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:

$Q = \frac{c(c-1)\sum^c_{j=1}(\sum^n_{i=1}w_i x_{ij} - \frac{1}{c}\sum^n_{i=1}w_i u_i)^2}{c\sum^n_{i=1}w_i u_i - \sum^n_{i=1} w_i u^2_i}$

where:

x_{ij}

is the data for

j

th of

c

categories of the

i

th of

n

observations,

x_{ij}\in {0,1}

,

w_i

u_i = \sum^c_{j=1} x_{ij}

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

See also