Wilcoxon Tests
What is the Purpose
of Wilcoxon Tests?
What are the
Assumptions?
How does the
Wilcoxon RankSum Test Work?
How does the
Wilcoxon MatchedPairs 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 positive and
negative.
• T is the smaller sum of ranks (or the sum
for the condition expected to have the
smaller sum).