This is a non-parametric version of the Repeated Measures ANOVA. The test statistic is:

\[\begin{align} Q =(g-1)\sum_{i=1}^n w_i \frac{ \sum_{j=1}^g\sum_{i=1}^{n} w_i (\bar{r}_{\cdot j} - \bar{r})^2}{\sum_{j=1}^g\sum_{i=1}^{n} w_i (r_{ij} - \bar{r})^2}\end{align}\]

where:

\(n_j\) is the number of observations in group \(j\) of \(g\) groups,

\(r_{ij}\) is the rank of the \(i\)th observation from group \(j\) where the ranking is computed within observations (e.g., if \(g=4\) then \(r_{ij} \in {{1,2,3,4}}\)), where 1 is assigned to the lowest value and the average rank is used for ties,

\(w_i\) is the Calibrated Weight,

\(\bar{r}_{\cdot j} = \frac{\sum_{i=1}^n{w_i r_{ij}}}{{\sum_{i=1}^n w_i}}\),

\( \bar{r} = \frac{g \sum_{i=1}^n w_i r_{ij}}{\sum_{j=1}^g\sum_{i=1}^n w_i}\),

\( p \approx \Pr(\chi^2_{g-1} \ge Q)\)

## See Also

ANOVA-Type Tests - Comparing Three or More Groups

Planned ANOVA-Type Tests