I'd like to calculate effect sizes using data from a published study. The aggregate sample size is provided but not the sample size for each of the three experimental conditions.

  • Is there a way to determine the sample size for each condition if provided the mean and standard error for each outcome across conditions as well as the t-statistic (a range for df is provided vs. the specifc df for each condition) across outcomes for each treatment comparison?
  • Also, is there a way, given these data, to compute the Cohen's d effect size without the sample size for each experimental condition?
  • 1
    $\begingroup$ Are the three experimental conditions independent or is it repeated measures? $\endgroup$ – John Sep 23 '11 at 19:33
  • $\begingroup$ The simplest approach would be to email the authors of the paper. $\endgroup$ – Karl Sep 25 '11 at 12:59
  • $\begingroup$ The conditions are independent. I did think about e-mailing the authors, but wanted that to be a last resort. Thanks for the responses; they were helpful. $\endgroup$ – sopa Sep 26 '11 at 12:09
  • Experiments are typically designed to have equal or approximately equal sample sizes. Thus, if you are happy with an approximation, then you might make the assumption that the sample sizes are equal. Alternatively, as @Karl notes, you could just email the authors if it is important.
  • With three experimental groups, then you will have three possible Cohen's Ds (A with B, A with C, and B with C). You can calculate Cohen's D if you have means and standard deviations. You can calculate standard deviations from standard errors and sample sizes. Depending on what information you have, you might have to make assumptions such as homogeneity of variance or equal sample sizes per group. Alternatively you could modify your assumptions, and see what effect this has on your estimates of Cohen's D.

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