out of three small,medium or large options for effect size in g power, how to justify the selection, if we have to directly place the value rather than calculating it separately while performing sample size estimation.
I think a logical justification for use of a categorical effect size would be based on previous studies. In general, (1) find other studies which are working with the same or very similar systems to your study, (2) narrow to studies which have similar design and statistical test, (3) extract or calculate the standard effect size found in similar study, and (4) compare to 'rules-of-thumb' and published nominal effect sizes correlating to numerical ranges.
For example, let's say a study similar to mine is used a t-test to compare two groups. A standard effect size (Cohen's d—difference in sample means divided by pooled standard deviation) was calculated (d = 0.23). Using a reference – in this case Cohen's Statistical Power Analysis for the Behavioral Sciences (1988) – I find that values near what I calculated are considered "small" standard effects.
Sample size(s), effect size, α (sig. level), and 1-ß (power) are related. I'll refer you to the following paper as a starting point for that discussion. http://www.jgme.org/doi/abs/10.4300/JGME-D-12-00156.1?code=gmed-site
Note: Standard effect sizes aren't analogous to practical effect size. Always place the effect in the context of the study and field of study. The practical effect size can help guide the standard effect size, though. For example, the practical difference may indicate an extreme (i.e., "very large" or "very small") standard effect size, but this still helps guide your sample size calculation.
Hello Manu,
you basically have two options here:
But you are right, justifying the assumed effect size is not easy, because both options are not ideal and have their issues. Other studies will always be "similar" but not equal and a pilot study will most likely have a small sample size. Apart from that, whether you choose a small or a medium effect size will influence your power analysis a lot. So you can consider the effect size being the weak spot of an a priori power analysis. There is no way around it, though.
Keep in mind that the 4 parameters effect size, alpha, beta and your sample size are interdependent and not set in stone until running the actual study.
Best,
Steffen
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