Wilcoxon Signed-Rank Test and Wilcoxon Rank-Sum Test

The Wilcoxon Signed-Rank Test (WSRT) is a part of non-parametric statistical tests that can be used for paired sample cases. Non-parametric statistics, also known as distribution-free statistics, do not require the assumption of a normal distribution for the population and can be used for small sample sizes.

Null Hypothesis (H0): There is no difference in average performance between the two groups.
Alternative Hypothesis (H1): There is a difference in average performance between the two groups.

Test Statistic: T0
Steps to calculate T0:

  • Determine the difference between the two paired sample groups (group 1 – group 2).
  • Take the absolute value of the differences so there are no negative values.
  • Rank the absolute differences.
  • Rank 1 is given to the smallest difference; if there are ties in absolute differences, assign the average rank.
  • Separate the ranks into positive and negative based on the original differences.
  • Sum all positive and negative ranks.

The test statistic T0 is the smaller of the two sums of ranks.
Compare the value of T0 with the table value T.
Accept H0 if T0 ≥ tα
Reject H0 if T0 < tα

The Wilcoxon Rank-Sum Test (WRST), also known as the Mann-Whitney Test, can be used to test the difference in means or medians between two independent (unpaired) sample groups as part of non-parametric statistical techniques.

Null Hypothesis (H0): Median of population 1 = Median of population 2
Alternative Hypothesis (Ha): Median of population 1 ≠ Median of population 2

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