52. Wilcoxon Signed-Rank Test

OBJECTIVE

Verify whether the difference in two groups is significantly different (in the case that the assumptions for parametric tests are not met).

DESCRIPTION

It is a non-parametric substitute of the t-test in the case that normality cannot be verified or the sample is too small (smaller than 30), but, differing from the Mann–Whitney test, it is used for paired samples (the groups are not independent). The example presented here is a “signed-rank Wilcoxon test” (for paired samples and as a counterpart of the parametric paired t-test).

The assumptions for this test are: the samples are from the same population, the pairs are chosen independently, the data are measured at least on an ordinal scale (continuous, discrete, or ordinal), and the distribution is not especially skewed (that is to say it is approximately symmetrical).

Wilcoxon Signed-Ranks Test

To perform the test, the difference between observations is calculated and ranked. When we have samples with fewer than 25 observations, we use a table with a t-critical value to verify the significance; specifically, we reject the null hypothesis (there is no difference in the samples) if T is lower than T-critical. If we have a larger sample, we can use the p-value for the assessment of the significance.

TEMPLATE

Download the Wilcoxon Signed-Rank excel template