Wilcoxon ranksum test gives a p=0

Question

I want to see if an app was effective in changing the behaviour of a group.

Data were taken at baseline and after intervention on the same group.

Since distribution doesn't follow normality I applied Wilcoxon signed-rank test and I get as a result a p=.000

Isn't weird? I can see that every subject in the experiment has had an improvement (min improvement 0.40%; max improvement 64%). Could this improvement be the reason for this weird p-value?

Thank you in advance.

Could be just floating errors – SmallChess May 20 '18 at 08:09 — SmallChess, May 20 '18 at 08:09

score 3 · Accepted Answer · answered May 20 '18 at 08:32

The p-value won't be exactly zero, but if every individual changed in the same direction (and that direction was one covered by the alternative), the p-value will be as small as it is possible to be.

If you also stated the sample size (and whether your alternative was one or two tailed), we could actually compute the exact p-value without knowing anything further.

For example, with a two tailed test and n=35 subjects doing both baseline and post-intervention measurement, with all improving you'd have a p-value of about $5.8\times 10^{-11}$ (58 trillionths; or 0.000000000058).

Some packages will print such small numbers, some will only print a fixed number of figures ... which in a case like that will all be 0.

Great explanation. As you said, p is not 0. In fact, it's possible to change settings in SPSS by editing the p-value cell, and see the actual value of p which, in my case is 4x10^-4 — Andrea, May 20 '18 at 14:36

Wilcoxon ranksum test gives a p=0

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