong; correlations between 0.45 and 0.75 are moderate, and those below 0.45 are considered weak.

Correlation vs. Causation

Causation means that one variable (often called the predictor variable or independent variable) causes the other (often called the outcome variable or dependent variable).

Experiments can be conducted to establish causation. An experiment isolates and manipulates the independent variable to observe its effect on the dependent variable and controls the environment in order that extraneous variables may be eliminated.

A correlation between variables, however, does not automatically mean that the change in one variable is the cause of the change in the values of the other variable. A correlation only shows if there is a relationship between variables.

While variables are sometimes correlated because one does cause the other, it could also be that some other factor, a confounding variable , is actually causing the systematic movement in our variables of interest.

Correlation does not always prove causation, as a third variable may be involved. For example, being a patient in a hospital is correlated with dying, but this does not mean that one event causes the other, as another third variable might be involved (such as diet and level of exercise).

“Correlation is not causation” means that just because two variables are related it does not necessarily mean that one causes the other.

A correlation identifies variables and looks for a relationship between them. An experiment tests the effect that an independent variable has upon a dependent variable but a correlation looks for a relationship between two variables.

This means that the experiment can predict cause and effect (causation) but a correlation can only predict a relationship, as another extraneous variable may be involved that it not known about.

1. Correlation allows the researcher to investigate naturally occurring variables that may be unethical or impractical to test experimentally. For example, it would be unethical to conduct an experiment on whether smoking causes lung cancer.

2 . Correlation allows the researcher to clearly and easily see if there is a relationship between variables. This can then be displayed in a graphical form.

Limitations

1 . Correlation is not and cannot be taken to imply causation. Even if there is a very strong association between two variables, we cannot assume that one causes the other.

For example, suppose we found a positive correlation between watching violence on T.V. and violent behavior in adolescence.

It could be that the cause of both these is a third (extraneous) variable – for example, growing up in a violent home – and that both the watching of T.V. and the violent behavior is the outcome of this.

2 . Correlation does not allow us to go beyond the given data. For example, suppose it was found that there was an association between time spent on homework (1/2 hour to 3 hours) and the number of G.C.S.E. passes (1 to 6).

It would not be legitimate to infer from this that spending 6 hours on homework would likely generate 12 G.C.S.E. passes.

How do you know if a study is correlational?

A study is considered correlational if it examines the relationship between two or more variables without manipulating them. In other words, the study does not involve the manipulation of an independent variable to see how it affects a dependent variable.

One way to identify a correlational study is to look for language that suggests a relationship between variables rather than cause and effect.

For example, the study may use phrases like “associated with,” “related to,” or “predicts” when describing the variables being studied.

Another way to identify a correlational study is to look for information about how the variables were measured. Correlational studies typically involve measuring variables using self-report surveys, questionnaires, or other measures of naturally occurring behavior.

Finally, a correlational study may include statistical analyses such as correlation coefficients or regression analyses to examine the strength and direction of the relationship between variables.

Why is a correlational study used?

Correlational studies are particularly useful when it is not possible or ethical to manipulate one of the variables.

For example, it would not be ethical to manipulate someone’s age or gender. However, researchers may still want to understand how these variables relate to outcomes such as health or behavior.

Additionally, correlational studies can be used to generate hypotheses and guide further research.

If a correlational study finds a significant relationship between two variables, this can suggest a possible causal relationship that can be further explored in future research.

What is the goal of correlational research?

The ultimate goal of correlational research is to increase our understanding of how different variables are related and to identify patterns in those relationships.

This information can then be used to generate hypotheses and guide further research aimed at establishing causality.

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Interpretation of correlations in clinical research

1 University of Utah Department of Orthopaedic Surgery Operations, Salt Lake City, Utah, USA

Jerry Bounsanga

Maren wright voss, background:.

Critically analyzing research is a key skill in evidence-based practice and requires knowledge of research methods, results interpretation, and applications, all of which rely on a foundation based in statistics. Evidence-based practice makes high demands on trained medical professionals to interpret an ever-expanding array of research evidence.

As clinical training emphasizes medical care rather than statistics, it is useful to review the basics of statistical methods and what they mean for interpreting clinical studies.

We reviewed the basic concepts of correlational associations, violations of normality, unobserved variable bias, sample size, and alpha inflation. The foundations of causal inference were discussed and sound statistical analyses were examined. We discuss four ways in which correlational analysis is misused, including causal inference overreach, over-reliance on significance, alpha inflation, and sample size bias.

Recent published studies in the medical field provide evidence of causal assertion overreach drawn from correlational findings. The findings present a primer on the assumptions and nature of correlational methods of analysis and urge clinicians to exercise appropriate caution as they critically analyze the evidence before them and evaluate evidence that supports practice.

Conclusion:

Critically analyzing new evidence requires statistical knowledge in addition to clinical knowledge. Studies can overstate relationships, expressing causal assertions when only correlational evidence is available. Failure to account for the effect of sample size in the analyses tends to overstate the importance of predictive variables. It is important not to overemphasize the statistical significance without consideration of effect size and whether differences could be considered clinically meaningful.

Introduction

It is common for physicians to underestimate the relevance and importance of their training in statistics and probability, at least until its relevance becomes clear in later clinical practice. 1 Evidence based practice is the standard of care, yet evaluating the quality of evidence can be a difficult process. The British Medical Journal established clear statistical guidelines for contributions to medical journals in the 1980’s. 2 A survey of medical residents showed near perfect agreement (95%) that understanding statistics they encounter in medical journals is important, but 75% said they lacked knowledge. 3 The average score on the basic biostatistics exam for the residents surveyed was 41% correct, showing both the objective and subjective need for a stronger statistical training foundation. An international survey of practicing doctors similarly found that doctors averaged scores of 40% when tested on the basics of statistical methods and epidemiology. 4

The efforts to improve the methods behind clinical science are ongoing. Consolidated Standards of Reporting Trials (CONSORT) have been established, 5 along with multiple other research and statistical method guidelines in recent years. 6 These guidelines are updated periodically 7 and endorsed or extended by specific clinical medical groups, 8 , 9 or medical journals. 10 – 13 Key to many of these guidelines are attempts to ensure that bias and error are minimized in research, ensuring interpretations are meaningful and accurate. It would not be practical to detail an exhaustive list of guidance and recommendations. However, with new information and research approaches constantly coming forward, physicians must have the ability to critically evaluate the quality of evidence presented. Critically analyzing research is a key skill in evidence based practice and requires knowledge of methods, results interpretation, and applicability—all three of which require an understanding of basic statistics. 14

The intention of this article is to serve as a basic primer regarding critical statistical concepts that appear in medical literature with a focus on the concept of correlation and how it is best utilized in clinical interpretation for understanding the relationships between health factors. At its foundation, correlational analysis quantifies the direction and strength of relationships between two variables. Understanding correlations can form the basis for interpreting applications of clinical research.

1. What Does Correlation Tell Us?

Correlation is concerned with association; it can look at any two measured concepts and compare their relationships. These measured concepts are often referred to as variables and are assigned letter labels (X, Y). Thus, the correlation is the measure of the relationship between X and Y, and it ranges from −1 to 1. Its value (or coefficient) is scaled within this range to assist in interpretation, with 0 indicating no relationship between variables X and Y, and −1 or 1 indicating the ability to perfectly predict X from Y or Y from X (see Figure 1 ). A correlation coefficient provides two pieces of information. First, it predicts where X (the measured value of interest) falls on a line given a known value of Y. Second, it expresses a reduction in variability associated with knowing Y, telling us something about the expected range of the X value. 15 Correlation takes into account the full range of scores, but as a statistical tool it is not very sensitive to scores on the very high or very low ends of our X value. The common Pearson correlation is best used to describe linear relationships. If the pattern of association between the two variables is, for example, a “U” shaped curve, the correlation results might be low, even though a defined relationship exists. 16

1) Perfect negative correlation between two variables; 2) No patterned relationship between 2 variables; 3) Perfect positive correlation between two variables

Correlation is not easily impacted by skewed or off-center data results. The nature of the data can be described by its parameters, like measures of central tendency, which inform us about the distribution of the data. Parametric tests make assumptions, such as the data are normally distributed, while non-parametric tests are called distribution-free tests because they make no assumptions about the distribution of the data. Yet even if the pattern of scores are not in a normal bell shaped curve or they don’t create a direct linear relationship, correlations can still be reliable. A number of correlation measures have been developed to handle different types of data (non-parametric tests like the kendall rank, spearman rank correlation, phi correlation, biserial correlation, point-biserial correlation and gamma correlation). Yet even the simple Pearson correlation handles extreme violations of normality (no bell shape to the pattern of scores) and scale. The Pearson correlation was tested by randomly drawing 5,000 small samples (n=5 to n=15) from a population of 10,000 to calculate the distribution of r values yielded (small samples might challenge parametric assumptions), and was still found to be a reliable indicator of the relationship between variables. 17 It is also possible to use transformations to normalize the distribution of data. Correlation can be a robust measure, in part from its ability to tolerate these violations of normally distributed data while staying sensitive to the individual case. The properties of correlation make the technique useful in interpreting the meaning derived from clinical data.

2. Use of Correlation

There are many concerns with the statistical techniques that are commonly utilized in the literature. Some concerns arise from a misunderstanding of the statistical measure and others from its misapplication. We discuss four ways in which correlational analysis is misused, including causal inference overreach, over-reliance on significance, alpha inflation, and sample size bias. Importantly, correlation is a measure of association, which is insufficient to infer causation. Correlation can only measure whether a relationship exists between two variables, but it does not indicate causal relationship. There must be a convincing body of evidence to take the next step on the path to inferring that one variable causes the other. Randomized controlled trials or more advanced statistical methods such as path analysis and structural equation modeling, coupled with proper research design, are needed in order to take the next step of inference in the causal chain, testing a causal hypothesis. While correlational analyses are by definition from non-experimental research, research without carefully controlled experimental conditions, it is nevertheless relevant to evidence-based practice. 18 Observational methods of study can be conducted using either a cross-sectional design (a snap-shot of prevalence at one time-point), a retrospective design (looking back to compare current with past attributes) or prospective design (documenting current occurrences and following up at a future time-point to make comparisons). Correlations drawn from cross-sectional studies cannot establish the temporal relationship that links cause with effect, yet adding a retrospective or prospective observational design provides additional strength to the association and helps support hypothesis generation to then later test the causal assertions with a different research design. 19

When non-experimental methods are used, it means the relationship seen between the two variables is vulnerable to bias from anything that was not measured (unobserved variables). Whether studying pain or function or treatment response, there are a host of possible factors that might be important to the observed correlational relationship between X and Y. Any given study has only measured and reported on a fraction of the potential variables of impact. These unobserved variables could potentially explain the observed relationship, so it would be premature to assume a treatment effect based on correlational data. The unobserved variables might be affecting the study variables, changing the relationship in a way that might alter the interpretation of the data. Thus interpretation of correlational findings must be quite cautious until further research is completed.

Another concern is the use (or abuse) of the term ‘statistically significant’ in correlational analysis. This concern is not new. The abuse of significance testing was noted in a 1987 review published in the New England Journal of Medicine. That article found that a number of components in clinical trials, such as having several measures of the outcome (i.e., multiple tests of function, health, or pain), repeated measures over time, including subgroup analyses, or multiple treatments in the same trial, can lead to a bias in reporting which exaggerates the size or importance of observed differences. 20 It is natural for researchers to want to thoroughly evaluate the potential difference between treatments conditions. This has been sometimes referred to as the kitchen sink approach and it presents a problem for using significance tests. Significance as a statistical procedure addresses the question of the probability of the hypothesized occurrence. If the probability ( p ) is less than say 5% or 1%, the researcher might feel comfortable making the assumption that the observed event was not due to chance. The 0.05 significance value was original proposed by Sir Ronald Fisher in 1925, but the 0.05 value was never intended as a hard and fast rule. 21 If researchers use a cut-off of p=0.05 to determine whether the effect they see in their research has occurred randomly by chance, running multiple tests can quickly move the needle from a rare to an expected event. Every analysis run with a p =0.05 alpha criteria yields a 5% chance that the “significant” finding is actually a chance occurrence, called a Type 1 error.

So we can see the difficulty that occurs when running 20 different analyses on the same data. This would produce a 64% chance that a significant p -value will show up erroneously, when there is no systematic relationship, and it is really just a chance occurrence (see Figure 2 ). This over analysis of the data can possibly create an interpretation that a test or treatment should be used when there was no actual treatment effect. This is the problem of alpha-inflation and it needs to be carefully considered both in conducting and interpreting correlational research. It can be corrected by planning ahead for the analyses that will be run and keeping them limited to key theoretical questions. 20 Additionally, alpha can be adjusted in the statistical calculation, for example with the Bonferroni correction, a procedure used to reduce alpha and statistically correct for the inflation created by multiple comparisons. It is performed by simply dividing the alpha value (α) by the number of hypotheses or measures ( m ) tested. If the study wanted to evaluate 5 different surgical placements, using the Bonferroni correction would adjust an original α=0.05 by applying the formula, α/ m or 0.05/5, yielding α=0.01, a stricter standard before a study finding would be considered significant. A Bonferroni correction is a conservative correction for multiple comparisons that reduces the Type 1 error, 22 though less conservative alternatives exist like the Tukey or the Holm-Sidak corrections. The main idea is that clinicians acknowledge the problem of multiple comparisons made in a single study and address the concern so that spurious relationships are not erroneously reported as significant. A lack of awareness about this issue can lead to naïve interpretations of study findings.

