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I am a beginner in using Wilcoxon test to get the p-value. After applying the test to my data, I got the p-value < 2.2e-16. Does that mean that the samples I have are significantly different from each other? I am suspicious of such a result. I have looked at other related questions (such as this question) but I didn't really understand what this value means.

Can someone please explain?

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    $\begingroup$ Depending on your field, this might commonly be reported as p < 0.001. $\endgroup$
    – APH
    Commented Apr 16, 2019 at 18:14

3 Answers 3

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2.2e-16 is the scientific notation of 0.00000000000000022, meaning it is very close to zero. Your statistical software probably uses this notation automatically for very small numbers. You may be able to change this in the settings.

The notation alone is no reason to be suspicious. The result itself might be, but you will have to be the judge of that.

< 2.2e-16 as the p value would indicate a significant result, meaning that the actual p value is even smaller than 2.2e-16 (a typical threshold is 0.05, anything smaller counts as statistically significant).

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Adding to Morphist's answer (+1 to Morphist), I would be suspicious of this if:

  • N was small

  • The difference was expected to be small

  • Other studies find small differences.

and so on.

I would make a density plot of the values in each of the groups and see if they look really different.

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You will reject your null hypothesis in this situation as the p < 0.01. If you are comparing difference with respect to some variable in two groups, then it means both groups have significance differences in the mean values of that variable.

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