Wilcoxon Tests What is the Purpose of Wilcoxon Tests? What are the Assumptions? How does the Wilcoxon Rank-Sum Test Work? How does the Wilcoxon Matched-

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Presentation transcript:

Wilcoxon Tests What is the Purpose of Wilcoxon Tests? What are the Assumptions? How does the Wilcoxon Rank-Sum Test Work? How does the Wilcoxon Matched- Pairs T Test Work?

What is the Purpose of Wilcoxon Tests? These are nonparametric alternatives to the independent and dependent samples t-tests. Based on ordinal data. Normal distributions are not required.

What is the Purpose of Wilcoxon Tests? Wilcoxon Rank-Sum Test is used in place of the independent samples t (between subjects design). Wilcoxon Matched-Pairs T Test is used in place of the dependent samples t (within subjects or matched groups design).

What Are the Assumptions? Wilcoxon Rank Sum: – Ordinal or higher level data – Independent observations Wilcoxon Matched-Pairs T: – Ordinal or higher level data – Paired observations – Minimum N of 6

How Does the Wilcoxon Rank-Sum Work? If the scores are not already ordinal, they are ranked from lowest to highest across both groups. The sum of ranks is calculated for each group.

How Does the Wilcoxon Rank-Sum Work? If the Ho is true, then the sum of ranks should be the same for the two groups. W is the smaller sum of ranks (or the sum for the group expected to have the smaller sum).

How Does the Wilcoxon Matched-Pairs T Work? Difference scores are calculated for each pair of scores. The difference scores are ranked from lowest to highest.

How Does the Wilcoxon Matched-Pairs T Work? The sum of ranks is computed separately for positive and negative difference scores. If the Ho is true, then the sum of ranks should be the same for the two groups. T is the smaller sum of ranks (or the sum for the condition expected to have the smaller sum).