Suppose we have an EEG study with 3 groups. The recorded numbers of participants for each group were 7, 3, and 7, respectively. The reviewer correctly claimed that this is not enough statistically significant to study the differences among the groups. I quote: "aiming for a medium effect size of Cohen’s f= 0.25 (#=0.05) and a power of 0.85 for condition x group interaction effects, one would need a total sample size of 48 subjects, thus at least 16 subjects per group." Which equation led to that conclusion? Suppose we reduce the number of groups to two. How would that change the minimum total number of subjects?
Thank you very much for your reply.
Hey Lukáš,
here is a useful link with information on power:
http://www.statsoft.com/textbook/power-analysis
..and a link to a free power calculator
http://www.gpower.hhu.de/
Dear Lukás,
in general, I pretty much agree with Lo J Bour's comment. However, you might also take into consideration looking at confidence intervals rather than following the "standard" concept of power analysis. See, e.g.,
Hoenig, J.M., & Heisey, D.M. (2001). The Abuse of Power. The American Statistician, 55:1, 19-24.
Also, it might be useful to consider á priori, what effect size would actually be of practical relevance in the context of your research problem, and then calculate sample sizes necessary to test on significance of group mean differences representing that specific effect size. In this context, the following article might also be of interest:
Fritz, C.O., Morris, P., & Richler, J. (2012). Effect Size Estimates: Current Use, Calculations, and Interpretation. Journal of Experimental Psychology: General, Vol. 141, No. 1, 2-18.
Regards, Klaus Blischke
Dear Lukas,
just an afterthought: especially when dealing with very small sample sizes (as reported in your above question), sample sizes should not differ, since that then could easily "screw up" your ANOVA results.
Klaus
HI,
Could some one please also share references of papers where power is calculated for the EEG studies?
Thanks in advance
Sharad
Dear Sharad Agarwal,
Power calculations are orthogonal to the measurement technique. The links and papers mentioned above can be applied to studies using EEG as well.
If you don't want to do these calculations by hand, I can recommend G-Power. There you have a lot of options to specify what kind of statistical tests you did/want to do and which kind of power analysis you want to perform. You can easily calculate the effect size (post-hoc) or the required sample size (a priori) among other stuff.
Here’s a link to the program:
http://www.gpower.hhu.de/
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