The analysis of unreplicated factorial experiments using all possible comparisons

Technometrics

Volumn 47, Issue 1, 2005, Pages 51-63

  Miller, Arden ^a  

^a UNIVERSITY OF AUCKLAND   (New Zealand)

Author keywords

Active contrast; Geometric approach; Half normal plot; Lenth's method; Likelihood ratio test; Model selection

Indexed keywords

COMPUTER SIMULATION; INTEGRAL EQUATIONS; LEAST SQUARES APPROXIMATIONS; MATHEMATICAL MODELS; MATRIX ALGEBRA; MAXIMUM LIKELIHOOD ESTIMATION; SET THEORY; STATISTICAL METHODS; VECTORS;

ACTIVE CONTRASTS; GEOMETRIC APPROACHES; HALF-NORMAL PLOTS; LENTH'S METHOD; LIKELIHOOD RATIO TESTS; MODEL SELECTION;

NUMERICAL ANALYSIS;

EID: 13444271750     PISSN: 00401706     EISSN: None     Source Type: Trade Journal    
DOI: 10.1198/004017004000000608     Document Type: Article

References (28)

1. Aboukalam, M. A. F., and Al-Shiha, A. A. (2001), "A Robust Analysis for Unreplicated Factorial Experiments," Computational Statistics and Data Analysis, 36, 31-46.
2. Al-Shiha, A. A., and Yang, S. (1999), "A Multistage Procedure for Analyzing Unreplicated Factorial Experiments," Diametrical Journal, 41, 659-670.
3. _ (2000), "Critical Values and Some Properties of a New Test Statistic for Analyzing Unreplicated Factorial Experiments," Biometrical Journal, 42, 605-616.
4. Birnbaum, A. (1959), "On the Analysis of Fractional Factorial Experiments Without Replication," Technometrics, 1, 343-357.
5. Benski, H. C. (1989), "Use of a Normality Test to Identify Significant Effects in Factorial Designs," Journal of Quality Technology, 21, 174-178.
6. Berk, K. N., and Picard, R. R. (1991), "Significance Tests for Saturated Orthogonal Arrays," Journal of Quality Technology, 23, 79-89.
7. Box, G. E. P., Hunter, W. G., and Hunter, J. S. (1978), Statistics for Experimenters, New York: Wiley.
8. Box, G. E. P., and Meyer, R. D. (1986), "An Analysis for Unreplicated Fractional Factorials," Technometrics, 28, 11-18.
9. Chipman, H. (1996), "Bayesian Variable Selection With Related Predictors," Canadian Journal of Statistics, 24, 17-36.
10. Daniel, C. (1959), "Use of Half-Normal Plots in Interpreting Factorial Two-Level Experiments," Technometrics, 1, 311-341.
11. Dong, F. (1993), "On the Identification of Active Contrasts in Unreplicated Fractional Factorials," Statistica Sinica, 3, 209-217.
12. Fang, K.-T., and Wang, Y. (1994), Number-Theoretic Methods in Statistics, London: Chapman & Hall.
13. Haaland, P. D., and O'Connell, M. A. (1995), "Inference for Effect-Saturated Fractional Factorials," Technometrics, 37, 82-93.
14. Hamada, M., and Balakrishnan, N. (1998), "Analyzing Unreplicated Factorial Experiments: A Review With Some New Proposals," Statistica Sinica, 8, 1-41.
15. Holms, A. G., and Berrettoni, J. N. (1969), "Chain-Pooling ANOVA for Two-Level Factorial Replication-Free Experiments," Technometrics, 11, 725-746.
16. Langsrud, O., and Næs, T. (1998), "A Unified Framework for Significance Testing in Fractional Factorials," Computational Statistics and Data Analysis, 28, 413-431.
17. k Factorial Design Without Replicates," Journal of Statistical Computation and Simulation, 41, 41-54.
18. Lenth, R. V. (1989), "Quick and Easy Analysis of Unreplicated Factorials," Technometrics, 31, 469-473.
19. Miller, A. E. (2003), "The Analysis of Unreplicated Factorial Experiments From a Geometric Perspective," The Canadian Journal of Statistics, 31, 311-327.
20. _ (2004), "Limits of Error Rates for the Analysis of Unreplicated Experiments," Communications in Statistics, Part A - Theory and Methods, 33, 1587-1606.
21. Saville, D. J., and Wood, G. R. (1991), Statistical Methods: The Geometric Approach, New York: Springer-Verlag.
22. _ (1996), Statistical Methods: A Geometric Primer, New York: Springer-Verlag.
23. Small, C. G. (1996), The Statistical Theory of Shape, New York: Springer-Verlag.
24. Venter, J. H., and Steel, S. J. (1996), "A Hypothesis-Testing Approach Toward Identifying Active Contrasts," Technometrics, 38, 161-169.
25. _ (1998), "Identifying Active Contrasts by Stepwise Testing," Technometrics, 40, 304-313.
26. Voss, D. T. (1988), "Generalized Modulus-Ratio Tests for Analysis of Factorial Designs With Zero Degrees of Freedom for Error," Communications in Statistics, Part A - Theory and Methods, 17, 3345-3359.
27. Ye, K. Q., Hamada, M., and Wu, C. F. J. (2001), "A Step-Down Method for Analyzing Unreplicated Factorial Designs," Journal of Quality Technology, 33, 140-152.
28. Wu, C. F. J., and Hamada, M. (2000), Experiments Planning, Analysis, and Parametric Design Optimization, New York: Wiley.