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} - j)}\end{align}\]

where:

\(x_{ij}\) is the value of the \(i\)th of \(n_j\) observations in the \(j\)th of \(s\) groups,

\(\bar{x}_j \) is the average in the \(j\)th group,

\(\bar{x}\) is the overall average,

\(w_{ij}\) is the calibrated weight,

and \(F\) is evaluated using the *F*-distribution with \(j-1\) and \(\sum^s_{j=1} \sum^{n_j}_{i = 1} w_{ij} - j \) degrees of freedom.

(This is Type III Sum of Squares ANOVA.)

## See Also

ANOVA-Type Tests - Comparing Three or More Groups