F-Test (ANCOVA)

The test statistic is:

[math]\displaystyle{ f = \frac{\sum^n_{i=1} w_i(\hat{y}_i - \bar{y})^2 / df_1}{\sum^n_{i=1} w_i(y_i - \hat{y}_i )^2 / df_2} }[/math]

where:

[math]\displaystyle{ y_i }[/math] is the [math]\displaystyle{ i }[/math]th of [math]\displaystyle{ n }[/math] observed values of a numeric variable,

[math]\displaystyle{ \hat{y}_i }[/math] is a value fitted by weighted least squares,

[math]\displaystyle{ df_1 = k }[/math],

[math]\displaystyle{ k }[/math] is the number of independent variables in the weighted least squares (excluding the constant),

[math]\displaystyle{ df_2 = \sum^n_{i=1}w_i - k - 1 }[/math],

[math]\displaystyle{ w_i }[/math] is the Calibrated Weight, and

[math]\displaystyle{ p \approx \Pr(F_{df_1,df_2} \ge f) }[/math].

See also