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

$u_{i}=\sum _{j=1}^{c}x_{ij}$

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

See also

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