by MikeKatz45
Last Updated September 12, 2019 02:19 AM

I've recently looked into the Wilcoxon Rank Sum test for comparing groups of continuous values. In particular I've been using R's `wilcox.test()`

function for this task.

While using the test on my real data I noticed I wasn't getting any instances of the test rejecting the alternative hypothesis and all outputs always said `alternative hypothesis: true location shift is not equal to 0`

. I proceeded to do a quick test in R to see how a rejected alternative hypothesis result would look like:

```
>test1 <- c(1, 2, 3, 4, 5)
>test2 <- c(1, 2, 3, 4, 5)
>test <- wilcox.test(test1, test2, alt="two.sided")
```

I was totally expecting a rejected alternative hypothesis here since both groups of values are equal but oh surprise:

```
> test
Wilcoxon rank sum test with continuity correction
data: test1 and test2
W = 12.5, p-value = 1
alternative hypothesis: true location shift is not equal to 0
```

By no means I'm experienced using Wilcoxon test, but I really can't see why the alternative hypothesis is accepted in this case. I know that the null hypothesis for this test expects the median of both groups to be equal, so I can't really tell why the example above didn't work as expected. Maybe this could be a matter of result interpretation in R? What would be a small example in which the alternative hypothesis would be rejected then?

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