F-Test (ANOVA)

The test statistics is:

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

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 $\sum _{j=1}^{s}\sum _{i=1}^{n_{j}}w_{ij}-j$ degrees of freedom.

(This is Type III Sum of Squares ANOVA.)

See also

• ANOVA-Type Tests - Comparing Three or More Groups