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:

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}

where:

x_{ij} is the data for jth of c categories of the ith of n observations,
x_{ij}\in {0,1},
w_i is the Calibrated Weight, and
u_i = \sum^c_{j=1} x_{ij}
p \approx \Pr(\chi^2_{c-1} \ge Q)

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