If you notice that the first term is a perfect square, and the second term is a perfect square, and you have a negative here, we can say that it is "the difference of two squares." What we want to do ...

The main effect of factor A is defined as the difference in the means of the two levels of A averaged over all the levels of B. For Figure 1b, the average for level a is τ = (0 + 1)/2 = 0.5 and ...