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I am trying to determine whether a paired T test or Wilcoxon ranked sum test is more appropriate to test for significance of improvement in the following:

Patients were surveyed for pain scores before treatment on 0-10 scale Patients were then given intervention Patients were then surveyed for pain score after treatment on 0-10 scale.

The data are effectively paired since datapoints exist for the same patient pre and post treatment.

Wilcoxon-signed-rank yields a very small P value over 24 patients. Very, very small (p<0.0001).

IS wilcoxon-SR appropriate for this application or should I be using a paired T test or chi-square test?

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  • $\begingroup$ Are the data (both pre- and post-treatment) distributed normally? $\endgroup$
    – a.powell
    Commented Jul 26, 2016 at 18:15
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    $\begingroup$ @a.powell 1. why would that be necessary? (rather than just the differences being approximately normal, say) 2. How would normality be possible? They're integers between 0 and 10 $\endgroup$
    – Glen_b
    Commented Jul 27, 2016 at 1:37
  • $\begingroup$ MG -- 1. what's your actual null (is it a null about means, or is it some more general null?) 2. Is the software you're using going to correctly handle the heavy ties you're likely to get in a signed rank test? (though 24 should be enough to use the normal approximation with adjustment for tied ranks reasonably successfully) $\endgroup$
    – Glen_b
    Commented Jul 27, 2016 at 1:40

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If your data is normally distributed -- you can analyze a number of ways, including a QQ Plot -- then it is fine to run a t-test. But, in order to make the least number of assumptions about the data it is best to use the non-parametric Wilcoxon Signed Rank test.

Due to the fact that you have very few samples (24) I would advise going the Wilcoxon Signed Rank path. I would thoroughly analyze this question because it appears to answer a lot on necessary questions.

Be sure to understand exactly how the type I error and the power behaves in your test.

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  • $\begingroup$ It might be worth noting that the loss of power of the Wilcoxon test is only about 4% if the variable is normally distributed. This amounts to losing 1 observation out of 24. $\endgroup$
    – David Smith
    Commented Jun 10, 2017 at 13:16

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