F-Test (ANCOVA)

The test statistic is:

$f=\frac{\sum _{i=1}^n{w}_i({\hat{y}}_i-\overline{y}{)}^2/d{f}_1}{\sum _{i=1}^n{w}_i(y_i-{\hat{y}}_i{)}^2/d{f}_2}$

where:

$y_i$ is the $i$th of $n$ observed values of a numeric variable,

${\hat{y}}_i$ is a value fitted by weighted least squares,

$d{f}_1=k$,

$k$ is the number of independent variables in the weighted least squares (excluding the constant),

$d{f}_2=\sum _{i=1}^n{w}_i-k-1$,

$w_i$ is the Calibrated Weight, and

$p\approx \mathrm{Pr}(F_{d{f}_1,d{f}_2}\ge f)$.

See also

• Reading Tables and Interpreting Significance Tests
• Overview of Statistical Testing in Q