Effect Sizes (ES) in statistics

In statistics, an effect size (ES) indicates the strength of the relationship between two variables.

In psychological experiments, researchers are interested in the strength of the effect of the Independent Variable on the Dependent Variable.

In psychotherapy studies, researchers may be interested in the effects of treatment on a measure of the dependent variable. A research questions may be framed: How effective is a set of 6 CBT sessions on the reduction of depression?

Psychologists have often described effect sizes as small, medium, or large.

Cohen's d

Cohen's d is a measure of effect size between two groups. The mean of one group is subtracted from a second group and divided by the pooled standard deviation of the two groups.

ES = (M1 - M2) / SD

Effect Size Label

0.2 Small

0.5 Medium

0.8 Large

Pearson Correlation Coefficient (r)

0.1 to 0.3 Small

0.3 to 0.5 Medium

0.5 to 1.0 Large

Converting Cohen's d to the correlation coefficient

r = d/ √ d²+ 4

Note. Negative values also indicate strength of a relationship.

Cite this post

Sutton, G. (2022, July 20). Effect sizes (ES) in statistics. Assessment, Statistics, and Research. Retrieved from https://statistics.suttong.com/2022/07/effect-sizes-es-in-statistics.html

References

Cohen, J. (1992). A power primer. Psychological Bulletin, 112(1), 155–159. https://doi.org/10.1037/0033-2909.112.1.155

Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Hillsdale, NJ: Lawrence Erlbaum Associates.

Sutton, G. W. (2020). Applied statistics: Concepts for counselors, second edition. Springfield, MO: Sunflower.

Link to an Index of Statistical Concepts in Psychology, Counseling, and Education

Reference for using scales in research:

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