Friedman Test for Correlated Samples

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

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}

where:

n_j is the number of observations in group j of ggroups,
r_{ij} is the rank of the ith 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,
n is the number of matched samples,
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