Tests the null hypothesis that all \(s\) categories of a categorical variable, \(x\),

are the same size. The test statistic is:

\[\begin{align} X^2 = \sum^s_{k=1} \frac{(o_{kj} - e_{kj})^2}{e_{kj}}\end{align}\]

where:

\(o_{k} = \sum^n_{i=1} w_i I_{x=k}\)

\(w_i\) is the Calibrated Weight of the \(i\)th of \(n\) observations,

\(e_{k} = \frac{ \sum^n_{i=1} w_i}{s}\)

\(p \approx \Pr(\chi^2_{(s-1)} \ge X^2)\)

## Next

ANOVA-Type Tests - Comparing Three or More Groups

Second Order Rao-Scott Test of Independence of a Contingency Table