sample size - power calculations

Hi, would be great if anybody could help me on this.

I want to estimate the impact of an independent variable x (lets say a social program) on the dependent variable y (lets say test results) using a social experiment. I understand all inputs needed to calculate the required sample size to test for differences in outcomes y if lets say half of the sample receives the social program and the other half does not.

My question: this seems to be independent of the total population which in the end should then benefit from program x. If this is true, what is the explanation for this? (as sample size calculations for means of a population do require some knowledge about the size of the population)

Thanks a lot!


Super Moderator
Hi there,

Statistical power calculations are indeed influenced by population size - for example the popular power calculators below use population size in their calculations:

However: the influence of power on differences in population become very small as the population becomes very large (around 20,000+); and researchers often don't have a very clear idea of what the actual population of interest is or its size; so by and large this influence is ignored and people tend to just assume that the population is very large or infinite, and therefore ignore this aspect.

Hope this makes sense - obviously it's a "psychological" explanation rather than a mathematical one!