Analyzing dispersion effects from replicated factorial experiments

Recent developments in quality engineering methods have led to considerable interest in the analysis of dispersion effects from designed experiments. A commonly used method for identifying important dispersion effects from replicated experiments is based on least squares analysis of the logarithm of the within-replication variance (Bartlett and Kendall 1946). Box and Meyer (1986) introduced a pooling technique for unreplicated two-level experiments. We extend this to replicated two-level experiments and compare its performance with the least squares analysis. We show that both of these methods can be obtained as special cases of maximum likelihood estimation under normal theory. The pooling technique is generally biased and is not recommended for model identification. The least squares analysis performs well as a model identification tool, but the estimators can be inefficient. In such cases we recommend that the parameters of the identified submodel be estimated by maximum likelihood. We derive some prop...

[1]  D. Kendall,et al.  The Statistical Analysis of Variance‐Heterogeneity and the Logarithmic Transformation , 1946 .

[2]  Satterthwaite Fe.  An approximate distribution of estimates of variance components. , 1946 .

[3]  C. Daniel.  Use of Half-Normal Plots in Interpreting Factorial Two-Level Experiments , 1959 .

[4]  Irene A. Stegun,et al.  Handbook of Mathematical Functions. , 1966 .

[5]  J. Nelder,et al.  The GLIM System Release 3. , 1979 .

[6]  D. Pregibon.  Goodness of Link Tests for Generalized Linear Models , 1980 .

[7]  Chan‐Fu Chen,et al.  Score Tests for Regression Models , 1983 .

[8]  S. Weisberg,et al.  Diagnostics for heteroscedasticity in regression , 1983 .

[9]  P. McCullagh,et al.  Generalized Linear Models , 1984 .

[10]  J. Pignatiello,et al.  Discussion: Off-Line Quality Control, Parameter Design, and the Taguchi Method , 1985 .

[11]  R. N. Kackar.  Off-Line Quality Control, Parameter Design, and the Taguchi Method , 1985 .

[12]  Gordon K. Smyth,et al.  Coupled and separable iterations in nonlinear estimation , 1985 .

[13]  Vijayan N. Nair,et al.  Testing in industrial experiments with ordered categorical data , 1986 .

[14]  Daryl Pregibon,et al.  A data analysis strategy for quality engineering experiments , 1986, AT&T Technical Journal.

[15]  George E. P. Box,et al.  Dispersion Effects From Fractional Designs , 1986 .

[16]  B. Efron.  Double Exponential Families and Their Use in Generalized Linear Regression , 1986 .

[17]  M. Aitkin.  Modelling variance heterogeneity in normal regression using GLIM , 1987 .

[18]  Daryl Pregibon,et al.  $k$-Statistics and Dispersion Effects in Regression , 1987 .

[19]  Raghu N. Kacker,et al.  Performance measures independent of adjustment , 1987 .

[20]  Neil R. Ullman,et al.  Signal-to-noise ratios, performance criteria, and transformations , 1988 .