F-Test (ANOVA)

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The test statistics is:

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)}


x_{ij} is the value of the ith of n_j observations in the jth of s groups,
\bar{x}_j is the average in the jth group,
\bar{x} is the overall average
w_{ij} is the calibrated weight.
and F is evaulated 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