Wilcoxon rank sum test

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]

MATLAB's ranksum is a two-sided test thus you're not testing for something smaller than zero but different from zero.

Answer 1

[the cyclist]

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]

Ahhh, Yes, Thanks Cyclist!