Professor of Sociology

Effect Sizes

I regularly forget standard rules of interpretation for effect sizes when running analyses. I figured I’d put these here so I can quickly refer to them when needed. For more details on most effect sizes, Wikipedia is always useful.

Cohen’s d

Cohen’s d is typically used when doing t-tests. The basic calculation is the difference between two means divided by a standard deviation (usually the pooled standard deviation). Here’s the interpretation.

Effect Sized
Very small0.01
Small0.20
Medium0.50
Large0.80
Very Large1.20
Huge2.00

The standard citations are to Jacob Cohen’s work:
Cohen, Jacob. 1988. Statistical Power Analysis for the Behavioral Sciences. Mahwah, N.J.: Lawrence Erlbaum.
Cohen, Jacob. 1992. “A Power Primer.” Psychological Bulletin 112(1):155–59.

However, the new citation is to Sawilowsky:
Sawilowsky, Shlomo S. 2009. “New Effect Size Rules of Thumb.” Journal of Modern Applied Statistical Methods 8(2):597–99.

Pearson’s r

Pearson’s r is a standard measure of correlation. It can also be calculated for other statistical tests.

Effect Sizer
Small0.10
Medium0.30
Large0.50

These interpretations also come from Cohen’s work:
Cohen, Jacob. 1988. Statistical Power Analysis for the Behavioral Sciences. Mahwah, N.J.: Lawrence Erlbaum.

R-Square (Coefficient of Determination)

Technically, R2 is not an effect size. It’s a measure of the amount of variation in the dependent variable that is accounted for by the independent variables. However, because it captures the magnitude or size of a relationship rather than the existence of a relationship, it can be interpreted as similar to an effect size. Cohen provided some rough measures for interpreting the magnitude of R2, though it is important to note that this will vary by what is under investigation.

Effect SizeR2
Small0.02
Medium0.13
Large0.26

These interpretations come from Cohen’s work:
Cohen, Jacob. 1988. Statistical Power Analysis for the Behavioral Sciences. Mahwah, N.J.: Lawrence Erlbaum.

Cohen’s F-Square

Cohen’s F2 is an effect size measure that can be used with OLS regression. It is calculated using R2, or the coefficient of determination.

Effect SizeF2
Small0.02
Medium0.15
Large0.35

These interpretations come from Cohen’s work:
Cohen, Jacob. 1988. Statistical Power Analysis for the Behavioral Sciences. Mahwah, N.J.: Lawrence Erlbaum.