Non-Parametric Tests

Non-parametric tests do not assume a particular distribution for the data. They are used when normality assumptions are questionable, when data are ordinal, or when sample sizes are very small. This lesson covers the sign test and the Wilcoxon signed-rank test.

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When to Use Non-Parametric Tests

Situation	Parametric test	Non-parametric alternative
One-sample location test (normal data)	One-sample t-test	Sign test or Wilcoxon signed-rank test
Paired data (normal differences)	Paired t-test	Sign test or Wilcoxon signed-rank test
Two independent samples (normal)	Two-sample t-test	Mann-Whitney U test

Non-parametric tests are generally less powerful than parametric tests when the parametric assumptions hold, but they are more robust when assumptions are violated.

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The Sign Test

The sign test is the simplest non-parametric test. It tests the median of a distribution.

One-Sample Sign Test

$H_0$H0​: The population median is $m_0$m0​. $H_1$H1​: The population median is not $m_0$m0​ (or $> m_0$>m0​ or $< m_0$<m0​).