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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