# Wilcoxon rank sum test

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Mohsen Davarynejad on 22 May 2012
I would like to check if my data is smaller than zero or not. Assume the following example.
A = -1*ones(15,1);
[p, h, Stats] = ranksum(A, zeros(15,1))
z-value < 1.96, So A is statistically smaller than zero. But if change the test like the following:
[p, h, Stats] = ranksum(A, zeros(14,1))
the z-value goes positive. Why is that?
Oleg Komarov on 22 May 2012
MATLAB's ranksum is a two-sided test thus you're not testing for something smaller than zero but different from zero.

the cyclist on 23 May 2012
The reason you get a positive z-score for
ranksum(A, zeros(14,1))
is that the z-score is based on ranks of the smaller sample relative to the larger sample. So, it is the ranks of zeros relative to A , and you get higher ranks.
The reason you get a negative z-score for
ranksum(A, zeros(15,1))
is that when the two input vectors have equal sample size, MATLAB arbitrarily bases the z-score on first input (A) relative to the second (zeros), so you get the negative z-score
You can see all this in action if you set a breakpoint inside the ranksum() function. [Lines 70-78 in R2012a.]
Mohsen Davarynejad on 23 May 2012
Ahhh, Yes, Thanks Cyclist!