The interaction effect of A and B is

The sum of squares due to factor A, denoted by SSA, is

Similarly, the sum of squares due to the AB interaction is

The total sum of squares SST is

To get the sum of squares due to error (i.e., SSE) we subtract the sum of all the 7 factor level combinations (except 1) from SST. The degree of freedom for any factor combination is 1 and that of SSE is 8(n – 1). The significance of the interaction effect AB is tested by constructing the F-statistic,

As we see from the previous discussion, if the number of factors k in a 2k factorial design increases, the total number of runs in a complete factorial design outgrows the resources of most experimenters. If the experimenter believes that higher-order interactions are negligible, the main effects and the lower-order interactions can be estimated by running only a fraction of the complete experiment. Let us assume that in a 23 factorial design the second-order interactions are not significant and the experimenter can provide only four conditions (i.e., experimental



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