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. There is also a table of effect size magnitudes at the back of Kotrlik JW and Williams HA (2003) [attachment:powmags.pdf here.] 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 |
|||
$$\kappa^text{2}$$ |
Mediation analysis |
0.01 |
0.09 |
0.25 |
|||
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 |
|||
[:FAQ/avsp: Average Spearman rho] |
Friedman test |
0.1 |
0.3 |
0.5 |
|||
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 $$\mbox{Partial } \eta^text{2} = \frac{\mbox{ SS(effect)} }{\mbox{SS(effect) + SS(error for that effect)} $$
$$kappa^text{2} = \frac{\mbox{ab}}{\mbox{Maximum value of ab}}$$ where a and b are the regression coefficients representing the independent variable to mediator effect and the mediator to outcome respectively to estimate the indirect effect of IV on outcome. See Preacher and Kelley (2011) for further details including MBESS procedure software for fitting this in R. For further details on mediation analysis see also [:FAQ/SobelTest: here.]
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.
Kotrlik, JW and Williams, HA (2003) The incorporation of effect size in information technology, learning, and performance research. Information Techology, Learning, and Performance Journal 21(1) 1-7.
Preacher, KJ and Kelley, K (2011) Effect size measures for mediation models: quantitative strategies for communicating indirect effects. Psychological Methods 16(2) 93-115.
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.