Back-calculation (a posteriori) of the minimum sample size for a mechanical experiment


I want to back-calculate the minimum sample size for a mechanical experiment.
I have a known mean and standard deviation of a statistical population. From the statistical population I chose two samples with means and standard variances I could estimate. My question is: How can I calculate a theoretical sampling size based on the means and standard deviations of the samples considering a confidence interval of 2σ.

Best regards


Less is more. Stay pure. Stay poor.
So you want to calculate a required sample size to have a difference between groups at least 2 standard deviations apart? Do you want the two groups to be the same size?

You did not describe the format/data type for the dependent variable.


Less is more. Stay pure. Stay poor.
I am still confused if there may be an issue with doing this our not. Typically if you conduct a power calculation post hoc it is biased since the study was already conducted. But you haven't conducted the study yet by have the actual data in your hands. Why not just use all of your data to maximize precision?

I haven't don't this by it seems straightforward. Here is a corollary paper on doing this for a rate as the outcome, which would be a little different.