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,
\(e_{k} = \frac{ \sum^n_{i=1} w_i}{s}\)
\(p \approx \Pr(\chi^2_{(s-1)} \ge X^2)\)
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ANOVA-Type Tests - Comparing Three or More Groups
Second Order Rao-Scott Test of Independence of a Contingency Table