The test statistic is:
\[\begin{align} F=\frac{\sum^s_{j=1} \sum^{n_j}_{i = 1} w_{ij}(\bar{x}_j - \bar{x})^2 / (j-1)}
{\sum^s_{j=1} \sum^{n_j}_{i=1} w_{ij}(\bar{x}_j - x_{ij})^2 / ((\sum^s_{j=1} \sum^{n_j}_{i = 1} w_{ij}-1) (j - 1))} \end{align}\]
where:
\(x_{ij}\) is the value of the \(i\)th of \(n_j\) observations in the \(j\)th of \(s\) groups, where \(x_{ij}\) has been 'centered' such that \(\sum^s_{j=1} x_{ij} = 0\forall i \)
\(x_{ij}\) is the average in the \(j\)th group,
\(\bar{x}\) is the overall average,
\(w_{ij}\) is the calibrated weight, and
\(p \approx \Pr(F_{(s-1),(\sum^s_{j=1} \sum^{n_j}_{i = 1} w_{ij}-1) (s - 1))} \ge F )\).