7.
Product and Process Comparisons
7.4. Comparisons based on data from more than two processes 7.4.2. Are the means equal?


The 2way
ANOVA is probably the most popular layout in Design of Experiments
The breakdown of the total (corrected for the mean) sums of squares

To begin with, let us define
a factorial experiment:
An experiment that utilizes every combination of factor levels as treatments is called a factorial experiment. In a factorial experiment with factor A at a levels and factor B at b levels, the model for the general layout can be written as where m is the overall mean response, t_{i} is the effect due to the ith level of factor A, b_{j} is the effect due to the jth level of factor B and g_{ij }is the effect due to any interaction between the ith level of A and the jth level of B. When an a x b factorial experiment is conducted with an equal number of observation per treatment combination, the total (corrected) sum of squares is partitioned as: SStotal = SS(A) + SS(B) + SS(AB) + SSE where AB represents the interaction between A and B. The resulting ANOVA table for an a x b factorial experiment
is
