Analyzing unreplicated two-level factorial designs by combining multiple tests

References

• Aboukalam, M. A. F., and A. A. Al-Shiha. 2001. A robust analysis for unreplicated factorial experiments. Computational Statistics & Data Analysis 36 (1):31–46. doi: 10.1016/S0167-9473(00)00027-X.
   Web of Science ®Google Scholar
• Al-Shiha, A. A., and S.-S. Yang. 1999. A multistage procedure for analyzing unreplicated factorial experiments. Biometrical Journal 41 (6):659–70. doi: 10.1002/(SICI)1521-4036(199910)41:6¡659::AID-BIMJ659¿3.0.CO;2-0.
   Web of Science ®Google Scholar
• Al-Shiha, A. A., and S.-S. Yang. 2000. Critical values and some properties of a new test statistic for analyzing unreplicated factorial experiments. Biometrical Journal 42 (5):605–16.
   Web of Science ®Google Scholar
• Benski, C., and E. Cabau. 1995. Unreplicated experimental designs in reliability growth programs. IEEE Transactions on Reliability 44 (2):199–205. doi: 10.1109/24.387371.
   Web of Science ®Google Scholar
• Benski, H. C. 1989. Use of a normality test to identify significant effects in factorial designs. Journal of Quality Technology 21 (3):174–8. doi: 10.1080/00224065.1989.11979166.
   Web of Science ®Google Scholar
• Berk, K. N., and R. R. Picard. 1991. Significance tests for saturated orthogonal arrays. Journal of Quality Technology 23 (2):79–89. doi: 10.1080/00224065.1991.11979297.
   Web of Science ®Google Scholar
• Birnbaum, A. 1959. On the analysis of factorial experiments without replication. Technometrics 1 (4):343–57. doi: 10.1080/00401706.1959.10489867.
   Google Scholar
• Birnbaum, A. 1961. A multi-decision procedure related to the analysis of single degrees of freedom. Annals of the Institute of Statistical Mathematics 12 (3):227–36.
   Web of Science ®Google Scholar
• Bissell, A. F. 1989. Interpreting mean squares in saturated fractional designs. Journal of Applied Statistics 16 (1):7–18. doi: 10.1080/02664768900000002.
   Google Scholar
• Bissell, A. F. 1992. Mean squares in saturated fractional designs revisited. Journal of Applied Statistics 19 (3):351–66.
   Google Scholar
• Box, G. E. P., and R. D. Meyer. 1986. An analysis for unreplicated fractional factorials. Technometrics 28 (1):11–8. doi: 10.1080/00401706.1986.10488093.
   Web of Science ®Google Scholar
• Chen, H. H., and C.-S. Cheng. 2006. Doubling and projection: A method of constructing two-level designs of resolution IV. The Annals of Statistics 34 (1):546–58. doi: 10.1214/009053605000000813.
   Web of Science ®Google Scholar
• Chen, Y. 2003. On the analysis of unreplicated factorial designs. PhD thesis, Department of Statistics, Universität Dortmund.
   Google Scholar
• Chen, Y., and J. Kunert. 2004. A new quantitative method for analysing unreplicated factorial designs. Biometrical Journal 46 (1):125–40. doi: 10.1002/bimj.200210005.
   Web of Science ®Google Scholar
• Daniel, C. 1959. Use of half-normal plots in interpreting factorial two-level experiments. Technometrics 1 (4):311–41. doi: 10.1080/00401706.1959.10489866.
   Google Scholar
• Dong, F. 1993. On the identification of active contrasts in unreplicated fractional factorials. Statistica Sinica 3 (1):209–17.
   Web of Science ®Google Scholar
• Elsawah, A. M. 2021. Multiple doubling: A simple effective construction technique for optimal two-level experimental designs. Statistical Papers 62 (6):2923–67. doi: 10.1007/s00362-020-01221-0.
   Web of Science ®Google Scholar
• Elsawah, A. M., and H. Qin. 2015. A new strategy for optimal foldover two-level designs. Statistics & Probability Letters 103:116–26. doi: 10.1016/j.spl.2015.04.020.
   Web of Science ®Google Scholar
• Haaland, P. D., and M. A. O’Connell. 1995. Inference for effect-saturated fractional factorials. Technometrics 37 (1):82–93. doi: 10.1080/00401706.1995.10485890.
   Web of Science ®Google Scholar
• Hamada, M., and N. Balakrishnan. 1998. Analyzing unreplicated factorial experiments: A review with some new proposals. Statistica Sinica 8 (1):1–28.
   Web of Science ®Google Scholar
• Holms, A. G., and J. N. Berrettoni. 1969. Chain-pooling ANOVA for two-level factorial replication-free experiments. Technometrics 11 (4):725–46. doi: 10.1080/00401706.1969.10490734.
   Web of Science ®Google Scholar
• Johnson, E. G., and J. W. Tukey. 1987. Graphical exploratory analysis of variance illustrated on a splitting of the Johnson and Tsao data. In Design, data & analysis, ed. L. M. Colin. New York: John Wiley & Sons, Inc.
