# Estimate random effect variance for power analysis in multilevel model

Is there a general convention on what variance to expect for a random intercept in a multilevel model? I need to provide an estimate for the power analysis. It is a within-subjects design. Thanks!

There are no absolute guidelines, but for instance Arend & Schäfer (2019) suggest, based on their literature review yielding average ICC of .30 that ICC = .30 could be considered a medium-sized ICC. (They also suggest that .05 could be considered a small ICC.)

Thus, if you use 1 for your level 1 residual variance in your power calculations (which is customary because it makes things easier), random intercept variance of ~ 0.43 will get you an ICC of .30.

Reference:

Arend, M. G., & Schäfer, T. (2019). Statistical power in two-level models: A tutorial based on Monte Carlo simulation. Psychological methods, 24(1), 1-19. https://psycnet.apa.org/doi/10.1037/met0000195

Edited because I left it out (thank you Erik Ruzek for pointing this out), the literature review mentioned reviewed psychological studies between 2010-2016 from several different fields of psychology. As Erik says, you should review multilevel studies from your own field to find a suitable number. Then, you can apply the above explained approach to this number.

To edit in some more clarification, random intercept variance is not a standardized parameter, its magnitude is scale-dependent, so you couldn't have e.g. a generally "medium-sized random intercept". ICC is a standardized parameter so you can use it and the fact that ICC is random intercept variance divided by total level 1 variance to get to an appropriate random intercept value.

To add onto Sointu's excellent response, you should be looking at longitudinal studies on the construct (or related constructs) of interest in your project. This will give you a sense of the size of ICCs found in previous research and will be a better guide than a generic number that comes from looking at studies outside your area. A simple Google search can be immensely helpful. E.g., "icc of construct_name" or "icc of scale_you_will_use".