Is it expected to (always?) obtain identical p-values from the the Wilcoxon rank sum test and from the Kruskal-Wallis test ?

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Sim
Sim 2024-8-27
评论： Sim 2024-8-27
In the examples here below I compare two datasets, "r1" and "r2", by using both the Wilcoxon rank sum test and the Kruskal-Wallis test.
As you can see in both examples, the p-values resulting from two different tests are the same.
Therefore, is it expected to (always?) obtain identical p-values from the the Wilcoxon rank sum test and from the Kruskal-Wallis test ?
% Example 1: log-normal distributed data
clear r1 r2 % rng(0,'twister');
par1 = 0;
par2 = 100;
r1 = (par2-par1).*round(lognrnd(1,1,1000,1)) + par1;
r2 = (par2-par1).*round(lognrnd(0.88,1.1,1000,1)) + par1;
group = [1 + zeros(size(r1)); 2 + zeros(size(r2))];
p_W = ranksum(r1,r2);
p_KW = kruskalwallis([r1;r2],group,'off');
disp('---------------------------')
disp('Log-normal distributed data')
disp(['Wilcoxon test p-value: ', num2str(p_W)])
disp(['Kruskal Wallis test p-value: ', num2str(p_KW)])
hold on; histogram(r1);histogram(r2)
---------------------------
Log-normal distributed data
Wilcoxon test p-value: 0.29949
Kruskal Wallis test p-value: 0.29947
% Example 2: bimodal distributed data (created with the Gaussian Mixture Model)
clear r1 r2
gmd1 = gmdistribution([-1; 2],cat(3,0.5,1.0),(ones(1,2) / 2));
r1 = random(gmd1,1000);
gmd2 = gmdistribution([-0.8; 1.9],cat(3,0.4,1.2),(ones(1,2) / 2));
r2 = random(gmd2,1000);
group = [1 + zeros(size(r1)); 2 + zeros(size(r2))];
p_W = ranksum(r1,r2);
p_KW = kruskalwallis([r1;r2],group,'off');
disp('---------------------------')
disp('Bimodal distributed data')
disp(['Wilcoxon test p-value: ', num2str(p_W)])
disp(['Kruskal Wallis test p-value: ', num2str(p_KW)])
hold on; histogram(r1);histogram(r2)
---------------------------
Bimodal distributed data
Wilcoxon test p-value: 0.73858
Kruskal Wallis test p-value: 0.73855
  2 个评论
dpb
dpb 2024-8-27
In the absence of ties and for two samples, yes...KW is an extenstion of rank sum that uses ordered ranks instead of the values directly; for no ties the order vector and the vector will always coincide.

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