Cochran's Q

This test is a non-parametric equivalent of Repeated Measures ANOVA which is applicable with binary data (i.e., proportions). The test statistic is:

$Q=\frac{c(c-1)\sum _{j=1}^c(\sum _{i=1}^n{w}_i{x}_{ij}-\frac{1}{c}\sum _{i=1}^n{w}_i{u}_i{)}^2}{c\sum _{i=1}^n{w}_i{u}_i-\sum _{i=1}^n{w}_i{u}_i^2}$

where:

$x_{ij}$ is the data for $j$th of $c$ categories of the $i$th of $n$ observations,

$x_{ij}\in 0,1$,

$w_i$ is the Calibrated Weight, and

$u_i=\sum _{j=1}^c{x}_{ij}$

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

See also

• ANOVA-Type Tests - Comparing Three or More Groups
• Planned ANOVA-Type Tests