Testing Multiple Dispersion Effects in Unreplicated Fractional Factorial Designs

In unreplicated 2k−p designs, the assumption of constant variance is commonly made. When the variance of the response differs between the two levels of a column in the effect matrix, that column produces a dispersion effect. In this article we show that two active dispersion effects may create a spurious dispersion effect in their interaction column. Most existing methods for dispersion-effect testing in unreplicated fractional factorial designs are subject to these spurious effects. We propose a method of dispersion-effect testing based on geometric means of residual sample variances. We show through examples from the literature and simulations that the proposed test has many desirable properties that are lacking in other tests.

[1]  D. Peña,et al.  A simple method to identify significant effects in unreplicated two-level factorial designs , 1992 .

[2]  B. Bergman,et al.  Dispersion effects from unreplicated designs in the 2 k-p series , 1997 .

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

[4]  P. C. Wang.  Tests for dispersion effects from orthogonal arrays , 1989 .

[5]  Narayanaswamy Balakrishnan,et al.  ANALYZING UNREPLICATED FACTORIAL EXPERIMENTS: A REVIEW WITH SOME NEW PROPOSALS , 1998 .

[6]  O. L. Davies,et al.  Design and analysis of industrial experiments , 1954 .

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

[8]  Virgil L Anderson,et al.  Design of Experiments , 2010 .

[9]  T. Loughin,et al.  A permutation test for effects in an unreplicated factorial design , 1997 .

[10]  D. Pregibon,et al.  Analyzing dispersion effects from replicated factorial experiments , 1988 .

[11]  B. Bergman,et al.  Dispersion Effects From 7 Unreplicated Designs in the 2 k—p Series , 1997 .

[12]  R. Wolfinger,et al.  Joint estimation of location, dispersion, and random effects in robust design , 1998 .

[13]  Cuthbert Daniel.  Applications of Statistics to Industrial Experimentation , 1976 .

[14]  Dennis K. J. Lin,et al.  Confounding of Location and Dispersion Effects in Unreplicated Fractional Factorials , 2001 .

[15]  R. Lenth.  Quick and easy analysis of unreplicated factorials , 1989 .

[16]  R. Carroll,et al.  Variance Function Estimation , 1987 .

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

[18]  A. Ferrer,et al.  Small samples estimation of dispersion effects from unreplicated data , 1993 .

[19]  R. Daniel Meyer,et al.  An Analysis for Unreplicated Fractional Factorials , 1986 .

[20]  Rafael Romero,et al.  A SIMPLE METHOD TO STUDY DISPERSION EFFECTS FROM NON- NECESSARILY REPLICATED DATA IN INDUSTRIAL CONTEXTS , 1995 .

[21]  Dennis K. J. Lin,et al.  A nonparametric dispersion test for unreplicated two-level fractional factorial designs , 2002 .

[22]  D. Montgomery.  USING FRACTIONAL FACTORIAL DESIGNS FOR ROBUST PROCESS DEVELOPMENT , 1990 .

[23]  G. Pan.  The Impact of Unidentified Location Effects on Dispersion-Effects Identification From Unreplicated Factorial Designs , 1999, Technometrics.