MATLAB: Different p-values for ranksum and kruskalwallis on two groups

boxplotkruskal-wallis test”notchranksumwilcoxon rank sum test

Why do I get different p-values when I’m using “Wilcoxon rank sum test” or “Kruskal-Wallis test” on two groups. Which test shoud I prefer?

[p_kruskal,t,stats] = kruskalwallis(X, gender);

[p_wilcoxon,h,stats] = ranksum(X (gender==1), X (gender==2));

I’d like to compare the distributions of this two groups using boxplot with the option of ‘notch’ on. Why even if the notches in the box plot overlap Wilcoxon suggest me that the medians of the two groups differ?

Best Answer

They are different tests, with different hypotheses. The ranksum test compares medians between two groups, assuming both share the same continuous distribution. The kruskalwallis test is to determine if the data from the groups are from the same distribution.

Use the test that addresses the problem you want to solve. If you want to determine if the medians differ, use ranksum. If you want to know if they are from the same distribution, use kruskallwallis.

‘Why even if the notches in the box plot overlap Wilcoxon suggest me that the medians of the two groups differ?’

That could be due to the sample sizes. Small absolute differences can become statistically significant if the sample sizes are large enough.

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MATLAB: Kruskalwallis test, mean or median

From the documentation section More About:

The Kruskal-Wallis test is a nonparametric version of classical one-way ANOVA, and an extension of the Wilcoxon rank sum test to more than two groups. It compares the medians of the groups of data in x to determine if the samples come from the same population (or, equivalently, from different populations with the same distribution).

(Underline added.)

MATLAB: Box plots for Kruskal-Wallis

Hello, when the end point of a notch is lower than the 25th quartile of your data, that folding effect will occur. This effect is common to small datasets or small group size (when between groups of data).

% To calculate the end points of the lower and upper notch
lowerNotch=median(data)-1.57*iqr(data)/sqrt(numel(data)); % iqr is interquartile range
upperNotch=median(data)+1.57*iqr(data)/sqrt(numel(data));
% For a small value of "n" the notch will tend to extend beyond either the 75th percentile or 25th percentile (the upper and lower ends of the box respectively.
% If you compute the 25th percentile of your data and compare it to the end point of the lower notch, you will
% find this to be true. However, that won't be the case with the upper notch based on your plot.

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MATLAB: Kruskalwallis test, mean or median

MATLAB: Box plots for Kruskal-Wallis

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