Actually the response is what is being measured. So that will be independent from n, the sample size! If you are measuring something in a cohort you do not expect the average value or the variance of the measured quantity to be any different if the number of measurements taken is 100 or 1000. Additionally, the p value is determined by the size of the area of overlap of the distributions of the two cohorts being tested, so since there is very little difference in the two cohort distributions if n=100 or n=1000, the p-value calculated for the two sample sizes should be practically the same.
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