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Kolmogorov-Smirnov and related goodness-of-fit tests

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I understand how to compare two distributions using the KS or related tests. But my situation is somewhat different. I have 15 distributions from one population (~100 samples per distribution) and 15 distributions from a different population. I can generate the mean +/- sdev distribution for each of the 2 populations. How do I use the KS, Anderson-Darling, or Cramer Von Mises tests with these data (i.e., N=15 sample distributions from each of 2 populations)? I want to test whether the two populations are significantly different from each other.
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Jeff Miller
Jeff Miller on 15 Mar 2021
I see that you are using the term "distribution" much differently than I originally thought. That is, for you a "distribution" is not a frequency distribution of randomly varying scores within a single condition, but rather a systematic change in scores across diameter position.
This graph does not display any information relevant to the question of whether the scores are Gaussian in the statistically relevant sense, which is whether the 15 scores that went into each one of the 2*100 plotted points all come from normal distributions (with potentially 200 different means).
For your question, I would consider using two-factor ANOVA. One factor is control vs drug treatment, with n=15 in each group. This is a "between-Ss" factor. The other factor is X dimension, with 100 levels. This is a "repeated measures" factor since each animal was measured at all levels. If you have a specific functional model for how Y changes across X, then you can remove the X factor and replace it with the parameters of that function (estimated separately for each animal).

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