Repeated Measures 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}-1) (j - 1))}

where:

x_{ij} is the value of the ith of n_j observations in the jth of s groups, where x_{ij} has been 'centered' such that \sum^s_{j=1} x_{ij} = 0\forall i
\bar{x}_j is the average in the jth 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 ).

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