As the number of comparisons increases, the alpha error rate increases; running 20 comparisons with no correction factor and a significance level set at 0.05 will result in 64% chance of a relationship appearing to be significant (better than 50/50 odds).

Exaggeration of significance testing leads to a third point - are the findings clinically meaningful? A significant finding does not infer a meaningful finding. This is because factors other than variance in scores influence the p -value or significance in a correlational analysis. Sample size is an important element in whether a non-random effect will be found. Small sample sizes might produce unstable, but significant, correlation estimates, so sample sizes greater than 150 to 200 have been recommended. 23 Yet, it is not uncommon for published papers to report significant effects through correlational analysis of sample sizes of less than 150 patients. 24 – 26 While reporting and publishing both the significant and non-significant results are important, given the instability that comes from a small sample size, there should be caution taken with interpretation until replication studies can verify the findings.

Likewise, large samples can also be problematic. A large sample might reveal a statistically significant difference between groups, but its effect might be minimal. In a classic example, a sample of 22,000 subjects showed a highly significant ( p <.00001) reduction in myocardial infarctions that prompted a general recommendation to take aspirin for myocardial infarction prevention. 27 The effect size, however, was less than a 1% reduction in risk, such that the risk of taking aspirin exceeded the benefit. Effect size is the standardized mean difference between groups and is a measure of the magnitude of between group differences. A significant p -value indicates only that a difference exists with no indication of size of the effect. Additionally, a confidence interval (CI) can be constructed for the effect size. CIs present a lower and upper range where the true population value is most likely to lie. 28 If a zero value is not included within the CI of the effect size, we have added assurance that the effect exists, with the size of the CI helpful in estimating the size of the effect. 29 It has been recommended that effect sizes or confidence intervals be included in all reported medical research so that the clinical significance of findings can be assessed. 20 , 28 , 30

3. Proper Interpretation of Correlation

Correlational analyses have been reported as one of the most common analytic techniques in research at the beginning of the 21 st century, particularly in health and epidemiological research. 15 Thus effective and proper interpretation is critical to understanding the literature. Cautious interpretation is particularly important, not only due to the interpretive concerns just detailed (causal inference overreach, over-reliance on significance, alpha inflation, and sample size bias), but also given the publication bias of journals to accept and publish studies with positive findings. 31 If clinicians are less likely to be exposed to under-published contradictory reports, based on null findings that treatments actually had no effect, the interpretation of the positive results must necessarily be cautious until confirmed through strong evidence.

One recent clinical example of correlational findings is an inference that because Cobb angle and sagittal balance are related to symptom severity in back pain, treatments should be aimed to improve sagittal balance. Studies used to draw these conclusions were making an important first step in identifying potentially relationships, but were not conclusive as they did not establish causal relationships, did not report effect sizes, and did not include control groups in the analyses. 32 – 34 The Pearson correlation or the Spearman correlation are tools that predict X from Y or Y from X. The nature of the correlation is symmetric, so that if the variables are inferred from a reversed direction (pain predicting spine function rather than spine function predicting pain), the same prediction holds true. 15 If one is looking for cause and effect, the correlational statistics cannot help. The mathematics of correlation tells us that Y is just as likely to precede X as to come after, because the prediction is the same regardless of which variable is inputted first. Effects cannot be determined directly through correlational analysis and perhaps the reverse relationship is the true relationship.

Because of the possibility of a bidirectional relationship, causal inference will be premature if relying purely on correlational statistics, no matter how many studies report the correlational finding. Correlation can be interpreted as the association between two variables. It cannot be used to indicate causal relationship. In fact, statistical tests cannot prove causal relationships but can only be used to test causal hypotheses. Misinterpretation of correlation is generally related to a lack of understanding of what a statistical test can or cannot do, as well as lacking knowledge in proper research design. Rather than jumping to an assumption of causality, the correlations should prompt the next stage of clinical research through randomly controlled clinical trials or the application of more complex statistical methods such as causal and path analysis. Perhaps a part of the tendency to jump too quickly to causal assertion arises from the nature of the questions asked in clinical research and the desire to quickly move to enhance patient care. New frameworks are emerging in the health sciences that challenge the appeal to a single cause by considering potential outcomes in a more complex ways. 35 Until then, understanding the nature of correlational analysis allows clinicians to be more cautious in interpreting study results.

Advances in research have led to many significant findings that are shaping how we diagnose and treat patients. As these findings might guide surgeons and clinicians into new treatment directions, it is important to consider the strength and nature of the research. Critically analyzing new evidence requires understanding of research methods and relevant statistical applications, all of which require an understanding of the analytic methodologies that lie behind the study findings.14 Evidence based practice is demanding new skills of trained medical professionals as they are presented with an ever-expanding array of research evidence. This short primer on theassumptions and nature of correlational methods of analysis can assist emerging physicians in understanding and exercising the appropriate caution as they critically analyze the evidence before them.

Acknowledgments

This investigation was supported by the University of Utah Department of Orthopaedics Quality Outcomes Research and Assessment, Study Design and Biostatistics Center, with funding in part from the National Center for Research Resources and the National Center for Advancing Translational Sciences, National Institutes of Health, through Grant 5UL1TR001067–02.

Declaration of Interests

The authors have no relevant affiliations or financial involvement with any organization or entity with a financial interest in or financial conflict with the subject matter or materials discussed in the manuscript. This includes employment, consultancies, honoraria, stock ownership or options, expert testimony, grants or patents received or pending, or royalties.

• Correlational Research Designs: Types, Examples & Methods

A human mind is a powerful tool that allows you to sift through seemingly unrelated variables and establish a connection with regards to a specific subject at hand. This skill is what comes to play when we talk about correlational research.

Correlational research is something that we do every day; think about how you establish a connection between the doorbell ringing at a particular time and the milkman’s arrival. As such, it is expedient to understand the different types of correlational research that are available and more importantly, how to go about it. 

What is Correlational Research?

Correlational research is a type of research method that involves observing two variables in order to establish a statistically corresponding relationship between them. The aim of correlational research is to identify variables that have some sort of relationship do the extent that a change in one creates some change in the other. 

This type of research is descriptive, unlike experimental research that relies entirely on scientific methodology and hypothesis. For example, correlational research may reveal the statistical relationship between high-income earners and relocation; that is, the more people earn, the more likely they are to relocate or not. 

What are the Types of Correlational Research?

Essentially, there are 3 types of correlational research which are positive correlational research, negative correlational research, and no correlational research. Each of these types is defined by peculiar characteristics. 

• Positive Correlational Research

Positive correlational research is a research method involving 2 variables that are statistically corresponding where an increase or decrease in 1 variable creates a like change in the other. An example is when an increase in workers’ remuneration results in an increase in the prices of goods and services and vice versa.  

• Negative Correlational Research

Negative correlational research is a research method involving 2 variables that are statistically opposite where an increase in one of the variables creates an alternate effect or decrease in the other variable. An example of a negative correlation is if the rise in goods and services causes a decrease in demand and vice versa. 

• Zero Correlational Research

Zero correlational research is a type of correlational research that involves 2 variables that are not necessarily statistically connected. In this case, a change in one of the variables may not trigger a corresponding or alternate change in the other variable.

Zero correlational research caters for variables with vague statistical relationships. For example, wealth and patience can be variables under zero correlational research because they are statistically independent. 

Sporadic change patterns that occur in variables with zero correlational are usually by chance and not as a result of corresponding or alternate mutual inclusiveness. 

Correlational research can also be classified based on data collection methods. Based on these, there are 3 types of correlational research: Naturalistic observation research, survey research and archival research. 

What are the Data Collection Methods in Correlational research? 

Data collection methods in correlational research are the research methodologies adopted by persons carrying out correlational research in order to determine the linear statistical relationship between 2 variables. These data collection methods are used to gather information in correlational research. 

The 3 methods of data collection in correlational research are naturalistic observation method, archival data method, and the survey method. All of these would be clearly explained in the subsequent paragraphs. 

• Naturalistic Observation

Naturalistic observation is a correlational research methodology that involves observing people’s behaviors as shown in the natural environment where they exist, over a period of time. It is a type of research-field method that involves the researcher paying closing attention to natural behavior patterns of the subjects under consideration.

This method is extremely demanding as the researcher must take extra care to ensure that the subjects do not suspect that they are being observed else they deviate from their natural behavior patterns. It is best for all subjects under observation to remain anonymous in order to avoid a breach of privacy. 

The major advantages of the naturalistic observation method are that it allows the researcher to fully observe the subjects (variables) in their natural state. However, it is a very expensive and time-consuming process plus the subjects can become aware of this act at any time and may act contrary. 

• Archival Data

Archival data is a type of correlational research method that involves making use of already gathered information about the variables in correlational research. Since this method involves using data that is already gathered and analyzed, it is usually straight to the point. 

For this method of correlational research, the research makes use of earlier studies conducted by other researchers or the historical records of the variables being analyzed. This method helps a researcher to track already determined statistical patterns of the variables or subjects. 

This method is less expensive, saves time and provides the researcher with more disposable data to work with. However, it has the problem of data accuracy as important information may be missing from previous research since the researcher has no control over the data collection process. 

• Survey Method

The survey method is the most common method of correlational research; especially in fields like psychology. It involves random sampling of the variables or the subjects in the research in which the participants fill a questionnaire centered on the subjects of interest. 

This method is very flexible as researchers can gather large amounts of data in very little time. However, it is subject to survey response bias and can also be affected by biased survey questions or under-representation of survey respondents or participants. 

These would be properly explained under data collection methods in correlational research. 

Examples of Correlational Research

Correlational research examples are numerous and highlight several instances where a correlational study may be carried out in order to determine the statistical behavioral trend with regards to the variables under consideration. Here are 3 case examples of correlational research. 

• You want to know if wealthy people are less likely to be patient. From your experience, you believe that wealthy people are impatient. However, you want to establish a statistical pattern that proves or disproves your belief. In this case, you can carry out correlational research to identify a trend that links both variables. 
• You want to know if there’s a correlation between how much people earn and the number of children that they have. You do not believe that people with more spending power have more children than people with less spending power. 

You think that how much people earn hardly determines the number of children that they have. Yet, carrying out correlational research on both variables could reveal any correlational relationship that exists between them. 

• You believe that domestic violence causes a brain hemorrhage. You cannot carry out an experiment as it would be unethical to deliberately subject people to domestic violence. 

However, you can carry out correlational research to find out if victims of domestic violence suffer brain hemorrhage more than non-victims. 

What are the Characteristics of Correlational Research? 

• Correlational Research is non-experimental

Correlational research is non-experimental as it does not involve manipulating variables using a scientific methodology in order to agree or disagree with a hypothesis. In correlational research, the researcher simply observes and measures the natural relationship between 2 variables; without subjecting either of the variables to external conditioning. 

• Correlational Research is Backward-looking

Correlational research doesn’t take the future into consideration as it only observes and measures the recent historical relationship that exists between 2 variables. In this sense, the statistical pattern resulting from correlational research is backward-looking and can seize to exist at any point, going forward. 

Correlational research observes and measures historical patterns between 2 variables such as the relationship between high-income earners and tax payment. Correlational research may reveal a positive relationship between the aforementioned variables but this may change at any point in the future. 

• Correlational Research is Dynamic

Statistical patterns between 2 variables that result from correlational research are ever-changing. The correlation between 2 variables changes on a daily basis and such, it cannot be used as a fixed data for further research. 

For example, the 2 variables can have a negative correlational relationship for a period of time, maybe 5 years. After this time, the correlational relationship between them can become positive; as observed in the relationship between bonds and stocks. 

• Data resulting from correlational research are not constant and cannot be used as a standard variable for further research. 

What is the Correlation Coefficient? 

A correlation coefficient is an important value in correlational research that indicates whether the inter-relationship between 2 variables is positive, negative or non-existent. It is usually represented with the sign [r] and is part of a range of possible correlation coefficients from -1.0 to +1.0. 

The strength of a correlation between quantitative variables is typically measured using a statistic called Pearson’s Correlation Coefficient (or Pearson’s r) . A positive correlation is indicated by a value of 1.0, a perfect negative correlation is indicated by a value of -1.0 while zero correlation is indicated by a value of 0.0. 

It is important to note that a correlation coefficient only reflects the linear relationship between 2 variables; it does not capture non-linear relationships and cannot separate dependent and independent variables. The correlation coefficient helps you to determine the degree of statistical relationship that exists between variables. 

What are the Advantages of Correlational Research?

