F-Test (ANOVA)

The test statistics is:

[math]\displaystyle{ 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)} }[/math]

where:

[math]\displaystyle{ x_{ij} }[/math] is the value of the [math]\displaystyle{ i }[/math]th of [math]\displaystyle{ n_j }[/math] observations in the [math]\displaystyle{ j }[/math]th of [math]\displaystyle{ s }[/math] groups,

[math]\displaystyle{ \bar{x}_j }[/math] is the average in the [math]\displaystyle{ j }[/math]th group,

[math]\displaystyle{ \bar{x} }[/math] is the overall average

[math]\displaystyle{ w_{ij} }[/math] is the calibrated weight.

and [math]\displaystyle{ F }[/math] is evaulated using the F-distribution with [math]\displaystyle{ j-1 }[/math] and [math]\displaystyle{ \sum^s_{j=1} \sum^{n_j}_{i = 1} w_{ij} - j }[/math] degrees of freedom.

(This is Type III Sum of Squares ANOVA.)

See also

• ANOVA-Type Tests - Comparing Three or More Groups