F-Test (ANOVA)

The test statistics is:

$F=\frac{\sum^s_{j=1} \sum^{n_j}_{i = 1} w_{ij}(\bar{x}_j - \bar{x})^2 / (j-1)} {\sum^s_{j=1} \sum^{n_j}_{i=1} w_{ij}(\bar{x}_j - x_{ij})^2 / (\sum^s_{j=1} \sum^{n_j}_{i = 1} w_{ij} - j)}$

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 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

• ANOVA-Type Tests - Comparing Three or More Groups