• In cases where carrying out experimental research is unethical, correlational research  can be used to determine the relationship between 2 variables. For example, when studying humans, carrying out an experiment can be seen as unsafe or unethical; hence, choosing correlational research would be the best option. 
• Through correlational research, you can easily determine the statistical relationship between 2 variables.
• Carrying out correlational research is less time-consuming and less expensive than experimental research. This becomes a strong advantage when working with a minimum of researchers and funding or when keeping the number of variables in a study very low. 
• Correlational research allows the researcher to carry out shallow data gathering using different methods such as a short survey. A short survey does not require the researcher to personally administer it so this allows the researcher to work with a few people. 

What are the Disadvantages of Correlational Research? 

• Correlational research is limiting in nature as it can only be used to determine the statistical relationship between 2 variables. It cannot be used to establish a relationship between more than 2 variables. 
• It does not account for cause and effect between 2 variables as it doesn’t highlight which of the 2 variables is responsible for the statistical pattern that is observed. For example, finding that education correlates positively with vegetarianism doesn’t explain whether being educated leads to becoming a vegetarian or whether vegetarianism leads to more education.
• Reasons for either can be assumed, but until more research is done, causation can’t be determined. Also, a third, unknown variable might be causing both. For instance, living in the state of Detroit can lead to both education and vegetarianism.
• Correlational research depends on past statistical patterns to determine the relationship between variables. As such, its data cannot be fully depended on for further research. 
• In correlational research, the researcher has no control over the variables. Unlike experimental research, correlational research only allows the researcher to observe the variables for connecting statistical patterns without introducing a catalyst. 
• The information received from correlational research is limited. Correlational research only shows the relationship between variables and does not equate to causation. 

What are the Differences between Correlational and Experimental Research?  

• Methodology

The major difference between correlational research and experimental research is methodology. In correlational research, the researcher looks for a statistical pattern linking 2 naturally-occurring variables while in experimental research, the researcher introduces a catalyst and monitors its effects on the variables. 

• Observation

In correlational research, the researcher passively observes the phenomena and measures whatever relationship that occurs between them. However, in experimental research, the researcher actively observes phenomena after triggering a change in the behavior of the variables. 

In experimental research, the researcher introduces a catalyst and monitors its effects on the variables, that is, cause and effect. In correlational research, the researcher is not interested in cause and effect as it applies; rather, he or she identifies recurring statistical patterns connecting the variables in research. 

• Number of Variables

research caters to an unlimited number of variables. Correlational research, on the other hand, caters to only 2 variables. 

• Experimental research is causative while correlational research is relational.
• Correlational research is preliminary and almost always precedes experimental research. 
• Unlike correlational research, experimental research allows the researcher to control the variables.

How to Use Online Forms for Correlational Research

One of the most popular methods of conducting correlational research is by carrying out a survey which can be made easier with the use of an online form. Surveys for correlational research involve generating different questions that revolve around the variables under observation and, allowing respondents to provide answers to these questions. 

Using an online form for your correlational research survey would help the researcher to gather more data in minimum time. In addition, the researcher would be able to reach out to more survey respondents than is plausible with printed correlational research survey forms . 

In addition, the researcher would be able to swiftly process and analyze all responses in order to objectively establish the statistical pattern that links the variables in the research. Using an online form for correlational research also helps the researcher to minimize the cost incurred during the research period. 

To use an online form for a correlational research survey, you would need to sign up on a data-gathering platform like Formplus . Formplus allows you to create custom forms for correlational research surveys using the Formplus builder. 

You can customize your correlational research survey form by adding background images, new color themes or your company logo to make it appear even more professional. In addition, Formplus also has a survey form template that you can edit for a correlational research study. 

You can create different types of survey questions including open-ended questions , rating questions, close-ended questions and multiple answers questions in your survey in the Formplus builder. After creating your correlational research survey, you can share the personalized link with respondents via email or social media.

Formplus also enables you to collect offline responses in your form.

Conclusion 

Correlational research enables researchers to establish the statistical pattern between 2 seemingly interconnected variables; as such, it is the starting point of any type of research. It allows you to link 2 variables by observing their behaviors in the most natural state. 

Unlike experimental research, correlational research does not emphasize the causative factor affecting 2 variables and this makes the data that results from correlational research subject to constant change. However, it is quicker, easier, less expensive and more convenient than experimental research. 

It is important to always keep the aim of your research at the back of your mind when choosing the best type of research to adopt. If you simply need to observe how the variables react to change then, experimental research is the best type to subscribe for. 

It is best to conduct correlational research using an online correlational research survey form as this makes the data-gathering process, more convenient. Formplus is a great online data-gathering platform that you can use to create custom survey forms for correlational research. 

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Home » Correlation Analysis – Types, Methods and Examples

Correlation Analysis – Types, Methods and Examples

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Correlation Analysis

Correlation analysis is a statistical method used to evaluate the strength and direction of the relationship between two or more variables . The correlation coefficient ranges from -1 to 1.

• A correlation coefficient of 1 indicates a perfect positive correlation. This means that as one variable increases, the other variable also increases.
• A correlation coefficient of -1 indicates a perfect negative correlation. This means that as one variable increases, the other variable decreases.
• A correlation coefficient of 0 means that there’s no linear relationship between the two variables.

Correlation Analysis Methodology

Conducting a correlation analysis involves a series of steps, as described below:

• Define the Problem : Identify the variables that you think might be related. The variables must be measurable on an interval or ratio scale. For example, if you’re interested in studying the relationship between the amount of time spent studying and exam scores, these would be your two variables.
• Data Collection : Collect data on the variables of interest. The data could be collected through various means such as surveys , observations , or experiments. It’s crucial to ensure that the data collected is accurate and reliable.
• Data Inspection : Check the data for any errors or anomalies such as outliers or missing values. Outliers can greatly affect the correlation coefficient, so it’s crucial to handle them appropriately.
• Choose the Appropriate Correlation Method : Select the correlation method that’s most appropriate for your data. If your data meets the assumptions for Pearson’s correlation (interval or ratio level, linear relationship, variables are normally distributed), use that. If your data is ordinal or doesn’t meet the assumptions for Pearson’s correlation, consider using Spearman’s rank correlation or Kendall’s Tau.
• Compute the Correlation Coefficient : Once you’ve selected the appropriate method, compute the correlation coefficient. This can be done using statistical software such as R, Python, or SPSS, or manually using the formulas.
• Interpret the Results : Interpret the correlation coefficient you obtained. If the correlation is close to 1 or -1, the variables are strongly correlated. If the correlation is close to 0, the variables have little to no linear relationship. Also consider the sign of the correlation coefficient: a positive sign indicates a positive relationship (as one variable increases, so does the other), while a negative sign indicates a negative relationship (as one variable increases, the other decreases).
• Check the Significance : It’s also important to test the statistical significance of the correlation. This typically involves performing a t-test. A small p-value (commonly less than 0.05) suggests that the observed correlation is statistically significant and not due to random chance.
• Report the Results : The final step is to report your findings. This should include the correlation coefficient, the significance level, and a discussion of what these findings mean in the context of your research question.

Types of Correlation Analysis

Types of Correlation Analysis are as follows:

Pearson Correlation

This is the most common type of correlation analysis. Pearson correlation measures the linear relationship between two continuous variables. It assumes that the variables are normally distributed and have equal variances. The correlation coefficient (r) ranges from -1 to +1, with -1 indicating a perfect negative linear relationship, +1 indicating a perfect positive linear relationship, and 0 indicating no linear relationship.

Spearman Rank Correlation

Spearman’s rank correlation is a non-parametric measure that assesses how well the relationship between two variables can be described using a monotonic function. In other words, it evaluates the degree to which, as one variable increases, the other variable tends to increase, without requiring that increase to be consistent.

Kendall’s Tau

Kendall’s Tau is another non-parametric correlation measure used to detect the strength of dependence between two variables. Kendall’s Tau is often used for variables measured on an ordinal scale (i.e., where values can be ranked).

Point-Biserial Correlation

This is used when you have one dichotomous and one continuous variable, and you want to test for correlations. It’s a special case of the Pearson correlation.

Phi Coefficient

This is used when both variables are dichotomous or binary (having two categories). It’s a measure of association for two binary variables.

Canonical Correlation

This measures the correlation between two multi-dimensional variables. Each variable is a combination of data sets, and the method finds the linear combination that maximizes the correlation between them.

Partial and Semi-Partial (Part) Correlations

These are used when the researcher wants to understand the relationship between two variables while controlling for the effect of one or more additional variables.

Cross-Correlation

Used mostly in time series data to measure the similarity of two series as a function of the displacement of one relative to the other.

Autocorrelation

This is the correlation of a signal with a delayed copy of itself as a function of delay. This is often used in time series analysis to help understand the trend in the data over time.

Correlation Analysis Formulas

There are several formulas for correlation analysis, each corresponding to a different type of correlation. Here are some of the most commonly used ones:

Pearson’s Correlation Coefficient (r)

Pearson’s correlation coefficient measures the linear relationship between two variables. The formula is:

   r = Σ[(xi – Xmean)(yi – Ymean)] / sqrt[(Σ(xi – Xmean)²)(Σ(yi – Ymean)²)]

• xi and yi are the values of X and Y variables.
• Xmean and Ymean are the mean values of X and Y.
• Σ denotes the sum of the values.

Spearman’s Rank Correlation Coefficient (rs)

Spearman’s correlation coefficient measures the monotonic relationship between two variables. The formula is:

   rs = 1 – (6Σd² / n(n² – 1))

• d is the difference between the ranks of corresponding variables.
• n is the number of observations.

Kendall’s Tau (τ)

Kendall’s Tau is a measure of rank correlation. The formula is:

   τ = (nc – nd) / 0.5n(n-1)

• nc is the number of concordant pairs.
• nd is the number of discordant pairs.

This correlation is a special case of Pearson’s correlation, and so, it uses the same formula as Pearson’s correlation.

Phi coefficient is a measure of association for two binary variables. It’s equivalent to Pearson’s correlation in this specific case.

Partial Correlation

The formula for partial correlation is more complex and depends on the Pearson’s correlation coefficients between the variables.

For partial correlation between X and Y given Z:

  rp(xy.z) = (rxy – rxz * ryz) / sqrt[(1 – rxz^2)(1 – ryz^2)]

• rxy, rxz, ryz are the Pearson’s correlation coefficients.

Correlation Analysis Examples

Here are a few examples of how correlation analysis could be applied in different contexts:

• Education : A researcher might want to determine if there’s a relationship between the amount of time students spend studying each week and their exam scores. The two variables would be “study time” and “exam scores”. If a positive correlation is found, it means that students who study more tend to score higher on exams.
• Healthcare : A healthcare researcher might be interested in understanding the relationship between age and cholesterol levels. If a positive correlation is found, it could mean that as people age, their cholesterol levels tend to increase.
• Economics : An economist may want to investigate if there’s a correlation between the unemployment rate and the rate of crime in a given city. If a positive correlation is found, it could suggest that as the unemployment rate increases, the crime rate also tends to increase.
• Marketing : A marketing analyst might want to analyze the correlation between advertising expenditure and sales revenue. A positive correlation would suggest that higher advertising spending is associated with higher sales revenue.
• Environmental Science : A scientist might be interested in whether there’s a relationship between the amount of CO2 emissions and average temperature increase. A positive correlation would indicate that higher CO2 emissions are associated with higher average temperatures.

Importance of Correlation Analysis

Correlation analysis plays a crucial role in many fields of study for several reasons:

• Understanding Relationships : Correlation analysis provides a statistical measure of the relationship between two or more variables. It helps in understanding how one variable may change in relation to another.
• Predicting Trends : When variables are correlated, changes in one can predict changes in another. This is particularly useful in fields like finance, weather forecasting, and technology, where forecasting trends is vital.
• Data Reduction : If two variables are highly correlated, they are conveying similar information, and you may decide to use only one of them in your analysis, reducing the dimensionality of your data.
• Testing Hypotheses : Correlation analysis can be used to test hypotheses about relationships between variables. For example, a researcher might want to test whether there’s a significant positive correlation between physical exercise and mental health.
• Determining Factors : It can help identify factors that are associated with certain behaviors or outcomes. For example, public health researchers might analyze correlations to identify risk factors for diseases.
• Model Building : Correlation is a fundamental concept in building multivariate statistical models, including regression models and structural equation models. These models often require an understanding of the inter-relationships (correlations) among multiple variables.
• Validity and Reliability Analysis : In psychometrics, correlation analysis is used to assess the validity and reliability of measurement instruments such as tests or surveys.

Applications of Correlation Analysis

Correlation analysis is used in many fields to understand and quantify the relationship between variables. Here are some of its key applications:

• Finance : In finance, correlation analysis is used to understand the relationship between different investment types or the risk and return of a portfolio. For example, if two stocks are positively correlated, they tend to move together; if they’re negatively correlated, they move in opposite directions.
• Economics : Economists use correlation analysis to understand the relationship between various economic indicators, such as GDP and unemployment rate, inflation rate and interest rates, or income and consumption patterns.
• Marketing : Correlation analysis can help marketers understand the relationship between advertising spend and sales, or the relationship between price changes and demand.
• Psychology : In psychology, correlation analysis can be used to understand the relationship between different psychological variables, such as the correlation between stress levels and sleep quality, or between self-esteem and academic performance.
• Medicine : In healthcare, correlation analysis can be used to understand the relationships between various health outcomes and potential predictors. For example, researchers might investigate the correlation between physical activity levels and heart disease, or between smoking and lung cancer.
• Environmental Science : Correlation analysis can be used to investigate the relationships between different environmental factors, such as the correlation between CO2 levels and average global temperature, or between pesticide use and biodiversity.
• Social Sciences : In fields like sociology and political science, correlation analysis can be used to investigate relationships between different social and political phenomena, such as the correlation between education levels and political participation, or between income inequality and social unrest.

