The Wilcoxon Signed Rank Test is a non-parametric statistical procedure designed to assess differences in central tendency between paired samples without requiring normality assumptions for the underlying data distribution, provided that the distribution of difference scores is approximately symmetric. As the non-parametric counterpart to the dependent t-test, it operates by ranking absolute deviations from zero and comparing summed positive versus negative ranks rather than calculating means. The test statistic $W$ represents the minimum sum of signed rank totals ($T^+$ or $T^-$), which are evaluated against a sampling distribution (either exact for small samples or normal approximation for $N \geq 25$) to determine statistical significance in detecting population differences between dependent groups within inferential statistics.
The Wilcoxon Signed Rank Test is a non-parametric statistical procedure designed to assess differences in central tendency between paired samples without requiring normality assumptions for the under…