Non-Parametric Tests

Wilcoxon Signed-Rank Test

A non-parametric test used to compare two related samples, matched samples, or repeated measurements on a single sample. Its the non-parametric alternative to the paired t-test. In YouTube analytics, this could be used to compare viewer engagement metrics before and after a channel makes significant changes to their content strategy.

Wilcoxon Z-Score

$Z$$=$$($$W$$-$$\frac{n(n+1)}{4}$$)$$\div$$√$$\frac{(n(n+1)(2n+1))}{24}$

Hypothesis

  • H₀: The differences between pairs have a median of zero
  • Hₐ: The differences between pairs have a median different from zero

Assumptions

  • Data are paired and come from the same population
  • Each pair is chosen randomly and independently
  • The differences between pairs are ordinal or continuous
  • The distribution of differences is symmetric

Wilcoxon Rank-Sum Test (Mann-Whitney U Test)

A non-parametric test used to determine whether two independent samples come from the same distribution. Its the non-parametric alternative to the independent samples t-test. For example, comparing engagement metrics between two different types of YouTube content or between two different channels.

Hypothesis

  • H₀: The two samples come from the same distribution
  • Hₐ: The two samples come from different distributions

Assumptions

  • Observations are independent
  • The data is ordinal or continuous
  • The distributions have similar shapes (but can have different locations)

Sign Test

A simple non-parametric test used to determine whether there is a median difference between paired observations. Its more robust but less powerful than the Wilcoxon signed-rank test, as it only considers the direction of differences, not their magnitude.

Hypothesis

  • H₀: The median difference between pairs is zero
  • Hₐ: The median difference between pairs is not zero

Assumptions

  • Data are paired
  • Pairs are independent
  • Data is ordinal (can be ranked)
  • No zero differences (ties are typically discarded)

When to Use

  • When data is ordinal or continuous but heavily skewed
  • When outliers are present
  • When sample size is small
  • When only the direction of difference matters, not the magnitude