Advantages and Disadvantages of Correlation Analysis

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What is a hypothesis?

A hypothesis is an assumption that is neither proven nor disproven. In the research process, a hypothesis is made at the very beginning and the goal is to either reject or not reject the hypothesis. In order to reject or or not reject a hypothesis, data, e.g. from an experiment or a survey, are needed, which are then evaluated using a hypothesis test .

Usually, hypotheses are formulated starting from a literature review. Based on the literature review, you can then justify why you formulated the hypothesis in this way.

An example of a hypothesis could be: "Men earn more than women in the same job in Austira."

To test this hypothesis, you need data, e.g. from a survey, and a suitable hypothesis test such as the t-test or correlation analysis . Don't worry, DATAtab will help you choose the right hypothesis test.

How do I formulate a hypothesis?

In order to formulate a hypothesis, a research question must first be defined. A precisely formulated hypothesis about the population can then be derived from the research question, e.g. men earn more than women in the same job in Austria.

Hypotheses are not simple statements; they are formulated in such a way that they can be tested with collected data in the course of the research process.

To test a hypothesis, it is necessary to define exactly which variables are involved and how the variables are related. Hypotheses, then, are assumptions about the cause-and-effect relationships or the associations between variables.

What is a variable?

A variable is a property of an object or event that can take on different values. For example, the eye color is a variable, it is the property of the object eye and can take different values (blue, brown,...).

If you are researching in the social sciences, your variables may be:

• Attitude towards environmental protection

If you are researching in the medical field, your variables may be:

• Body weight
• Smoking status

What is the null and alternative hypothesis?

There are always two hypotheses that are exactly opposite to each other, or that claim the opposite. These opposite hypotheses are called null and alternative hypothesis and are abbreviated with H0 and H1 .

Null hypothesis H0:

The null hypothesis assumes that there is no difference between two or more groups with respect to a characteristic.

The salary of men and women does not differ in Austria.

Alternative hypothesis H1:

Alternative hypotheses, on the other hand, assume that there is a difference between two or more groups.

The salary of men and women differs in Austria.

The hypothesis that you want to test or that you have derived from the theory usually states that there is an effect e.g. gender has an effect on salary . This hypothesis is called an alternative hypothesis.

The null hypothesis usually states that there is no effect e.g. gender has no effect on salary . In a hypothesis test, only the null hypothesis can be tested; the goal is to find out whether the null hypothesis is rejected or not.

Types of hypotheses

What types of hypotheses are available? The most common distinction is between difference and correlation hypotheses , as well as directional and non-directional hypotheses .

Differential and correlation hypotheses

Difference hypotheses are used when different groups are to be distinguished, e.g., the group of men and the group of women. Correlation hypotheses are used when the relationship or correlation between variables is to be tested, e.g., the relationship between age and height.

Difference hypotheses

Difference hypotheses test whether there is a difference between two or more groups.

Examples of difference hypotheses are:

• The "group" of men earn more than the "group" of women.
• Smokers have a higher risk of heart attack than non-smokers
• There is a difference between Germany, Austria and France in terms of hours worked per week.

Thus, one variable is always a categorical variable, e.g., gender (male, female), smoking status (smoker, nonsmoker), or country (Germany, Austria, and France); the other variable is at least ordinally scaled, e.g., salary, percent risk of heart attack, or hours worked per week.

Correlation hypotheses

Correlation hypotheses test correlations between two variables, for example height and body weight

Correlation hypotheses are, for example:

• The taller a person is, the heavier he is.
• The more horsepower a car has, the higher its fuel consumption.
• The better the math grade, the higher the future salary.

As can be seen from the examples, correlation hypotheses often take the form "The more..., the higher/lower...". Thus, at least two ordinally scaled variables are being examined.

Directional and non-directional hypotheses

Hypotheses are divided into directional and non-directional or one-sided and two-sided hypotheses. If the hypothesis contains words like "better than" or "worse than", the hypothesis is usually directional.

In the case of a non-directional hypothesis, one often finds building blocks such as "there is a difference between" in the formulation, but it is not stated in which direction the difference lies.

• With a non-directional hypothesis , the only thing of interest is whether there is a difference in a value between the groups under consideration.
• In a directional hypothesis , what is of interest is whether one group has a higher or lower value than the other.

Non-directional hypotheses

Non-directional hypotheses test whether there is a relationship or a difference, and it does not matter in which direction the relationship or difference goes. In the case of a difference hypothesis, this means there is a difference between two groups, but it does not say whether one of the groups has a higher value.

• There is a difference between the salary of men and women (but it is not said who earns more!).
• There is a difference in the risk of heart attack between smokers and non-smokers (but it is not said who has the higher risk!).

In regard to a correlation hypothesis, this means there is a relationship or correlation between two variables, but it is not said whether this relationship is positive or negative.

• There is a correlation, between height and weight.
• There is a correlation between horsepower and fuel consumption in cars.

In both cases it is not said whether this correlation is positive or negative!

Directional hypotheses

Directional hypotheses additionally indicate the direction of the relationship or the difference. In the case of the difference hypothesis a statement is made which group has a higher or lower value.

• Men earn more than women

In the case of a correlation hypothesis, a statement is made as to whether the correlation is positive or negative.

• The taller a person is the heavier he is
• The more horsepower a car has, the higher its fuel economy

The p-value for directional hypotheses

Usually, statistical software always calculates the non-directional test and then also outputs the p-value for this.

To obtain the p-value for the directional hypothesis, it must first be checked whether the effect is in the right direction. Then the p-value must be divided by two. This is because the significance level is not split on two sides, but only on one side. More about this in the tutorial about the p-value .

If you select a directed alternative hypothesis in DATAtab for the calculated hypothesis test, the conversion is done automatically and you only need to read the result.

Step-by-step instructions for testing hypotheses

• Literature research
• Formulation of the hypothesis
• Define scale level
• Determine significance level
• Determination of hypothesis type
• Which hypothesis test is suitable for the scale level and hypothesis type?

Next tutorial about hypothesis testing

The next tutorial is about hypothesis testing. You will learn what hypothesis tests are, how to find the right one and how to interpret it.

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Correlational research is a type of research design used to examine the relationship between two or more variables. In correlational research, researchers measure the extent to which two or more variables are related, without manipulating or controlling any of the variables.

Whether you are a beginner or an experienced researcher, chances are you’ve heard something about correlational research. It’s time that you learn more about this type of study more in-depth, since you will be using it a lot.

• What is correlation?
• When to use it?
• How is it different from experimental studies?
• What data collection method will work?

Grab your pen and get ready to jot down some notes as our paper writing service is going to cover all questions you may have about this type of study. Let’s get down to business! 

What Is Correlational Research: Definition

A correlational research is a preliminary type of study used to explore the connection between two variables. In this type of research, you won’t interfere with the variables. Instead of manipulating or adjusting them, researchers focus more on observation.  Correlational study is a perfect option if you want to figure out if there is any link between variables. You will conduct it in 2 cases:

• When you want to test a theory about non-causal connection. For example, you may want to know whether drinking hot water boosts the immune system. In this case, you expect that vitamins, healthy lifestyle and regular exercise are those factors that have a real positive impact. However, this doesn’t mean that drinking hot water isn’t associated with the immune system. So measuring this relationship will be really useful.
• When you want to investigate a causal link. You want to study whether using aerosol products leads to ozone depletion. You don’t have enough expenses for conducting complex research. Besides, you can’t control how often people use aerosols. In this case, you will opt for a correlational study.

Correlational Study: Purpose

Correlational research is most useful for purposes of observation and prediction. Researcher's goal is to observe and measure variables to determine if any relationship exists. In case there is some association, researchers assess how strong it is. As an initial type of research, this method allows you to test and write the hypotheses. Correlational study doesn’t require much time and is rather cheap.

Correlational Research Design

Correlational research designs are often used in psychology, epidemiology , medicine and nursing. They show the strength of correlation that exists between the variables within a population. For this reason, these studies are also known as ecological studies.  Correlational research design methods are characterized by such traits:

• Non-experimental method. No manipulation or exposure to extra conditions takes place. Researchers only examine how variables act in their natural environment without any interference.
• Fluctuating patterns. Association is never the same and can change due to various factors.
• Quantitative research. These studies require quantitative research methods . Researchers mostly run a statistical analysis and work with numbers to get results.
• Association-oriented study. Correlational study is aimed at finding an association between 2 or more phenomena or events. This has nothing to do with causal relationships between dependent and independent variables .

Correlational Research Questions

Correlational research questions usually focus on how one variable related to another one. If there is some connection, you will observe how strong it is. Let’s look at several examples.

Correlational Research Types

Depending on the direction and strength of association, there are 3 types of correlational research:

• Positive correlation If one variable increases, the other one will grow accordingly. If there is any reduction, both variables will decrease.

• Negative correlation All changes happen in the reverse direction. If one variable increases, the other one should decrease and vice versa.

• Zero correlation No association between 2 factors or events can be found.

Correlational Research: Data Collection Methods

There are 3 main methods applied to collect data in correlational research:

• Surveys and polls
• Naturalistic observation
• Secondary or archival data.

It’s essential that you select the right study method. Otherwise, it won’t be possible to achieve accurate results and answer the research question correctly. Let’s have a closer look at each of these methods to make sure that you make the right choice.

Surveys in Correlational Study

Survey is an easy way to collect data about a population in a correlational study. Depending on the nature of the question, you can choose different survey variations. Questionnaires, polls and interviews are the three most popular formats used in a survey research study. To conduct an effective study, you should first identify the population and choose whether you want to run a survey online, via email or in person.

Naturalistic Observation: Correlational Research

Naturalistic observation is another data collection approach in correlational research methodology. This method allows us to observe behavioral patterns in a natural setting. Scientists often document, describe or categorize data to get a clear picture about a group of people. During naturalistic observations, you may work with both qualitative and quantitative research information. Nevertheless, to measure the strength of association, you should analyze numeric data. Members of a population shouldn’t know that they are being studied. Thus, you should blend in a target group as naturally as possible. Otherwise, participants may behave in a different way which may cause a statistical error. 

Correlational Study: Archival Data

Sometimes, you may access ready-made data that suits your study. Archival data is a quick correlational research method that allows to obtain necessary details from the similar studies that have already been conducted. You won’t deal with data collection techniques , since most of numbers will be served on a silver platter. All you will be left to do is analyze them and draw a conclusion. Unfortunately, not all records are accurate, so you should rely only on credible sources.

Pros and Cons of Correlational Research

Choosing what study to run can be difficult. But in this article, we are going to take an in-depth look at advantages and disadvantages of correlational research. This should help you decide whether this type of study is the best fit for you. Without any ado, let’s dive deep right in.

Advantages of Correlational Research

Obviously, one of the many advantages of correlational research is that it can be conducted when an experiment can’t be the case. Sometimes, it may be unethical to run an experimental study or you may have limited resources. This is exactly when ecological study can come in handy.  This type of study also has several benefits that have an irreplaceable value:

• Works well as a preliminary study
• Allows examining complex connection between multiple variables
• Helps you study natural behavior
• Can be generalized to other settings.

If you decide to run an archival study or conduct a survey, you will be able to save much time and expenses.

Disadvantages of Correlational Research

There are several limitations of correlational research you should keep in mind while deciding on the main methodology. Here are the advantages one should consider:

• No causal relationships can be identified
• No chance to manipulate extraneous variables
• Biased results caused by unnatural behavior
• Naturalistic studies require quite a lot of time.

As you can see, these types of studies aren’t end-all, be-all. They may indicate a direction for further research. Still, correlational studies don’t show a cause-and-effect relationship which is probably the biggest disadvantage. 

Difference Between Correlational and Experimental Research

Now that you’ve come this far, let’s discuss correlational vs experimental research design . Both studies involve quantitative data. But the main difference lies in the aim of research. Correlational studies are used to identify an association which is measured with a coefficient, while an experiment is aimed at determining a causal relationship.  Due to a different purpose, the studies also have different approaches to control over variables. In the first case, scientists can’t control or otherwise manipulate the variables in question. Meanwhile, experiments allow you to control variables without limit. There is a  causation vs correlation  blog on our website. Find out their differences as it will be useful for your research.

Example of Correlational Research

Above, we have offered several correlational research examples. Let’s have a closer look at how things work using a more detailed example.

Example You want to determine if there is any connection between the time employees work in one company and their performance. An experiment will be rather time-consuming. For this reason, you can offer a questionnaire to collect data and assess an association. After running a survey, you will be able to confirm or disprove your hypothesis.

Correlational Study: Final Thoughts

That’s pretty much everything you should know about correlational study. The key takeaway is that this type of study is used to measure the connection between 2 or more variables. It’s a good choice if you have no chance to run an experiment. However, in this case you won’t be able to control for extraneous variables . So you should consider your options carefully before conducting your own research. 

