Product and Process Comparisons
7.4. Comparisons based on data from more than two processes
7.4.2. Are the means equal?
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, ti is the effect due to the i-th level of factor A, bj is the effect due to the j-th level of factor B and gij is the effect due to any interaction between the i-th level of A and the j-th 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