Empirical Modeling and Data Analysis for Engineers and Applied Scientists by Scott A. Pardo

Empirical Modeling and Data Analysis for Engineers and Applied Scientists by Scott A. Pardo

Author:Scott A. Pardo
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham


Compare the statistic |t| to a 100(1−α/2) percentile of a central Student’s t distribution, t1−α/2. If |t| > t1−α/2, then reject H0.

Under the alternative hypothesis that β k  = λ ≠ ν 0, the statistic has a non-central t distribution (Johnson et al. 1995) with dfe degrees of freedom and non-centrality parameter :

Note that the value of c kk is dependent upon the number of runs and replicates. It is also dependent on the way in which the factors are coded.

Suppose the experiment consists of a three factor Box-Behnken design with Helmert coding, and replication only at the center point . Furthermore, suppose that three center points are run. Thus, the experiment consists of 15 runs, as illustrated in Table 7.9. The design matrix would include the columns X1, X2, and X3 in Table 7.9, and additional columns for the intercept, the three two-way cross-product terms and the three second-order terms. In total, the design matrix, X, would have 10 columns and 15 rows.Table 7.9Three factor Box-Behnken design—from Minitab 16



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