   Google Scholar
• Juan, J., and D. Pefña. 1992. A simple method to identify significant effects in unreplicated two-level factorial designs. Communications in Statistics - Theory and Methods 21 (5):1383–403. doi: 10.1080/03610929208830854.
   Web of Science ®Google Scholar
• Le, N. D., and R. H. Zamar. 1992. A global test for effects in 2k factorial design without replicates. Journal of Statistical Computation and Simulation 41 (1-2):41–54. doi: 10.1080/00949659208811390.
   Google Scholar
• Lenth, R. V. 1989. Quick and easy analysis of unreplicated factorials. Technometrics 31 (4):469–73. doi: 10.1080/00401706.1989.10488595.
   Web of Science ®Google Scholar
• Loh, W.-Y. 1992. Identification of active contrasts in unreplicated factorial experiments. Computational Statistics & Data Analysis 14 (2):135–48. doi: 10.1016/0167-9473(92)90169-G.
   Web of Science ®Google Scholar
• Loughin, T. M., and W. Noble. 1997. A permutation test for effects in an unreplicated factorial design. Technometrics 39 (2):180–90. doi: 10.1080/00401706.1997.10485083.
   Web of Science ®Google Scholar
• Malekzadeh, A., and M. Kharrati-Kopaei. 2019. Inferences on the common mean of several heterogeneous log-normal distributions. Journal of Applied Statistics:1-18 46 (6):1066–83. doi: 10.1080/02664763.2018.1531980.
   Web of Science ®Google Scholar
• Miller, A. 2005. The analysis of unreplicated factorial experiments using all possible comparisons. Technometrics 47 (1):51–63. doi: 10.1198/004017004000000608.
   Web of Science ®Google Scholar
• Montgomery, D. C. 1984. Design and analysis of experiments. 2nd ed. New York: John Wiley & Sons.
   Google Scholar
• Montgomery, D. C. 2009. Introduction to statistical quality control. New York: John Wiley & Sons.
   Google Scholar
• Sadooghi-Alvandi, S. M., and M. Kharrati-Kopaei. 2015. Non-existence of a best test for analyzing unreplicated two-level factorial designs, unpublished manuscript. Shiraz, Iran: Shiraz University.
   Google Scholar
• Schneider, H., W. J. Kasperski, and L. Weissfeld. 1993. Finding significant effects for unreplicated fractional factorials using the n smallest contrasts. Journal of Quality Technology 25 (1):18–27. doi: 10.1080/00224065.1993.11979412.
   Web of Science ®Google Scholar
• Seheult, A., and J. Tukey. 1982. Some resistant procedures for analyzing 2n factorial experiments. Utilitas Mathematica B 21:57–98.
   Google Scholar
• Shenavari, Z., and M. Kharrati-Kopaei. 2018. A method for testing additivity in unreplicated two-way layouts based on combining multiple interaction tests. International Statistical Review 86 (3):469–87. doi: 10.1111/insr.12262.
   Web of Science ®Google Scholar
• Venter, J. H., and S. J. Steel. 1996. A hypothesis-testing approach toward identifying active contrasts. Technometrics 38 (2):161–9. doi: 10.1080/00401706.1996.10484461.
   Web of Science ®Google Scholar
• Voss, D. T. 1988. Generalized modulus-ratio tests for analysis of factorial designs with zero degrees of freedom for error. Communications in Statistics - Theory and Methods 17 (10):3345–59. doi: 10.1080/03610928808829808.
   Web of Science ®Google Scholar
• Voss, D. T. 1999. Analysis of orthogonal saturated designs. Journal of Statistical Planning and Inference 78 (1-2):111–30. doi: 10.1016/S0378-3758(98)00210-9.
   Web of Science ®Google Scholar
• Voss, D. T., and W. Wang. 2006. On adaptive testing in orthogonal saturated designs. Statistica Sinica 16 (1):227–34.
   Web of Science ®Google Scholar
• Weng, L.-C., A. M. Elsawah, and K.-T. Fang. 2021. Cross-entropy loss for recommending efficient fold-over technique. Journal of Systems Science and Complexity 34 (1):402–39. doi: 10.1007/s11424-020-9267-9.
   Web of Science ®Google Scholar
• Wu, S. S., and W. Wang. 2007. Step-up simultaneous tests for identifying active effects in orthogonal saturated designs. Annals of Statistics 35 (1):449–63.
   Web of Science ®Google Scholar
• Ye, K. Q., M. Hamada, and C. F. J. Wu. 2001. A step-down Lenth method for analyzing unreplicated factorial designs. Journal of Quality Technology 33 (2):140–52. doi: 10.1080/00224065.2001.11980063.
   Web of Science ®Google Scholar
• Zahn, D. A. 1975a. An empirical study of the half-normal plot. Technometrics 17 (2):201–11. doi: 10.2307/1268352.
   Web of Science ®Google Scholar
• Zahn, D. A. 1975b. Modifications of and revised critical values for the half-normal plot. Technometrics 17 (2):189–200.
   Web of Science ®Google Scholar