Analysis of Fractional Factorial Experiments

If an orthogonal basis is used for the levels, then the sum of squares due to each regressor, SSRj, is given by  

When I = 2 and the proposed 1 encoding is used, then, by definition, the basis is orthonormal, and Equation (4.27) reduces to 

To determine whether a given regressor should be in the model, calculate for each regressor the E-statistic as follows  

The value obtained from Eq. (4.30) is compared with the critical E-value denoted as E(0.95, 1, / (n - 1)). If E, is greater than E-critical, then the regressor should be kept in the model. Otherwise, the given regressor can be eliminated from the model. The ejfect due to an interaction is equal to twice the corresponding calculated regression parameter. 

---