– YME is the predicted value obtained from a regression of Y on the main effects and fake factors.
There is no need to include the block factor in YME because of the fold-over structure of the design. The block factor is included in Y2nd.
 – Y2nd is given by Y2nd = Y - YME.
Note: In a DSD, the columns YME and Y2nd are orthogonal.
 • Stage 1: The response Y is used to identify main effects. Stage 1 identifies the main effects that are considered active.
 • Stage 2: The response Y2nd is used to identify second-order effects. Stage 2 considers all second-order terms in the active main effects from Stage 1 and determines a subset of these containing effects considered to be active.
 2 Using YME, main effects are tested against this estimate. Main effects with p-values less than a threshold p-value are considered active. The threshold values are the following:
 – For one error degree of freedom, the threshold value is 0.20.
 – For two error degrees of freedom, the threshold value is 0.10.
 – For more than two error degrees of freedom, the threshold value is 0.05.
 3 If no main effect has a p-value less than the threshold value, conclude that there are no active main effects and no active two-factor effects. The procedure terminates.
 4 If active main effects are found, then variability from the inactive main effects is pooled into the error variance constructed in (1).
 1 The absolute values of the estimated effects, using YME as the response, are ordered from largest to smallest.
 2 For each 1 ≤ i < m, the effect with the ith largest absolute value is tested against the adjusted residual sum of squares for the model containing that effect and all effects with larger absolute values.
 3 The effects in the model with the smallest p-value are considered to be the active effects.
 4
 • For one error degree of freedom, the threshold value is 0.20.
 • For two error degrees of freedom, the threshold value is 0.10.
 • For more than two error degrees of freedom, the threshold value is 0.05.
 1 The variability for Y2nd is tested against the error estimate from Stage 1 to determine if there is additional variability due to second-order effects.
 – If the p-value for this test exceeds the threshold value the procedure terminates and no active second-order effects are identified.
 2 If the p-value for this test is less than or equal to the threshold value, then subsets of size k, k = 1,2,3,... are successively tested, starting with k = 1.
 3 For each k, the residual sum of squares for each subset of that size is tested against the error estimate from Stage 1. The subset with the smallest RMSE is identified.
 4 The procedure continues until a k is found whose RMSE is smaller than the Stage 1 RMSE.
 5 The effects in the subset preceding the one that corresponds to the terminal value of k are considered to be the active two-factor effects.

Help created on 9/19/2017