F-Test (ANOVA)

The test statistics is:

$F=\frac{\sum _{j=1}^s\sum _{i=1}^{n_j}{w}_{ij}({\overline{x}}_j-\overline{x}{)}^2/(j-1)}{\sum _{j=1}^s\sum _{i=1}^{n_j}{w}_{ij}({\overline{x}}_j-x_{ij}{)}^2/(\sum _{j=1}^s\sum _{i=1}^{n_j}{w}_{ij}-j)}$

where:

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

${\overline{x}}_j$ is the average in the $j$th group,

$\overline{x}$ 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