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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!

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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!

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  • $\begingroup$ 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
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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.

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  • $\begingroup$ 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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