# Puzzling behavior of ranksum

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Paul on 3 May 2017
Commented: Star Strider on 24 Jul 2017
I performed a ranksum test on two vectors of 80 and 88 entries, both with 0 median and in all respects fairly similar. I assumed ranksum would tell me the difference between the two vectors was insignificant but surprisingly ranksum returned a p < 0.05. I started playing around to try and understand the output better and came across the following puzzling behavior of ranksum:
As I added an identical number of 0's(5,10,20,50..) to the end of both vectors and redid the ranksum test, the p-value it output became smaller. The more 0's I added to both vectors the smaller the p-value I received upon testing. This seemed strange to me because by adding identical entries to both vectors all sample statistics should converge, right? And the more similar the sample statistics the more likely they were drawn from the same distribution?
I have been reading quite a lot about the Wilcoxon Rank Sum test but have not come across an explanation for this behavior. I'm not a statistician and I'm getting at the end of my wits here. If anybody could tell me what I'm missing it would be greatly appreciated!
Best, Paul

Star Strider on 3 May 2017
I’ve not used the Wilcoxon Rank-Sum test in a while, but as I recall (and a brief review just now supports, at least as I read it), the p-value is the probability that the two medians are different (or one greater or less than the other in a one-tailed test). So a low p-value would be interpreted to mean that the probability of different medians is low, and a high p-value the probability of different medians is high.
This is counter-intuitive with respect to the interpretation of the t-test, for example, where a low p-value indicates a low probability that the means are the same, and a high p-value a high probability that the means are the same.
I would be interested to read others’ interpretations and clarifications.
Star Strider on 24 Jul 2017
My pleasure.
As I read it, larger vectors result in larger values for the test statistic, so a lower p-value. More data (with the same distribution) would reduce the p-value with every statistical test I’m familiar with.

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