Dear Statalisters,

I'm using Stata 17.0.

By looking at this paper: https://www.jstor.org/stable/pdf/2532393.pdf

and at Table 4 in particular, I see that, given the standardized effect Delta, in the case of compound simmetry (as I think it is for "power repeated", given that only one parameter for correlation is required, but Table 3 shows that things don't change in the case of autoregressive models) the required sample size should:

1) decrease with the number of repeated measurement.

2) increase with correlation.

Instead, it seems to me that, with the "power repeated" command, when the between/within factor is of interest (time/treatment interaction) the following formula holds:

delta=sqrt(((vareffect)*nrepeated)/(1-correlation))

and I've noticed that sample size, given Delta:

1) Increases with the number of repeated measures. In fact, with the increase in the number of repeated measures, to get the same value of Delta, a lower explained variance is required, leading to a higher required sample size. Example:

Code:
power repeated, nrepeated(2) ngroups(2) corr(0.9) factor(bwithin) power(0.8) vareffect(0.0045)

power repeated, nrepeated(3) ngroups(2) corr(0.9) factor(bwithin) power(0.8) vareffect(0.003)
 
power repeated, nrepeated(4) ngroups(2) corr(0.9) factor(bwithin) power(0.8) vareffect(0.00225)

power repeated, nrepeated(10) ngroups(2) corr(0.9) factor(bwithin) power(0.8) vareffect(0.0009)
We can see that, by increasing the number of repeated measures (2, 3, 4, 10), the decrease in the within/between variance in order to keep Delta equal to 0.3 leads to an increase in the required sample size (90, 110, 124, 176).

2) Does not depend on correlation. In fact, by counterbalancing an increase in correlation with a decrease in explained variance to keep Delta constant, also the sample size remains constant. Example:

Code:
power repeated, nrepeated(2) ngroups(2) corr(0.729) factor(bwithin) power(0.8) vareffect(0.012195)

power repeated, nrepeated(2) ngroups(2) corr(0.81) factor(bwithin) power(0.8) vareffect(0.00855)

power repeated, nrepeated(2) ngroups(2) corr(0.9) factor(bwithin) power(0.8) vareffect(0.0045)
Here we see that, by increasing correlation and decreasing explained variance in order to keep Delta fixed at 0.3, the required sample size remains constant at 90.

In particular, I find point 1 particularly hard to understand: I expect, by increasing the number of repeated measurements and by keeping the effect size the same, to gain power, thus to need a lower sample size.

Can you explain to me what I'm missing?