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Frequently Asked Questions About Correlational Study

1. what is a correlation.

Correlation is a connection that shows to which extent two or more variables are associated. It doesn’t show a causal link and only helps to identify a direction (positive, negative or zero) or the strength of association.

2. How many variables are in a correlation?

There can be many different variables in a correlation which makes this type of study very useful for exploring complex relationships. However, most scientists use this research to measure the association between only 2 variables.

3. What is a correlation coefficient?

Correlation coefficient (ρ) is a statistical measure that indicates the extent to which two variables are related. Association can be strong, moderate or weak. There are different types of p coefficients: positive, negative and zero.

4. What is a correlational study?

Correlational study is a type of statistical research that involves examining two variables in order to determine association between them. It’s a non-experimental type of study, meaning that researchers can’t change independent variables or control extraneous variables.

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Correlation Hypothesis

Understanding the relationships between variables is pivotal in research. Correlation hypotheses delve into the degree of association between two or more variables. In this guide, delve into an array of correlation hypothesis examples that explore connections, followed by a step-by-step tutorial on crafting these thesis statement hypothesis effectively. Enhance your research prowess with valuable tips tailored to unravel the intricate world of correlations.

What is Correlation Hypothesis?

A correlation hypothesis is a statement that predicts a specific relationship between two or more variables based on the assumption that changes in one variable are associated with changes in another variable. It suggests that there is a correlation or statistical relationship between the variables, meaning that when one variable changes, the other variable is likely to change in a consistent manner.

What is an example of a Correlation Hypothesis Statement?

Example: “If the amount of exercise increases, then the level of physical fitness will also increase.”

In this example, the correlation hypothesis suggests that there is a positive correlation between the amount of exercise a person engages in and their level of physical fitness. As exercise increases, the hypothesis predicts that physical fitness will increase as well. This hypothesis can be tested by collecting data on exercise levels and physical fitness levels and analyzing the relationship between the two variables using statistical methods.

100 Correlation Hypothesis Statement Examples

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Discover the intriguing world of correlation through a collection of examples that illustrate how variables can be linked in research. Explore diverse scenarios where changes in one variable may correspond to changes in another, forming the basis of correlation hypotheses. These real-world instances shed light on the essence of correlation analysis and its role in uncovering connections between different aspects of data.

• Study Hours and Exam Scores : If students study more hours per week, then their exam scores will show a positive correlation, indicating that increased study time might lead to better performance.
• Income and Education : If the level of education increases, then income levels will also rise, demonstrating a positive correlation between education attainment and earning potential.
• Social Media Usage and Well-being : If individuals spend more time on social media platforms, then their self-reported well-being might exhibit a negative correlation, suggesting that excessive use could impact mental health.
• Temperature and Ice Cream Sales : If temperatures rise, then the sales of ice cream might increase, displaying a positive correlation due to the weather’s influence on consumer behavior.
• Physical Activity and Heart Rate : If the intensity of physical activity rises, then heart rate might increase, signifying a positive correlation between exercise intensity and heart rate.
• Age and Reaction Time : If age increases, then reaction time might show a positive correlation, indicating that as people age, their reaction times might slow down.
• Smoking and Lung Capacity : If the number of cigarettes smoked daily increases, then lung capacity might decrease, suggesting a negative correlation between smoking and respiratory health.
• Stress and Sleep Quality : If stress levels elevate, then sleep quality might decline, reflecting a negative correlation between psychological stress and restorative sleep.
• Rainfall and Crop Yield : If the amount of rainfall decreases, then crop yield might also decrease, illustrating a negative correlation between precipitation and agricultural productivity.
• Screen Time and Academic Performance : If screen time usage increases among students, then academic performance might show a negative correlation, suggesting that excessive screen time could be detrimental to studies.
• Exercise and Body Weight : If individuals engage in regular exercise, then their body weight might exhibit a negative correlation, implying that physical activity can contribute to weight management.
• Income and Crime Rates : If income levels decrease in a neighborhood, then crime rates might show a positive correlation, indicating a potential link between socio-economic factors and crime.
• Social Support and Mental Health : If the level of social support increases, then individuals’ mental health scores may exhibit a positive correlation, highlighting the potential positive impact of strong social networks on psychological well-being.
• Study Time and GPA : If students spend more time studying, then their Grade Point Average (GPA) might display a positive correlation, suggesting that increased study efforts may lead to higher academic achievement.
• Parental Involvement and Academic Success : If parents are more involved in their child’s education, then the child’s academic success may show a positive correlation, emphasizing the role of parental support in shaping student outcomes.
• Alcohol Consumption and Reaction Time : If alcohol consumption increases, then reaction time might slow down, indicating a negative correlation between alcohol intake and cognitive performance.
• Social Media Engagement and Loneliness : If time spent on social media platforms increases, then feelings of loneliness might show a positive correlation, suggesting a potential connection between excessive online interaction and emotional well-being.
• Temperature and Insect Activity : If temperatures rise, then the activity of certain insects might increase, demonstrating a potential positive correlation between temperature and insect behavior.
• Education Level and Voting Participation : If education levels rise, then voter participation rates may also increase, showcasing a positive correlation between education and civic engagement.
• Work Commute Time and Job Satisfaction : If work commute time decreases, then job satisfaction might show a positive correlation, indicating that shorter commutes could contribute to higher job satisfaction.
• Sleep Duration and Cognitive Performance : If sleep duration increases, then cognitive performance scores might also rise, suggesting a potential positive correlation between adequate sleep and cognitive functioning.
• Healthcare Access and Mortality Rate : If access to healthcare services improves, then the mortality rate might decrease, highlighting a potential negative correlation between healthcare accessibility and mortality.
• Exercise and Blood Pressure : If individuals engage in regular exercise, then their blood pressure levels might exhibit a negative correlation, indicating that physical activity can contribute to maintaining healthy blood pressure.
• Social Media Use and Academic Distraction : If students spend more time on social media during study sessions, then their academic focus might show a negative correlation, suggesting that excessive online engagement can hinder concentration.
• Age and Technological Adaptation : If age increases, then the speed of adapting to new technologies might exhibit a negative correlation, suggesting that younger individuals tend to adapt more quickly.
• Temperature and Plant Growth : If temperatures rise, then the rate of plant growth might increase, indicating a potential positive correlation between temperature and biological processes.
• Music Exposure and Mood : If individuals listen to upbeat music, then their reported mood might show a positive correlation, suggesting that music can influence emotional states.
• Income and Healthcare Utilization : If income levels increase, then the frequency of healthcare utilization might decrease, suggesting a potential negative correlation between income and healthcare needs.
• Distance and Communication Frequency : If physical distance between individuals increases, then their communication frequency might show a negative correlation, indicating that proximity tends to facilitate communication.
• Study Group Attendance and Exam Scores : If students regularly attend study groups, then their exam scores might exhibit a positive correlation, suggesting that collaborative study efforts could enhance performance.
• Temperature and Disease Transmission : If temperatures rise, then the transmission of certain diseases might increase, pointing to a potential positive correlation between temperature and disease spread.
• Interest Rates and Consumer Spending : If interest rates decrease, then consumer spending might show a positive correlation, suggesting that lower interest rates encourage increased economic activity.
• Digital Device Use and Eye Strain : If individuals spend more time on digital devices, then the occurrence of eye strain might show a positive correlation, suggesting that prolonged screen time can impact eye health.
• Parental Education and Children’s Educational Attainment : If parents have higher levels of education, then their children’s educational attainment might display a positive correlation, highlighting the intergenerational impact of education.
• Social Interaction and Happiness : If individuals engage in frequent social interactions, then their reported happiness levels might show a positive correlation, indicating that social connections contribute to well-being.
• Temperature and Energy Consumption : If temperatures decrease, then energy consumption for heating might increase, suggesting a potential positive correlation between temperature and energy usage.
• Physical Activity and Stress Reduction : If individuals engage in regular physical activity, then their reported stress levels might display a negative correlation, indicating that exercise can help alleviate stress.
• Diet Quality and Chronic Diseases : If diet quality improves, then the prevalence of chronic diseases might decrease, suggesting a potential negative correlation between healthy eating habits and disease risk.
• Social Media Use and Body Image Dissatisfaction : If time spent on social media increases, then feelings of body image dissatisfaction might show a positive correlation, suggesting that online platforms can influence self-perception.
• Income and Access to Quality Education : If household income increases, then access to quality education for children might improve, suggesting a potential positive correlation between financial resources and educational opportunities.
• Workplace Diversity and Innovation : If workplace diversity increases, then the rate of innovation might show a positive correlation, indicating that diverse teams often generate more creative solutions.
• Physical Activity and Bone Density : If individuals engage in weight-bearing exercises, then their bone density might exhibit a positive correlation, suggesting that exercise contributes to bone health.
• Screen Time and Attention Span : If screen time increases, then attention span might show a negative correlation, indicating that excessive screen exposure can impact sustained focus.
• Social Support and Resilience : If individuals have strong social support networks, then their resilience levels might display a positive correlation, suggesting that social connections contribute to coping abilities.
• Weather Conditions and Mood : If sunny weather persists, then individuals’ reported mood might exhibit a positive correlation, reflecting the potential impact of weather on emotional states.
• Nutrition Education and Healthy Eating : If individuals receive nutrition education, then their consumption of fruits and vegetables might show a positive correlation, suggesting that knowledge influences dietary choices.
• Physical Activity and Cognitive Aging : If adults engage in regular physical activity, then their cognitive decline with aging might show a slower rate, indicating a potential negative correlation between exercise and cognitive aging.
• Air Quality and Respiratory Illnesses : If air quality deteriorates, then the incidence of respiratory illnesses might increase, suggesting a potential positive correlation between air pollutants and health impacts.
• Reading Habits and Vocabulary Growth : If individuals read regularly, then their vocabulary size might exhibit a positive correlation, suggesting that reading contributes to language development.
• Sleep Quality and Stress Levels : If sleep quality improves, then reported stress levels might display a negative correlation, indicating that sleep can impact psychological well-being.
• Social Media Engagement and Academic Performance : If students spend more time on social media, then their academic performance might exhibit a negative correlation, suggesting that excessive online engagement can impact studies.
• Exercise and Blood Sugar Levels : If individuals engage in regular exercise, then their blood sugar levels might display a negative correlation, indicating that physical activity can influence glucose regulation.
• Screen Time and Sleep Duration : If screen time before bedtime increases, then sleep duration might show a negative correlation, suggesting that screen exposure can affect sleep patterns.
• Environmental Pollution and Health Outcomes : If exposure to environmental pollutants increases, then the occurrence of health issues might show a positive correlation, suggesting that pollution can impact well-being.
• Time Management and Academic Achievement : If students improve time management skills, then their academic achievement might exhibit a positive correlation, indicating that effective planning contributes to success.
• Physical Fitness and Heart Health : If individuals improve their physical fitness, then their heart health indicators might display a positive correlation, indicating that exercise benefits cardiovascular well-being.
• Weather Conditions and Outdoor Activities : If weather is sunny, then outdoor activities might show a positive correlation, suggesting that favorable weather encourages outdoor engagement.
• Media Exposure and Body Image Perception : If exposure to media images increases, then body image dissatisfaction might show a positive correlation, indicating media’s potential influence on self-perception.
• Community Engagement and Civic Participation : If individuals engage in community activities, then their civic participation might exhibit a positive correlation, indicating an active citizenry.
• Social Media Use and Productivity : If individuals spend more time on social media, then their productivity levels might exhibit a negative correlation, suggesting that online distractions can affect work efficiency.
• Income and Stress Levels : If income levels increase, then reported stress levels might exhibit a negative correlation, suggesting that financial stability can impact psychological well-being.
• Social Media Use and Interpersonal Skills : If individuals spend more time on social media, then their interpersonal skills might show a negative correlation, indicating potential effects on face-to-face interactions.
• Parental Involvement and Academic Motivation : If parents are more involved in their child’s education, then the child’s academic motivation may exhibit a positive correlation, highlighting the role of parental support.
• Technology Use and Sleep Quality : If screen time increases before bedtime, then sleep quality might show a negative correlation, suggesting that technology use can impact sleep.
• Outdoor Activity and Mood Enhancement : If individuals engage in outdoor activities, then their reported mood might display a positive correlation, suggesting the potential emotional benefits of nature exposure.
• Income Inequality and Social Mobility : If income inequality increases, then social mobility might exhibit a negative correlation, suggesting that higher inequality can hinder upward mobility.
• Vegetable Consumption and Heart Health : If individuals increase their vegetable consumption, then heart health indicators might show a positive correlation, indicating the potential benefits of a nutritious diet.
• Online Learning and Academic Achievement : If students engage in online learning, then their academic achievement might display a positive correlation, highlighting the effectiveness of digital education.
• Emotional Intelligence and Workplace Performance : If emotional intelligence improves, then workplace performance might exhibit a positive correlation, indicating the relevance of emotional skills.
• Community Engagement and Mental Well-being : If individuals engage in community activities, then their reported mental well-being might show a positive correlation, emphasizing social connections’ impact.
• Rainfall and Agriculture Productivity : If rainfall levels increase, then agricultural productivity might exhibit a positive correlation, indicating the importance of water for crops.
• Social Media Use and Body Posture : If screen time increases, then poor body posture might show a positive correlation, suggesting that screen use can influence physical habits.
• Marital Satisfaction and Relationship Length : If marital satisfaction decreases, then relationship length might show a negative correlation, indicating potential challenges over time.
• Exercise and Anxiety Levels : If individuals engage in regular exercise, then reported anxiety levels might exhibit a negative correlation, indicating the potential benefits of physical activity on mental health.
• Music Listening and Concentration : If individuals listen to instrumental music, then their concentration levels might display a positive correlation, suggesting music’s impact on focus.
• Internet Usage and Attention Deficits : If screen time increases, then attention deficits might show a positive correlation, implying that excessive internet use can affect concentration.
• Financial Literacy and Debt Levels : If financial literacy improves, then personal debt levels might exhibit a negative correlation, suggesting better financial decision-making.
• Time Spent Outdoors and Vitamin D Levels : If time spent outdoors increases, then vitamin D levels might show a positive correlation, indicating sun exposure’s role in vitamin synthesis.
• Family Meal Frequency and Nutrition : If families eat meals together frequently, then nutrition quality might display a positive correlation, emphasizing family dining’s impact on health.
• Temperature and Allergy Symptoms : If temperatures rise, then allergy symptoms might increase, suggesting a potential positive correlation between temperature and allergen exposure.
• Social Media Use and Academic Distraction : If students spend more time on social media, then their academic focus might exhibit a negative correlation, indicating that online engagement can hinder studies.
• Financial Stress and Health Outcomes : If financial stress increases, then the occurrence of health issues might show a positive correlation, suggesting potential health impacts of economic strain.
• Study Hours and Test Anxiety : If students study more hours, then test anxiety might show a negative correlation, suggesting that increased preparation can reduce anxiety.
• Music Tempo and Exercise Intensity : If music tempo increases, then exercise intensity might display a positive correlation, indicating music’s potential to influence workout vigor.
• Green Space Accessibility and Stress Reduction : If access to green spaces improves, then reported stress levels might exhibit a negative correlation, highlighting nature’s stress-reducing effects.
• Parenting Style and Child Behavior : If authoritative parenting increases, then positive child behaviors might display a positive correlation, suggesting parenting’s influence on behavior.
• Sleep Quality and Productivity : If sleep quality improves, then work productivity might show a positive correlation, emphasizing the connection between rest and efficiency.
• Media Consumption and Political Beliefs : If media consumption increases, then alignment with specific political beliefs might exhibit a positive correlation, suggesting media’s influence on ideology.
• Workplace Satisfaction and Employee Retention : If workplace satisfaction increases, then employee retention rates might show a positive correlation, indicating the link between job satisfaction and tenure.
• Digital Device Use and Eye Discomfort : If screen time increases, then reported eye discomfort might show a positive correlation, indicating potential impacts of screen exposure.
• Age and Adaptability to Technology : If age increases, then adaptability to new technologies might exhibit a negative correlation, indicating generational differences in tech adoption.
• Physical Activity and Mental Health : If individuals engage in regular physical activity, then reported mental health scores might exhibit a positive correlation, showcasing exercise’s impact.
• Video Gaming and Attention Span : If time spent on video games increases, then attention span might display a negative correlation, indicating potential effects on focus.
• Social Media Use and Empathy Levels : If social media use increases, then reported empathy levels might show a negative correlation, suggesting possible effects on emotional understanding.
• Reading Habits and Creativity : If individuals read diverse genres, then their creative thinking might exhibit a positive correlation, emphasizing reading’s cognitive benefits.
• Weather Conditions and Outdoor Exercise : If weather is pleasant, then outdoor exercise might show a positive correlation, suggesting weather’s influence on physical activity.
• Parental Involvement and Bullying Prevention : If parents are actively involved, then instances of bullying might exhibit a negative correlation, emphasizing parental impact on behavior.
• Digital Device Use and Sleep Disruption : If screen time before bedtime increases, then sleep disruption might show a positive correlation, indicating technology’s influence on sleep.
• Friendship Quality and Psychological Well-being : If friendship quality increases, then reported psychological well-being might show a positive correlation, highlighting social support’s impact.
• Income and Environmental Consciousness : If income levels increase, then environmental consciousness might also rise, indicating potential links between affluence and sustainability awareness.

