What is the Wilcoxon Sign Test?

The Wilcoxon Signed Rank test is a non-parametric analysis that statistically compared of the average of two dependent samples and assess for significant differences.

The Wilcoxon sign test is the non-parametric alternative of the  dependent samples t-test.

Questions Answered:

Are test scores different from 4^th grade to 5^th grade on the same students?

Does a particular diet drug have an effect on BMI when tested one the same individuals?

Assumptions:

Data comes from two matched, or dependent, populations.

The data is continuous.

Because it is a non-parametric test it does not require a special distribution of the dependent variable in the analysis.

The Wilcoxon Sign test is a repeated measures test of dependency. Conducting this test closely resembles performing a Mann-Whitney U-test (also referred to as the Wilcoxon 2-sample t-test). It also aligns with the basic principle of the dependent samples t-test, as the Wilcoxon sign test, like the dependent samples t-test, evaluates the difference in observations when the observations are matched.

However this test pools all differences, ranks them and applies a negative sign to all the ranks where the difference between the two observations is negative. Researchers call this the signed rank.Whereas the dependent samples t-test tests whether the average difference between two observations is 0 the Wilcoxon test tests whether the difference between two observations has a mean signed rank of 0.  Thus it is much more robust against outliers and heavy tail distributions. .  Thus, researchers consider it the best test for comparing mean scores when the dependent variable is not normally distributed.