REFERENCES
- J.H. Zar, Biostatistical Analysis, Prentice–Hall Inc. Simon and Schuster/A Viacom Company, New Jersey, NJ, 1999.
- M. Mendeş, E. Başinar, and F. Gürbüz, Confidence interval for test power in Welch, James-second order and Alexander–Govern tests: A simulation study, Y.Y.Ü. Fen Bilimleri Enstitüsü Dergisi 10(1) (2005), pp. 16–22.
- B.L. Welch, On the comparison of several mean values: An alternative approach, Biometrika 38 (1951), pp. 933–943.
- M.B. Brown, A.B. Forsythe, The small sample behaviour of some statistics which test the equality of several means, Technometrics 16 (1974), pp. 129–132. doi: 10.1080/00401706.1974.10489158
- G.S. James, The comparison of several groups of observations when ratios of the population variances are unknow, Biometrika 38 (1951), pp. 324–329.
- R.A. Alexander and D.M. Govern, A new and simpler approximation for ANOVA under variance heterogeneity, J. Educ. Stat. 19 (1994), pp. 91–101. doi: 10.2307/1165140
- E.R. Ott, Analysis of means: A graphical procedure, İndus. Qual. Cont. 24 (1967), pp. 101–109.
- P.F. Raming, Application of the analysis of means, J. Qual. Technol. 15 (1983), pp. 19–25.
- P.P. Nelson, Multiple comparisons of means using simultaneous confidence intervals, J. Qual. Technol. 21 (1989), pp. 232–241.
- P.P. Nelson, P.S. Wludyka, and K.A.F. Copeland, The analysis of means: A graphical method for comparing means, rates and proportions, ASA-SIAM Series on Statistics and Applied Probability, SIAM, Philadelphia, ASA, Alexandria, VA, 2005.
- P.P. Nelson, The analysis of means for balanced experimental designs, J. Qual. Technol. 15 (1983), pp. 45–54.
- A.J. Tomarken and R.C. Serlin, Comparison of ANOVA alternatives under variance heterogeneity and specific noncentrality structures, Psychol. Bullet. 99(1) (1986), pp. 90–99. doi: 10.1037/0033-2909.99.1.90
- A.D. Beuckelaer, A closer examination on some parametric alternatives to the ANOVA F-test, Stat. Pap. 37(4) (1996), pp. 291–305. doi: 10.1007/BF02926110
- L. Myers, Comparability of the James’ second-order approximation test and the Alexander and Govern a statistic for non-normal heteroscedastic data, J. Stat. Comput. Simul. 60(3) (1998), pp. 207–222. doi: 10.1080/00949659808811888
- W. Pei-Chen, Modern one-way ANOVA F methods: Trimmed means, one step M-estimators and bootstrap methods, J. Quant. Res. 1 (2007), pp. 155–173.
- K. Moder, Alternatives to F test in one way ANOVA in case of heterogeneity of variances (a simulation study), Psychol. Test Assess. Model. 52(4) (2010), pp. 343–353.
- B.J. Winer, D.R. Brown, and K.M. Michels, Statistical Principles in Experimental Design, McGraw–Hill Companies, New York, NY, 1991.
- E.G. Schilling, A systematic approach to the analysis of means, J. Qual. Technol. 5(4) (1973), pp. 92–108, 147–159.
- P.R. Nelson, Power curves for the analysis of means, Technometrics 27(1) (1985), pp. 65–73.
- P.R. Nelson, Additional uses for the analysis of means and extended tables of critical values, Technometrics 35(1) (1993), pp. 61–71. doi: 10.1080/00401706.1993.10484994
- E.R. Ott and E.G. Schilling, Process Quality Control: Troubleshooting and İnterpretation of Data, 2nd ed., McGraw–Hill Companies, New York, NY, 1990.
- P.P. Nelson and E.J. Dudewicz, Exact analysis of means with unequal variances, Technometrics 44 (2002), pp. 152–160. doi: 10.1198/004017002317375109
- L.S. Nelson, Factors for the analysis of means, J. Qual. Technol. 6 (1974), pp. 175–181.
- P.G. Mathews, Design of Experiments with MINITAB, ASQ (American Society for Quality) Press, Milwaukee, WI, 2005.
- S. Balamurali and M. Kalyanasundaram, An investigation of the effects of misclassification errors on the analysis of means, Tamsui Oxford J. Inform. Math. Sci. 27(2) (2011), pp. 117–136.
- W.G. Cochran, Some methods for strengthening the common χ2-tests, Biometrics 10 (1954), pp. 417–451. doi: 10.2307/3001616
- J.C. Bradley, Robustness? Br. J. Math. Stat. Psychol. 31 (1978), pp. 144–152. doi: 10.1111/j.2044-8317.1978.tb00581.x
- T.P. Ryan, Statistical Methods for Quality Improvement, 2nd ed., John Wiley & Sons, New York, NY, 2000.
- T.H. Hsuing and S. Olejnik, Type I error rates and statistical power of the James second-order test and the univariate F test in two-way fixed-effects ANOVA models under heteroscedasticity and/or nonnormality, J. Exp. Educ. 65(1) (1996), pp. 57–71. doi: 10.1080/00220973.1996.9943463
- P.J. Schneider and D.A. Penfield, Alexander and Govern's approximation: Providing an alternative to ANOVA under variance heterogeneity, J. Exp. Educ. 65(3) (1997), pp. 271–286. doi: 10.1080/00220973.1997.9943459
- M. Mendeş, The comparison of some parametric alternative tests to one-way analysis of variance in terms of Type I error rates and test power under non-normality and homogeneity of variance. Ph.D. thesis, Ankara University Graduate School of Natural and Applied Sciences Department of Animal Science (unpublished), 2002.
- D.A. Penfield, Choosing a two-sample location test, J. Exper. Educ. 62 (1994), pp. 343–360. doi: 10.1080/00220973.1994.9944139