Correlational Hypothesis Interpretation Statement Examples

Explore the art of interpreting correlation hypotheses with these illustrative examples. Understand the implications of positive, negative, and zero correlations, and learn how to deduce meaningful insights from data relationships.

• Relationship Between Exercise and Mood : A positive correlation between exercise frequency and mood scores suggests that increased physical activity might contribute to enhanced emotional well-being.
• Association Between Screen Time and Sleep Quality : A negative correlation between screen time before bedtime and sleep quality indicates that higher screen exposure could lead to poorer sleep outcomes.
• Connection Between Study Hours and Exam Performance : A positive correlation between study hours and exam scores implies that increased study time might correspond to better academic results.
• Link Between Stress Levels and Meditation Practice : A negative correlation between stress levels and meditation frequency suggests that engaging in meditation could be associated with lower perceived stress.
• Relationship Between Social Media Use and Loneliness : A positive correlation between social media engagement and feelings of loneliness implies that excessive online interaction might contribute to increased loneliness.
• Association Between Income and Happiness : A positive correlation between income and self-reported happiness indicates that higher income levels might be linked to greater subjective well-being.
• Connection Between Parental Involvement and Academic Performance : A positive correlation between parental involvement and students’ grades suggests that active parental engagement might contribute to better academic outcomes.
• Link Between Time Management and Stress Levels : A negative correlation between effective time management and reported stress levels implies that better time management skills could lead to lower stress.
• Relationship Between Outdoor Activities and Vitamin D Levels : A positive correlation between time spent outdoors and vitamin D levels suggests that increased outdoor engagement might be associated with higher vitamin D concentrations.
• Association Between Water Consumption and Skin Hydration : A positive correlation between water intake and skin hydration indicates that higher fluid consumption might lead to improved skin moisture levels.

Alternative Correlational Hypothesis Statement Examples

Explore alternative scenarios and potential correlations in these examples. Learn to articulate different hypotheses that could explain data relationships beyond the conventional assumptions.

• Alternative to Exercise and Mood : An alternative hypothesis could suggest a non-linear relationship between exercise and mood, indicating that moderate exercise might have the most positive impact on emotional well-being.
• Alternative to Screen Time and Sleep Quality : An alternative hypothesis might propose that screen time has a curvilinear relationship with sleep quality, suggesting that moderate screen exposure leads to optimal sleep outcomes.
• Alternative to Study Hours and Exam Performance : An alternative hypothesis could propose that there’s an interaction effect between study hours and study method, influencing the relationship between study time and exam scores.
• Alternative to Stress Levels and Meditation Practice : An alternative hypothesis might consider that the relationship between stress levels and meditation practice is moderated by personality traits, resulting in varying effects.
• Alternative to Social Media Use and Loneliness : An alternative hypothesis could posit that the relationship between social media use and loneliness depends on the quality of online interactions and content consumption.
• Alternative to Income and Happiness : An alternative hypothesis might propose that the relationship between income and happiness differs based on cultural factors, leading to varying happiness levels at different income ranges.
• Alternative to Parental Involvement and Academic Performance : An alternative hypothesis could suggest that the relationship between parental involvement and academic performance varies based on students’ learning styles and preferences.
• Alternative to Time Management and Stress Levels : An alternative hypothesis might explore the possibility of a curvilinear relationship between time management and stress levels, indicating that extreme time management efforts might elevate stress.
• Alternative to Outdoor Activities and Vitamin D Levels : An alternative hypothesis could consider that the relationship between outdoor activities and vitamin D levels is moderated by sunscreen usage, influencing vitamin synthesis.
• Alternative to Water Consumption and Skin Hydration : An alternative hypothesis might propose that the relationship between water consumption and skin hydration is mediated by dietary factors, influencing fluid retention and skin health.

Correlational Hypothesis Pearson Interpretation Statement Examples

Discover how the Pearson correlation coefficient enhances your understanding of data relationships with these examples. Learn to interpret correlation strength and direction using this valuable statistical measure.

• Strong Positive Correlation : A Pearson correlation coefficient of +0.85 between study time and exam scores indicates a strong positive relationship, suggesting that increased study time is strongly associated with higher grades.
• Moderate Negative Correlation : A Pearson correlation coefficient of -0.45 between screen time and sleep quality reflects a moderate negative correlation, implying that higher screen exposure is moderately linked to poorer sleep outcomes.
• Weak Positive Correlation : A Pearson correlation coefficient of +0.25 between social media use and loneliness suggests a weak positive correlation, indicating that increased online engagement is weakly related to higher loneliness.
• Strong Negative Correlation : A Pearson correlation coefficient of -0.75 between stress levels and meditation practice indicates a strong negative relationship, implying that engaging in meditation is strongly associated with lower stress.
• Moderate Positive Correlation : A Pearson correlation coefficient of +0.60 between income and happiness signifies a moderate positive correlation, suggesting that higher income is moderately linked to greater happiness.
• Weak Negative Correlation : A Pearson correlation coefficient of -0.30 between parental involvement and academic performance represents a weak negative correlation, indicating that higher parental involvement is weakly associated with lower academic performance.
• Strong Positive Correlation : A Pearson correlation coefficient of +0.80 between time management and stress levels reveals a strong positive relationship, suggesting that effective time management is strongly linked to lower stress.
• Weak Negative Correlation : A Pearson correlation coefficient of -0.20 between outdoor activities and vitamin D levels signifies a weak negative correlation, implying that higher outdoor engagement is weakly related to lower vitamin D levels.
• Moderate Positive Correlation : A Pearson correlation coefficient of +0.50 between water consumption and skin hydration denotes a moderate positive correlation, suggesting that increased fluid intake is moderately linked to better skin hydration.
• Strong Negative Correlation : A Pearson correlation coefficient of -0.70 between screen time and attention span indicates a strong negative relationship, implying that higher screen exposure is strongly associated with shorter attention spans.

Correlational Hypothesis Statement Examples in Psychology

Explore how correlation hypotheses apply to psychological research with these examples. Understand how psychologists investigate relationships between variables to gain insights into human behavior.

• Sleep Patterns and Cognitive Performance : There is a positive correlation between consistent sleep patterns and cognitive performance, suggesting that individuals with regular sleep schedules exhibit better cognitive functioning.
• Anxiety Levels and Social Media Use : There is a positive correlation between anxiety levels and excessive social media use, indicating that individuals who spend more time on social media might experience higher anxiety.
• Self-Esteem and Body Image Satisfaction : There is a negative correlation between self-esteem and body image satisfaction, implying that individuals with higher self-esteem tend to be more satisfied with their physical appearance.
• Parenting Styles and Child Aggression : There is a negative correlation between authoritative parenting styles and child aggression, suggesting that children raised by authoritative parents might exhibit lower levels of aggression.
• Emotional Intelligence and Conflict Resolution : There is a positive correlation between emotional intelligence and effective conflict resolution, indicating that individuals with higher emotional intelligence tend to resolve conflicts more successfully.
• Personality Traits and Career Satisfaction : There is a positive correlation between certain personality traits (e.g., extraversion, openness) and career satisfaction, suggesting that individuals with specific traits experience higher job contentment.
• Stress Levels and Coping Mechanisms : There is a negative correlation between stress levels and adaptive coping mechanisms, indicating that individuals with lower stress levels are more likely to employ effective coping strategies.
• Attachment Styles and Romantic Relationship Quality : There is a positive correlation between secure attachment styles and higher romantic relationship quality, suggesting that individuals with secure attachments tend to have healthier relationships.
• Social Support and Mental Health : There is a negative correlation between perceived social support and mental health issues, indicating that individuals with strong social support networks tend to experience fewer mental health challenges.
• Motivation and Academic Achievement : There is a positive correlation between intrinsic motivation and academic achievement, implying that students who are internally motivated tend to perform better academically.

Does Correlational Research Have Hypothesis?

Correlational research involves examining the relationship between two or more variables to determine whether they are related and how they change together. While correlational studies do not establish causation, they still utilize hypotheses to formulate expectations about the relationships between variables. These good hypotheses predict the presence, direction, and strength of correlations. However, in correlational research, the focus is on measuring and analyzing the degree of association rather than establishing cause-and-effect relationships.

How Do You Write a Null-Hypothesis for a Correlational Study?

The null hypothesis in a correlational study states that there is no significant correlation between the variables being studied. It assumes that any observed correlation is due to chance and lacks meaningful association. When writing a null hypothesis for a correlational study, follow these steps:

• Identify the Variables: Clearly define the variables you are studying and their relationship (e.g., “There is no significant correlation between X and Y”).
• Specify the Population: Indicate the population from which the data is drawn (e.g., “In the population of [target population]…”).
• Include the Direction of Correlation: If relevant, specify the direction of correlation (positive, negative, or zero) that you are testing (e.g., “…there is no significant positive/negative correlation…”).
• State the Hypothesis: Write the null hypothesis as a clear statement that there is no significant correlation between the variables (e.g., “…there is no significant correlation between X and Y”).

