I am trying to calculate sample size based on required effect size for my test (site found here: http://www.sample-size.net/sample-size-means/)

My inputs are as follows:

α (two-tailed) = .05

β = 0.100

Split of Test Vs. Control = .5

Desired Effect Size = .03

Standard deviation of the outcome in the population =

My confusion is in regards to this last step - is this the pooled Standard Deviation of my two groups? Not sure what to input here...any help would be appreciated!


As indicated by Stephan, this is the pooled standard deviation. If the effect size that you have specified is a Cohen's d type effect size, then use 1 as your standard deviation. I assume you are aware that this is a very small effect size you are designing your study to detect? You are also designing for a high level of power (1-$\beta$). The two of these combined will result in your needing a very large sample size. Designing for power = .80 is common but this is simply a convention created by Cohen and more power is always better!

  • $\begingroup$ If you are not using Cohen's d, then your effect size should be your expected mean difference and the standard deviation should be your expected (population) within-group (pooled) standard deviation. $\endgroup$ – dbwilson May 11 '17 at 21:21
  • $\begingroup$ Hi DBwilson - this is great and I believe this calculator is Cohen's D. Why exactly does that mean SD is "1" and not pooled SD? $\endgroup$ – user3682157 May 11 '17 at 22:14
  • $\begingroup$ 1 Is the pooled SD. That is, with a Cohen's d, you've rescaled the data to have a pooled SD of 1. The reason this calculator has the option to specify the SD is so that you can use something other that the Cohen's d. $\endgroup$ – dbwilson May 12 '17 at 10:49

Yes, it is. This particular sample size calculator does not allow including unequal variances in the treatment and control group.

If you expect and plan for this, then first of all, congratulations - you are being more statistically sophisticated than most researchers. In such a case, get a friendly statistician to hack together a few lines of R to run a simulation-based sample size calculation.

  • $\begingroup$ Hi Stephan - so this calculator is calculating Cohen's D effect size. With that in mind, I am confused if I should be putting in "1" or the pooled variance of my two samples... $\endgroup$ – user3682157 May 11 '17 at 21:10

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