This is a straightforward question. In order to calculate a sample size needed for a paired t-test, it is required to know ahead of time the standard error of the paired differences. But what if this is unknown? Is there a crude estimation of the standard error that can be used?
1 Answer
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The $t$ test prominently uses the standard errors. If you can't specify the standard error, you can't calculate the power for the $t$ test, and therefore, you can't calculate the sample size you need for a specified power.
Your best bet likely is to plug a range of "reasonable" standard errors (or, equivalently, effect sizes) into the formula. What is "reasonable" will depend on your domain of application, and your prior knowledge about the effect you are studying.
answered Apr 28, 2020 at 13:59