Factor-level pooling test ($F=\frac{({\mathrm{RSS}}_R-{\mathrm{RSS}}_F)/q}{{\mathrm{RSS}}_F/(n-p_F)}$)

To pool factor levels in a normal linear model, impose equality of their fitted means while retaining any needed interaction terms. Compare the resulting nested model with the full model using a nested-model F-test. For two cells each of size $m$, pooling their fitted means adds $(m/2)({\overline{Y}}_1-{\overline{Y}}_2{)}^2$ to the residual sum of squares. If pooling two pairs separately within two other-factor levels, there are four restrictions.