Cochran's Q
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This test is a non-parametric equivalent of Repeated Measures ANOVA which is applicable with binary data (i.e., proportions). The test statistic is:
[math]\displaystyle{ Q = \frac{c(c-1)\sum^c_{j=1}(\sum^n_{i=1}w_i x_{ij} - \frac{1}{c}\sum^n_{i=1}w_i u_i)^2}{c\sum^n_{i=1}w_i u_i - \sum^n_{i=1} w_i u^2_i} }[/math]
where:
- [math]\displaystyle{ x_{ij} }[/math] is the data for [math]\displaystyle{ j }[/math]th of [math]\displaystyle{ c }[/math] categories of the [math]\displaystyle{ i }[/math]th of [math]\displaystyle{ n }[/math] observations,
- [math]\displaystyle{ x_{ij}\in {0,1} }[/math],
- [math]\displaystyle{ w_i }[/math] is the Calibrated Weight, and
- [math]\displaystyle{ u_i = \sum^c_{j=1} x_{ij} }[/math]
- [math]\displaystyle{ p \approx \Pr(\chi^2_{c-1} \ge Q) }[/math]