Hello Kai-Xuan,

The overly rigid interpretation of sphericity in repeated measures anova is that all pairs of measures have equal correlation. So, for a given set of observations, the average or median correlation is likely a better indication of what the "common" correlation might be. If you use average, it is better to apply the Fisher-z transformation since correlations are not a linear scale: convert each correlation to its Fisher-z equivalent, average the z-values, then convert back to the r-metric (here's a link to a simple explanation: https://www.statisticshowto.datasciencecentral.com/fisher-z/).

On the other hand, if you're simply trying to be conservative with respect to selecting an appropriate sample size for a prospective study, you could go with the lowest observed pairwise relationship. Note that doing so will likely end up calling for more cases (larger N) than would really be necessary.

Good luck with your work.

Thanks, Mr. Morse.

Finally, I caculated an average r by means of Fish-z-transformation. That makes sense.

My Dear I have paper in this subject in my researchgate you can download it easy

and send me any notes about relation between your subject and my paper

all thanks

Thanks, Prof. Fadhil Abdulabbas Abidi.