My Project compares pre-test and post-test ratios in addition to pre-test and past-test Likert scale. I planned to use Wilcoxon signed rank. I only have a sample size of 4. Can I still use Wilcoxon or is there another test that would be appropriate?
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$\begingroup$ It's challenging to draw conclusions from a sample of size n = 4. Found this thread Wilcoxon signed-ranks test with small samples which may be instructive. $\endgroup$– dipetkovCommented May 18 at 23:57
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No, WSRt is NOT appropriate for sample sizes less than 6, as it will NEVER return a significant result (no matter what your $H_0$ or $H_a$ are) (for the traditional significance of .05). That is because the sum of ranks can not reach the critical values.
Also, WSRt is very sensitive to the symmetry (of the parent distribution) assumption (if you are using it as a test of the median). But with a sample size of 4 (or 6, or other such small value), you have no way to assess whether that assumption is warranted.
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$\begingroup$ You are putting inappropriate weight on arbitrary thresholds for ‘statistical significance’. But to the original question, Likert scales are not great candidates for the Wilcoxon signed rank test because the difference between two ordinal variables is not necessarily ordinal. For this and other reasons, the rank difference test is much preferred for paired data. Details are here. The rank difference test, unlike WSR, does not depend on Y being perfectly transformed before differences are taken. $\endgroup$ Commented May 23 at 11:43
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$\begingroup$ I was just using the "traditional" .05 significance threshold. But yes, for other significance levels, WSRt could work, or could require even a larger sample size. I actually considered also commenting on the (mis)-use of Likert scales, but I did not, to simply answer the OP's very first post. But indeed, how to properlyy test Likert scores could/should be its own post. One could as well comment on the usefulness/reasonableness of doing any statistics, with any test, with a sample size of 4. But... $\endgroup$ Commented May 23 at 20:33