Rules of thumb on magnitudes of effect sizes
Taken from Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Hillsdale, NJ: Lawrence Erlbaum Associates. An overview of commonly used effect sizes in psychology is given by Vacha-Haase and Thompson (2004).
Effect Size |
Use |
Small |
Medium |
Large |
|||
Correlation |
|
0.1 |
0.3 |
0.5 |
|||
$$\eta^text{2}$$ |
one-way anova (regression) |
0.01 |
0.06 |
0.14 |
|||
Cohen's f |
one-way anova (regression) |
0.10 |
0.25 |
0.40 |
|||
$$\eta^text{2}$$ |
Multiple regression |
0.02 |
0.13 |
0.26 |
|||
Cohen's f |
Multiple Regression |
0.14 |
0.39 |
0.59 |
|||
Cohen's d |
t-tests |
0.2 |
0.5 |
0.8 |
|||
Cohen's $$\omega$$ |
chi-square |
0.1 |
0.3 |
0.5 |
|||
Odds Ratios |
2 by 2 tables |
1.5 |
3.5 |
9.0 |
|||
Also:Haddock et al (1998) state that $$\sqrt{3/\pi}$$ multiplied by the log of the odds ratio is a standardised difference equivalent to Cohen's d.
[http://www.sportsci.org/resource/stats/effectmag.html Further details on the derivation of the Odds Ratio effect sizes]
- [:FAQ/baserat: Cohen's d adjusted for base rates]
- [:FAQ/dunlap: A quick guide to choice of sample sizes for Cohen's effect sizes]
Definitions
$$\mbox{Cohen's d} = \frac{\mbox{difference between a pair of group means}}{\mbox{averaged group standard deviation}}$$
$$\eta^text{2} = \frac{\mbox{ SS(effect)} }{\mbox{Sum of SS(effects having the same error term as effect of interest) + SS(the error associated with these effects)} $$
$$\mbox{Cohen's f} = \sqrt{\frac{\etatext{2} }{1 - \etatext{2}} }$$
There is also a $$\mbox{Partial } \eta^text{2} = \frac{\mbox{ SS(effect)} }{\mbox{SS(effect) + SS(error for that effect)} $$
Suggestion : Use the square of a pearson correlation for effect sizes for partial $$\etatext{2}$$ giving 0.01 (small), 0.09 (medium) and 0.25 (large) giving intuitively larger values than $$\etatext{2}$$.
$$\omega = \sqrt{ \sum_text{1}text{no. groups} \frac{\mbox{(observed proportion - expected proportion)}text{2}}{ \mbox{ expected proportion}}}$$
* [wiki:FAQ/oddsr Odds Ratio definition]
References
Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Hillsdale, NJ: Erlbaum
Haddock, CK, Rinkdskopf, D. & Shadish, C. (1998) Using odds ratios as effect sizes for meta-analysis of dichotomous data: A primer on methods and issues. Psychological Methods 3 339-353.
Tabachnick, BG and Fidell, LS (2007) Using multivariate statistics. Fifth Edition. Pearson Education:London.
Vacha-Haase, T and Thompson, B (2004) How to estimate and interpret various effect ssizes. Journal of Counseling Psychology 51(4) 473-481.