What Is Correlation Hypothesis Formula?

The correlation hypothesis is often expressed in the form of a statement that predicts the presence and nature of a relationship between two variables. It typically follows the “If-Then” structure, indicating the expected change in one variable based on changes in another. The correlation hypothesis formula can be written as:

“If [Variable X] changes, then [Variable Y] will also change [in a specified direction] because [rationale for the expected correlation].”

For example, “If the amount of exercise increases, then mood scores will improve because physical activity has been linked to better emotional well-being.”

What Is a Correlational Hypothesis in Research Methodology?

A correlational hypothesis in research methodology is a testable hypothesis statement that predicts the presence and nature of a relationship between two or more variables. It forms the basis for conducting a correlational study, where the goal is to measure and analyze the degree of association between variables. Correlational hypotheses are essential in guiding the research process, collecting relevant data, and assessing whether the observed correlations are statistically significant.

How Do You Write a Hypothesis for Correlation? – A Step by Step Guide

Writing a hypothesis for correlation involves crafting a clear and testable statement about the expected relationship between variables. Here’s a step-by-step guide:

• Identify Variables : Clearly define the variables you are studying and their nature (e.g., “There is a relationship between X and Y…”).
• Specify Direction : Indicate the expected direction of correlation (positive, negative, or zero) based on your understanding of the variables and existing literature.
• Formulate the If-Then Statement : Write an “If-Then” statement that predicts the change in one variable based on changes in the other variable (e.g., “If [Variable X] changes, then [Variable Y] will also change [in a specified direction]…”).
• Provide Rationale : Explain why you expect the correlation to exist, referencing existing theories, research, or logical reasoning.
• Quantitative Prediction (Optional) : If applicable, provide a quantitative prediction about the strength of the correlation (e.g., “…for every one unit increase in [Variable X], [Variable Y] is predicted to increase by [numerical value].”).
• Specify Population : Indicate the population to which your hypothesis applies (e.g., “In a sample of [target population]…”).

Tips for Writing Correlational Hypothesis

• Base on Existing Knowledge : Ground your hypothesis in existing literature, theories, or empirical evidence to ensure it’s well-informed.
• Be Specific : Clearly define the variables and direction of correlation you’re predicting to avoid ambiguity.
• Avoid Causation Claims : Remember that correlational hypotheses do not imply causation. Focus on predicting relationships, not causes.
• Use Clear Language : Write in clear and concise language, avoiding jargon that may confuse readers.
• Consider Alternative Explanations : Acknowledge potential confounding variables or alternative explanations that could affect the observed correlation.
• Be Open to Results : Correlation results can be unexpected. Be prepared to interpret findings even if they don’t align with your initial hypothesis.
• Test Statistically : Once you collect data, use appropriate statistical tests to determine if the observed correlation is statistically significant.
• Revise as Needed : If your findings don’t support your hypothesis, revise it based on the data and insights gained.

Crafting a well-structured correlational hypothesis is crucial for guiding your research, conducting meaningful analysis, and contributing to the understanding of relationships between variables.

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ORIGINAL RESEARCH article

The relationship between attachment and depression among college students: the mediating role of perfectionism.

• 1 School of Humanities and Social Sciences, Anhui Agricultural University, Hefei, China
• 2 College of Arts, Humanities and Social Sciences, Edinburgh College of Arts, University of Edinburgh, Edinburgh, United Kingdom

Objectives: Explore the relationship between adult attachment and depression among college students, and the mechanism of perfectionism.

Study design: Questionnaire survey.

Methods: A questionnaire survey was conducted nationwide, totally 313 valid questionnaires were received. The survey collected information such as adult attachment (Adult Attachment Scale, AAS), depression (The Center for Epidemiologic Studies Depression Scale, CESD), and perfectionism (The Frost Multidimensional Perfectionism Scale, FMPS). Then used SPSS26.0 to analyze the collected data.

Results: There were significant differences in perfectionism and depression between secure attachment and insecure attachment in college students. Perfectionism plays a partial mediating role in the relationship between the close-depend composite dimension, anxiety dimension of attachment and depression.

Conclusion: The closeness-dependence dimension of attachment significantly and negatively predicted perfectionism and depression; the anxiety dimension of attachment significantly and positively predicted perfectionism and depression; and perfectionism partially mediated the effect of both the closeness-dependence dimension of attachment on depression and the anxiety dimension of attachment on depression. Attachment can directly affect college students’ depression, but also indirectly through perfectionism.

Introduction

With the popularization of psychological knowledge and attention to psychological issues from all sectors of society, more and more people see the importance of mental health. Especially to young people who are at a critical stage of their development. The transition from academic to social life at university means that university students face a variety of challenges from the outside world as well as from themselves, such as establishing new interpersonal relationships, solving problems in life alone, and learning more specialized knowledge, making them more prone to psychological problems than other people. This is especially true in the context of the epidemic, which has put university students under even more pressure, not least because of depression, a psychological disorder that has become a common sight in recent years. The study of the mechanisms that lead to depression among university students is of great relevance to address and prevent depression among university students.

Attachment characteristics will also be the subject of this thesis as a necessary factor influencing interpersonal interaction patterns, intimate relationship development and other life issues that important university students need to address. Attachment is the initial connection between children and the world, and through various stages of growth and development, the attachment characteristics of adults can differ from those of children. Individuals with a tendency toward perfectionism are chronically unhappy and therefore also depressed. This study will therefore examine the correlated and internal mechanisms of attachment characteristics, perfectionism, and depression in university students.

Literature review

Depression is an affective disorder, a psychological condition characterized by low mood, hopelessness, and helplessness ( Su et al., 2011 ). Some studies have shown that the incidence of depression among university students is much higher than that of people in other stages ( Ibrahim et al., 2013 ). College students from rural areas who come to the city for study have a higher risk of depression, which may be related to the inadaptability to the learning or living environment and excessive mental or economic pressure ( He et al., 2018 ). In recent years, some scholars have also compared the detection rate of depression among university students in Guangdong before and after the epidemic, and the data showed that the detection rate of major depression was higher in 2020 than in 2022, with little difference in the detection rate of moderate depression and a higher detection rate of mild depression in 2022 ( Li et al., 2022 ).

People who are depressed often feel sad, depressed, lack interest in activities or things they used to enjoy, fail to experience pleasure in life, have reduced self-confidence, blame themselves, often feel fatigued, and are mentally inactive ( Su et al., 2011 ). Maladjustment can lead to depressive symptoms, depressive episodes, and even life-threatening behaviors such as suicide and homicide ( Li, 2018 ). Depression can also seriously affect the normal life of studying and working of university students. At present, depression is an important global public health problem, and its prevention and control are of great significance ( Wang et al., 2020 ). Therefore, we should pay attention to the study of depression among university students and explore its mechanisms in depth to obtain more effective coping strategies.

Adult attachment refers to an adult’s recollection and reproduction of their early childhood attachment experiences and current evaluation of childhood attachment experiences ( Shi and Wei, 2007 ). Attachment theory suggests that attachment enables individuals to form strong and secure affectional ties with significant others and is one of the main sources of security and a sense of control ( Liu et al., 2022 ). In contrast to infants and children who have a single object of attachment, adults have a much wider range of attachments, including parents, relatives, friends, and lovers. Attachment is a relatively stable structure that manipulates external consciousness, guides relationships with parents, and influences strategies and behaviors in subsequent relationships ( Wang et al., 2005 ). Also, different attachment characteristics and types of attachment are reflected in the individual’s unique interpersonal and intimate relationship management. Establishing and maintaining secure and satisfying social relationships is a basic human need, but the deprivation of this need affects interpersonal relationships in adulthood and may create insecure adult attachment patterns ( Mikulincer and Shaver, 2019 ).

The current available research suggests that people with insecure attachment types are at higher risk of chronic major depression ( Li et al., 2019 ), where the types of insecure attachment are preoccupied attachment and fearful attachment. Conradi and Jonge (2009) have shown that insecure attachment has a very important impact on the generation, development, and maintenance of depressed mood. A study found that individuals with insecure attachment were 3.9 times more likely to suffer from depression than individuals with secure attachment ( Shi et al., 2013 ). Studies of university students have also found that depressive status scores are significantly and positively correlated with attachment avoidance and attachment anxiety scores ( Ma et al., 2023 ).

Perfectionism has been conceptualized as a personality variable that underlies a variety of psychological difficulties. Recently, however, theorists and researchers have begun to distinguish between two distinct types of perfectionism, one a maladaptive form that results in emotional distress, and a second form that is relatively benign, perhaps even adaptive ( Bieling et al., 2004 ). Some studies have found that the development of depression are associated with negative perfectionists’ tendency to focus excessively on mistakes, self-doubt, and expectation criticism ( Zhang et al., 2013 ). It has been suggested that insecure attachment and negative perfectionism are risk factors for the formation of an obsessive-compulsive personality ( Xu et al., 2021 ).

Rice and Mirzadeh (2000) examined the relationship between attachment, perfectionism and depression and showed that subjects with insecure attachment were more likely to be maladaptive perfectionists and to experience more significant depression than those with secure attachment. Research on perfectionism and attachment has also found a significant positive correlation between attachment anxiety dimensions and negative perfectionism in adults ( Ma et al., 2010 ). A study explored the mediating role of perfectionism between attachment and depression, and found that attachment anxiety and attachment avoidance both promote the formation of negative dimensions of perfectionism, which in turn leads to depression ( Xin-Chun et al., 2013 ). A study on the relationship between attachment styles and positive/negative perfectionism, anger, and emotional regulation among college students showed that unsafe attachment styles (avoidance and conflict) can predict negative perfectionism, safe attachment types (avoidance and conflict) can predict emotional regulation, and attachment patterns can determine many behaviors, emotions, and adult relationships, which are necessary for personality growth and mental health foundations ( Nader et al., 2017 ).

Purpose and hypothesis of the study

The purpose of this study is to explore the mechanism of the relationship between attachment characteristics, depression, and perfectionism among college students.

There are three hypotheses in this study: (1) Attachment characteristics significantly predict depression and perfectionism, (2) Perfectionism significantly predicts depression, and (3) Perfectionism mediates the relationship between attachment characteristics and depression in college students.

Materials and methods

Participants.

This study used the university student population in different regions as the subjects and used the online distribution method to collect a total of 313 valid questionnaires. There were 130 male students (41.5%) and 183 female students (58.5%); 104 only children (33.2%) and 209 non-only children (66.8%); 32 first year university students; 52 s year students, 54 third year students, 140 fourth year students and 35 postgraduate students.

Adult attachment

The revised Adult Attachment Scale (AAS) ( Wu et al., 2004 ) was used to measure attachment characters. The scale was revised and developed by Wili Wu et al. and divided into three subscales of closeness, dependence, and anxiety, each with 6 questions each, for a total of 18 questions. A 5-point scale was used, in which the closeness and dependence subscales were combined into a composite closeness-dependence dimension, which was juxtaposed with the anxiety dimension, with higher scores indicating a stronger characteristic dimension. Based on the mean scores of the two dimensions there are four further types of attachment: secure, preoccupied, rejective and fearful, the latter three being insecure attachments. In the present study, the Cronbach’s alpha coefficients for the closeness-dependence dimension and the anxiety dimension of the scale were 0.774 and 0.866, respectively.

The Center for Epidemiologic Studies Depression Scale (CES-D) ( Wang et al., 1999 ) was used to measure depression, it contains 20 items on a 4-point scale, scored on a scale of 0, 1, 2 and 3, with the higher the score the more depressed they are. Unlike the SDS, the CES-D is not used to clinically judge depressed patients and is therefore more appropriate for the group of university students in this study, focusing on measuring depressed state of mind. In this study, the Cronbach’s alpha coefficient for the scale was 0.902.

Perfectionism

The Frost Multidimensional Perfectionism Scale (FMPS) ( Zi and Zhou, 2006 ) was used to measure perfectionism, developed and revised by Zi Fei et al., is divided into 27 entries and five dimensions. The dimensions are organization, concern over mistakes, parental expectations, personal standards, and doubts about action. The organization dimension is positive perfectionism, and the remaining four dimensions represent negative perfectionism. The scale is rated on a 5-point scale, with higher scores indicating a higher tendency toward perfectionism. In this study the Cronbach’s alpha coefficient for the total scale was 0.916 and the Cronbach’s alpha coefficients for each subscale were 0.834, 0.901, 0.842, 0.824 and 0.730, respectively.

Data analysis

The raw data from the returned questionnaires were processed using SPSS 26.0 software and firstly, the Harman single factor test was used to test for common method bias. The results of the test showed that the variance explained by the first common factor was 22.206%, which was below the threshold of 40%, and therefore there was no serious common method bias in this study. The mediating role of perfectionism in the relationship between attachment characteristics and depression was also tested using Model 4 in the SPSS plug-in Process v3.5.

