Hello Mohamed,

I'm not certain that thinking about power analysis in meta-analysis would always make sense. A chief reason is, in advance of the study, one doesn't know the population size. As well, the population depends on the criteria imposed on membership (e.g., only studies involving randomized treatment; only studies using measures X or Y; only studies using females without disabilities as participants; only studies with intervention lasting at least three weeks) and your willingness to chase down unpublished sources, thesis/dissertation sources, etc. (which impacts what, for you, is the accessible population).

That said, if you're concerned about questions such as, will a meta-regression have any chance of showing study characteristics as related to outcomes (effect sizes), then you could perform a post-mortem power analysis. In other words, for the number of independent ES values you found (your operative N), the number of study predictors you used, the alpha level you would apply, and the target strength of relationship you'd like to be able to detect (should it exist; this is your ES for the power analysis), you could compute a post hoc power. That presumes, of course, that the population is (essentially) infinite. If you were sufficiently fortunate to have identified and captured all of the independent ES values that truly exist, you have the population, and no inference is needed! Your values would, in that instance, be the parameters.

Good luck with your work!

Power analysis for a meta-analysis is discussed in detail in Chapter 29 of the book "Introduction to Meta-Analysis" by Borenstein, Hedges, Higgins, & Rothstein.

Thank you so much Prof. David and Prof. Gordon.