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I'm not really sure to what degree this is a statistical question but thought this might be the best place to start. If my questions prove only my ignorance please vote it down and I'll delete the thread hopefully making more accurate google searches in the future

Greetings,

could anyone please explain why there is no (to my knowledge) concise description (agreement) on how to compute power and sample size for a planned experiment involving factorial repeated measures?

In my field (psychology) balanced repeated measures designs are very common. With the replicability crisis going on, preregistering experiments and establishing a desired sample size beforehand is considered best practice. Also, reviewers seem to ask for power "numbers" (whatever it mean).

Even CV has little guidance on this matter: Report power of 4-way repeated measures ANOVA?; Determine sample size for three-way ANOVA with repeated measures; Repeated measures or two-way ANOVA, and power analysis for some unanswered questions.

There is https://stats.stackexchange.com/a/35994/133561 R code for simulating power in logistic regression or https://stats.stackexchange.com/a/21243/133561 for why online calculators might not be the best choice.

When looking for guidance to satisfy my future reviewer I only found blog posts with opinions (to say the most) and not really some citable methodology (with this one be closest to useful https://approachingblog.wordpress.com/2018/01/24/powering-your-interaction-2/). It makes me wonder why there is so much confusion and so little explanation at a basic, non mathematical level.

What I would like to know is:

  1. How to calculate the sample size upfront in context of purely repeated measures designs (varying from two level A * B setups to four level A * B * C * D setups, where complex fixed effects interactions are of interest)
  2. How to reply reviewers when for some reasons one could not (or didn't know how) compute power or desired sample size before running the experiment
  3. How to approach replication scenarios when one knows effect sizes for a published experiment and based on that would like to plan a powerful replication.
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