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# Tag Info

Accepted

### Can we interpret the null of the Mann–Whitney U test, i.e. $P(x_i > y_j) = P(y_j > x_i)$, as equivalent to $F = G$ (where $F$ and $G$ are ECDFs)?

If the two distributions are identical, then of course the p-value will be close to 1, as your own answer illustrates. But the Wilcoxon-Mann-Whitney (WMW) test is only a test on stochastic dominance, ...
• 98k

### Can we interpret the null of the Mann–Whitney U test, i.e. $P(x_i > y_j) = P(y_j > x_i)$, as equivalent to $F = G$ (where $F$ and $G$ are ECDFs)?

With Matlab, I tried to verify that, when the null of the Mann-Whitney U-test (MWU) (aka Wilcoxon rank sum (WRS) test), $𝐻_0$: $𝑃(x_i > 𝑦_𝑗) = 𝑃(𝑦_𝑗 > 𝑥_𝑖)$, is satisfied, i.e. when (I ...
• 406
Accepted

### Null hypotheses of two-sample Kolmogorov-Smirnov, two-sample Anderson-Darling, and (two-sample) Wilcoxon rank sum test

The null for a 2-sample Kolmogorov-Smirnov test (KS) is that the 2 samples come from exactly the same distribution; a KS test of $N(0,1)$ against $N(1,1)$ will be significant (for adequate sample ...
• 3,330