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Correlation coefficient the Pearson r in statistics

 

The term correlation can refer to a statistic and a type of research. 

Understanding correlations is an important building block of many complex ideas in statistics and research methods. My focus in this post is on the common correlation statistic, also called the Pearson r.

The Pearson r is a statistical value that tells the strength and direction of the relationship between two normally distributed variables measured on an interval or ratio scale.

Researchers examine the two sets of values and calculate a summary statistic called a correlation coefficient. The longer name for a common correlation statistic is the Pearson Product Moment Correlation Coefficient but sometimes it is referred to as the Pearson r. The symbol for correlation is a lower case and italicized r.  In behavioural research, we normally round values to two decimal points. A moderately strong positive correlation example is r = .78.

      Sometimes, the relationship between the two variables is negative. For example, the relationship between depression and self-esteem is often negative. As depression increases, self-esteem decreases. An example of a negative correlation would be written as r = -.45. The minus sign tells us that as one variable increases, the other variable decreases. The relationship is commonly described in journal articles as an inverse relationship.

An example from published research is the relationship between perceived stress and humility couples experience as they transition to parenthood. As a part of their work, Jennifer Ripley and her research team (2016) found that the correlation between a measure of perceived stress and a measure of humility ranged from -.33 to -.45, which indicates that high stress is associated with low humility.

The relationship between two variables not only varies in a positive or negative direction but it also varies in terms of strength. Large r values indicate a stronger relationship. When r = .75 or -.75, the relationship is of equal strength but in different directions. Relationships with a low number such as r = .15 or r = -.11 indicate weak relationships.

      When r values are at or near zero, we say there is no relationship between the variables. For example, we may find no relationship between scores on questionnaires about humility and depression.

Correlation is not causation

The fact that two variables have a strong relationship does not mean one variable causes the other.

Read more about correlations in Chapter 13 of 

Applied Statistics Concepts for Counselors on AMAZON or GOOGLE








Graphing the Correlations

This is an example of fictitious data illustrating a positive correlation between anxiety and depression. Anxiety and depression are different states but both may be present.



The following is an example of  fictitious data illustrating a negative correlation between self-esteem and depression. A high self-esteem score of 8 reflects low depression. Low self-esteem near 2 reflects a high level of depression at 7.


Applications

Correlations are commonly calculated in many research projects where the relationship between variables is important.

Correlations are also important to understanding the reliability of test scores and test validity.

Key concepts

Correlation coefficient

Pearson Product Moment Correlation

Inverse relationship

Positive correlation

Negative correlation

Link to A-Z list of Statistical Terms



References

Ripley, J. S., Garthe, R. C., Perkins, A., Worthington, E. J., Davis, D. E., Hook, J. N., & ... Eaves, D. (2016). Perceived partner humility predicts subjective stress during transition to parenthood. Couple and Family Psychology: Research and Practice, 5(3), 157-167. doi:10.1037/cfp0000063

Sutton, G. W. (2020). Applied statistics: Concepts for counselors, second edition. Springfield, MO: Sunflower. AMAZON  Paperback ISBN-10: 168821772X, ISBN-13: 978-168217720    website: counselorstatistics


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