# 5.4.5 - Wilcoxon Signed Ranks Test - Teradata Warehouse Miner

## Teradata Warehouse Miner User Guide - Volume 3Analytic Functions

Product
Release Number
5.4.5
Published
February 2018
Language
English (United States)
Last Update
2018-05-04
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The Wilcoxon Signed Ranks Test is an alternative analogous to the t-test for correlated samples. The correlated-samples t-test makes assumptions about the data, and can be properly applied only if certain assumptions are met:
1. the scale of measurement has the properties of an equal-interval scale
2. differences between paired values are randomly selected from the source population
3. the source population has a normal distribution.
If any of these assumptions are invalid, the t-test for correlated samples should not be used. Of cases where these assumptions are unmet, the most common are those where the scale of measurement fails to have equal-interval scale properties, e.g., a case in which the measures are from a rating scale. When data within two correlated samples fail to meet one or another of the assumptions of the t-test, an appropriate non-parametric alternative is the Wilcoxon Signed-Rank Test, a test based on ranks. Assumptions for this test are:
1. The distribution of difference scores is symmetric (implies equal interval scale)
2. difference scores are mutually independent
3. difference scores have the same mean

The original measures are replaced with ranks resulting in analysis only of the ordinal relationships. The signed ranks are organized and summed, giving a number, W. When the numbers of positive and negative signs are about equal (i.e., there is no tendency in either direction), the value of W will be near zero, and the null hypothesis will be supported. Positive or negative sums indicate there is a tendency for the ranks to have significance so there is a difference in the cases in the specified direction.

Given a table name and names of paired numeric columns, a Wilcoxon test is produced. The Wilcoxon tests whether a sample comes from a population with a specific mean or median. The null hypothesis is that the samples come from populations with the same mean or median. The alternative hypothesis is that the samples come from populations with different means or medians (two-tailed test), or that in addition the difference is in a specific direction (upper-tailed or lower-tailed tests). Output is a p-value, which when compared to the user’s threshold, determines whether the null hypothesis should be rejected.