Effect size

An effect size is a standardized way to report the strength of an apparent relationship. For example, assume that you are evaluating a new treatment for OCD. The effect size of the treatment answers the following question: "how much does a typical patient benefit from the treatment?".

It is important to note the distinction between effect size and statistical significance. In particular, statistical significance indicates the likelihood that an observed phenomenon is real, regardless of the strength of the phenomenon. Therefore, it is possible to have a small effect size that is statistically significant. It is considered best practice is to always report an effect size with each statistically significant result.

How to calculate effect size

The way effect size is measured depends on the statistical test being conducted. Most of the online tests on this site report an effect size.

Instructions
Difference between two means If you have the means and standard deviations of the two data sets, use the Cohen's d calculator at the bottom of this page.
Correlation The correlation coefficient is reported on the correlation page.
Regression r-squared is reported on the regression page.
Independent t-test
  • Enter your data here: Compare two sets
  • Effect sizes calculated: r and Cohen's d
Paired t-test
  • Enter your data here: Compare two sets
  • Effect sizes calculated: r and Cohen's d
Wilcoxon rank-sum test
Mann-Whitney test
Wilcoxon signed-rank test
One-way ANOVA
  • Enter your data here: Compare more than two means
  • Effect sizes calculated: f squared, generalized eta squared (η2), generalized omega squared (ω2)*
Repeated measures ANOVA
  • Enter your data here: Compare more than two means
  • Effect sizes calculated: f squared, generalized eta squared (η2), generalized omega squared (ω2)*

* Effect sizes are computed using the methods outlined in the paper "Olejnik, S. & Algina, J. 2003. Generalized Eta and Omega Squared Statistics: Measures of Effect Size for Some Common Research Designs Psychological Methods. 8:(4)434-447".

Cohen's d calculator

If you are comparing two populations, Cohen's d can be used to compute the effect size of the difference between the two population means. By convention, the Cohen's d is categorized as follows:

Cohen's dInterpretation
0.2A small effect
0.5A medium effect
0.8 +A large effect

The following calculator computes Cohen's d using the mean and standard deviation of the two samples:

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