Sign Test

Non-parameter Statistic

3 requirements

1. The problem objective is to compare two populations.
2. The data are ordinal.
3. The experimental design is matched pairs

The Hypothesis

$H_0$ : The 2 population locations are the same

That also means

$H_0$ : $p=.5$

Recall the Binomially Distribution

Standardized test statistic is

$z=\frac{x-np}{\sqrt{np(1-p)}}$

$x$ is the number that are positive.

The Friedman Test and the Sign Test

The relationship between them is same as between the Kruskal Wallis Test and the Wilcoxon Rank Sum Test .