Analysis of the characteristics of attachment, depression and perfectionism among university students

The AAS scores were transformed by combining the closeness-dependence subscale and the dependence subscale into a composite closeness-dependence dimension and calculating the mean closeness-dependence score; the anxiety subscale was used as a separate anxiety dimension and the mean anxiety score was calculated. The mean scores of the two dimensions were compared and categorized. Those with mean scores of closeness-dependence greater than 3 and mean scores of anxiety less than 3 were classified as secure attachment, while the rest were classified as insecure attachment. Insecure attachment was further classified into three different types of attachment: those with a mean score of closeness-dependence greater than 3 and a mean score of anxiety greater than 3 were preoccupied attachment, those with a mean score of closeness-dependence less than 3 and a mean score of anxiety less than 3 were rejective attachment, and those with a mean score of closeness-dependence less than 3 and a mean score of anxiety greater than 3 were fearful attachment. In this study, only 154 (49.2%) were secure attachment, while 54 (17.3%) were preoccupied attachment, 40 (12.8%) were rejective attachment and 65 (20.8%) were fearful attachment.

Of all subjects, 141 (45.05%) experienced some degree of depression.

In the current study, college students’ attachment characteristics, depression and perfectionism did not differ significantly ( p  > 0.05) in the demographic variables of gender, whether they were an only child, and grade level.

The AAS scale scores were transformed to classify the subjects into secure attachment and insecure attachment, 154 in total for the former and 159 in total for the latter, and independent samples t -tests were conducted. The results yielded significant differences ( p  < 0.001) between secure attachment subjects and insecure attachment subjects on both depression and perfectionism. As shown in Table 1 , subjects with insecure attachment scored significantly higher on depression and perfectionism than those with secure attachment.

Table 1 . Analysis of differences in depression and perfectionism among college students with different attachment types ( N  = 313).

Correlation analysis of attachment characteristics, depression, and perfectionism among university students

Pearson correlation analysis was conducted using SPSS 26.0 on the three variables of attachment characteristics, depression and perfectionism, and the results indicated that all three variables were correlated, which was consistent with the premise of the mediating effect test. The results of the specific correlation analysis are shown in Table 2 .

Table 2 . Correlation analysis of attachment characteristics, depression, and perfectionism among university students ( N  = 313).

The closeness-dependence dimension of attachment was negatively associated with depression and perfectionism, while the anxiety dimension of attachment was positively associated with depression and perfectionism. This means that attachment closeness-dependence scores negatively predict depression and perfectionism, while attachment anxiety dimensions positively predict depression and perfectionism scores. Perfectionism also positively predicted depression.

A test of the mediating role of perfectionism between attachment characteristics and depression among university students

Model 4 in the SPSS plug-in Process prepared by Hayes ( Hayes, 2018 ) was used to test for the mediating effect of perfectionism and the results are shown in Table 3 . Before perfectionism was placed as a mediating variable, the closeness-dependence dimension of attachment was a significant negative predictor of depression ( β  = −0.42, t  = −8.25, p  < 0.001), the anxiety dimension of attachment was a significant positive predictor of depression ( β  = 0.37, t  = 6.99, p  < 0.001). The closeness- dependence dimension of attachment was a significant negative predictor of perfectionism ( β  = −0.25, t  = −4.88, p  < 0.001) and the anxiety dimension of attachment was a significant positive predictor of perfectionism ( β  = 0.43, t  = 8.35, p  < 0.001). When perfectionism was added as a mediating variable, the closeness-dependence dimension of attachment was still a significant negative predictor of depression ( β  = −0.36, t  = −6.98, p  < 0.001) The perfectionism dimension of attachment was also a significant positive predictor of depression ( β  = 0.27, t  = 5.32, p  < 0.001); after adding perfectionism as a mediating variable, the anxiety dimension of attachment was still a significant positive predictor of depression ( β  = 0.26, t  = 4.63, p  < 0.001), and perfectionism was also a significant positive predictor of depression ( β  = 0.25, t  = 4.38, p  < 0.001). The results of the analysis of the mediating effect can be represented in Figure 1 .

Table 3 . Mediating role of perfectionism between attachment and depression ( N  = 313).

Figure 1 . Graph showing the results of the test for the mediating role of perfectionism.

The mediating effects of the attachment closeness-dependence dimension and the anxiety dimension with their respective effect sizes are shown in Table 4 .

Table 4 . Attachment mediated effects and effect sizes.

The Bootstrap 95% confidence interval for the direct effect of the closeness-dependence dimension of attachment on depression was [−0.51, −0.29], excluding 0, indicating that its direct effect was significant; the Bootstrap 95% confidence interval for the mediating effect of perfectionism between the closeness-dependence dimension of attachment and depression was [−0.13, −0.04], excluding 0, indicating that the mediating effect of perfectionism was significant. The Bootstrap 95% confidence interval for the total effect of attachment closeness -dependence dimension on depression was [−0.59, −0.36], excluding 0, indicating a significant total effect and an effect value of −0.48. Thus, it can be suggested that perfectionism partially mediates the relationship between attachment closeness-dependence dimension and depression, with a mediating effect of 16.67%.

The Bootstrap 95% confidence interval for the direct effect of the anxiety dimension of attachment on depression was [0.09, 0.23], which did not contain 0, indicating a significant direct effect; the Bootstrap 95% confidence interval for the mediating effect of perfectionism between the anxiety dimension of attachment and depression was [0.03, 0.10], which did not contain 0, indicating a significant mediating effect of perfectionism between the anxiety dimension of attachment and depression. The Bootstrap 95% confidence interval for the total effect of attachment anxiety dimension on depression was [0.16, 0.29], excluding 0, indicating a significant total effect with an effect value of 0.23. It can therefore be shown that perfectionism partially mediates between attachment anxiety dimension and depression, with a mediating effect of 30.43%.

Status of attachment characteristics, perfectionism, and depression among university students

In this study, a total of 45.05% of the university students who participated in the questionnaire experienced some degree of depression, and there were no significant differences in the demographic variables of depression scores in gender, whether they were an only child, or grade level. This also suggests, to some extent, that depression is somewhat prevalent in the university population. In addition, subjects with insecure attachment types were more likely to experience depressive mood than those with secure attachment types. This is in line with the findings of some scholars on adolescent depression and parent–child attachment: secure parent–child attachment reduces the risk of adolescent depression ( Lai et al., 2022 ). The need for excessive attention and commitment is not always met, leading to severe feelings of loss, further doubts, and anxiety about the safety of the relationship ( Shaver et al., 2005 ). College students with insecure attachment types experience more abuse, neglect, separation, and loss in their early years of interaction with their primary caregivers, and such early adverse experiences are often associated with depression ( Whiffen et al., 1999 ). It also points to the important role that attachment plays in the development of adolescents and even university students.

The mechanism by which adult attachment affects depression lies in the internal negative self-model, i.e., the negative evaluation of the self is an important factor in forming depression ( Yang, 2005 ). Individuals with high scores on the anxiety dimension of attachment often fear that the attachment partner will leave them, and one of the reasons for this is a lack of self-confidence and doubt. Because of their negative perceptions of themselves, these groups do not see themselves as worthy of love and therefore feel insecure that they may be abandoned at any time, even if they have established an intimate relationship. Insecure attachment individuals are more likely to have problems in making emotional connections with external objects than secure attachment individuals, e.g., individuals with preoccupied attachment (high closeness-dependence, high anxiety) have a stronger desire to connect with others and a high level of insecurity about existing connections, so they often seek approval from others, are completely focused on others, are dependent on others, easily lose themselves and are in constant fear of relationship breakdown ( Zhang, 2021 ).

In this study, perfectionism was also scored significantly higher in insecure attachment individuals than in secure attachment individuals. Some scholars believe that doing things perfectly and not making mistakes is a means of survival for children who grow up in harsh, punishing, harsh or even abusive families to avoid unnecessary harm or enhance their control over uncertain environments ( Flett et al., 2012 ). Maladaptive perfectionism has overly idealistic expectations and ideas about real life, thinking that they can easily achieve success or achieve goals, often ignoring objective conditions, and often feeling lost and inadequate in the process ( Rice and Ashby, 2007 ). One of the characteristics of perfectionism is that they always set much higher goals for themselves and too difficult to achieve them, so perfectionistic individuals are chronically unfulfilled and dissatisfied with themselves. The insecure attachment individuals’ negative evaluation of self also contributes to the pursuit of high goals. At the same time, prolonged failure to achieve goals can lead to new negative evaluations of the self, which are likely to be accompanied by devaluation of the self, forming a pattern of internal evaluations that can lead to depression. Researcher found that perfectionists’ rigid core thinking produces low levels of unconditional self-acceptance, accompanied by low self-liking and a low sense of self-competence, which in turn leads to depression ( Scott, 2007 ). The Beck depression model suggests that negative notions of self and others increase an individual’s susceptibility to depression ( Kernis et al., 1991 ). It has been shown that maladaptive perfectionist individuals act with excessive consideration for the correctness of their behavior, hesitate to act and fear failure, and are more likely to adopt negative coping styles in stressful situations, leading to anxiety, depression, and other negative emotions ( Zhang et al., 2014 ).

The mediating role of perfectionism between attachment and depression

The results of the analysis of the mediating role of perfectionism found that the direct effects of the closeness-dependence dimension and the anxiety dimension on depression were significantly weakened after perfectionism was introduced between attachment characteristics and depression as the mediated variable, indicating that perfectionism partially mediates the relationship between both the closeness- dependence composite dimension of adult attachment and the anxiety dimension and depression, meaning that university students’ attachment can directly affect their depression levels, as well as indirectly affect depression levels by influencing perfectionist tendencies.

The closeness-dependence dimension of attachment reflects the degree to which individuals are comfortable in intimate relationships and assess whether they have someone to rely on when needed ( Zhang et al., 2014 ). Individuals with higher levels of comfort in intimate relationships are more likely to feel satisfied and therefore less likely to have negative evaluations of themselves. As shown in the study, scores on the closeness-dependence dimension of attachment were significantly and negatively correlated with scores on perfectionism and depression. It has been found that individuals with higher levels of attachment anxiety have lower levels of emotion expression ( Yao and Zhao, 2021 ), and that the prolonged lack of emotional expression can easily lead to depression. Insecure attachment individuals have negative attitudes toward interpersonal interactions and have less social support than other people, making it more difficult for them to get out of difficult situations when they have negative life events or encounter difficulties and setbacks.

The results of this study show that the closeness-dependence dimension of attachment is negatively related to perfectionism, while the anxiety dimension of attachment is positively related to perfectionism, meaning that individuals with low closeness-dependence and high anxiety in intimate relationships, i.e., Those who do not adapt well to intimate relationships or who have not experienced success in previous intimate relationships, are prone to perfectionism. Perfectionists are also overly concerned with their own behavior and performance. This group believes that they must be complimented and praised by others, and they show a desire for attention and a fear of being rejected by others ( Stoeber et al., 2017 ). This is why these people tend to experience disappointment in their daily lives and in their interpersonal interactions, resulting in a decline in self-confidence, a decrease in interest and depression.

Implications of the research

This study investigates the mechanisms by which attachment affects depression in university students and has implications for the prevention and intervention of depression in university students. Firstly, it can draw attention to the importance of building secure attachments and creating a good family environment from early childhood to avoid the risk of depression early. At the same time, for attachment characteristics that are difficult to change early in the formative years, it is possible to intervene in depression by changing the mediating variables in this study, guiding individuals to set reasonable goals, and taking more encouraging measures to improve their self-esteem.

Limitations of the research

This study also has certain limitations, firstly, from the research method, the method of questionnaire collection adopted in this study is online collection method, thus there are limitations in controlling the confounding variables. Moreover, the sample size of this study is still not sufficiently random in terms of grade and major, so there may be some errors. Finally, as perfectionism only partially mediates the results from this study and has a low effect size, there are many potential influences in related areas that need to be further explored.

There were significant differences in perfectionism and depression between secure attachment and insecure attachment in university students, with insecure attachment individuals scoring higher in perfectionism and depression than secure attachment individuals.

The closeness-dependence dimension of attachment significantly and negatively predicted perfectionism and depression; the anxiety dimension of attachment significantly and positively predicted perfectionism and depression; and perfectionism partially mediated the effect of both the closeness-dependence dimension of attachment on depression and the anxiety dimension of attachment on depression.

Data availability statement

The raw data supporting the conclusions of this article will be made available by the authors, without undue reservation.

Ethics statement

The studies involving humans were approved by the Ethics Committee of Anhui Agriculture University. The studies were conducted in accordance with the local legislation and institutional requirements. The participants provided their written informed consent to participate in this study.

Author contributions

FF: Conceptualization, Supervision, Writing – review & editing, Funding acquisition, Formal analysis. JW: Writing – original draft, Data curation, Methodology.

The author(s) declare that no financial support was received for the research, authorship, and/or publication of this article.

Conflict of interest

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Publisher’s note

All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.

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Keywords: collge students, attachment, depression, perfectionism, medating effects

Citation: Fang F and Wang J (2024) The relationship between attachment and depression among college students: the mediating role of perfectionism. Front. Psychol . 15:1352094. doi: 10.3389/fpsyg.2024.1352094

Received: 16 December 2023; Accepted: 02 April 2024; Published: 15 April 2024.

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*Correspondence: Jingwen Wang, [email protected]

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