Comparison of one-way ANOVA tests under unequal variances in terms of median p-values

References

• Alexander, R. A, and D. M. Govern. 1994. A new and simpler approximation for ANOVA under variance heterogeneity. Journal of Educational Statistics 19 (2):91–101. doi:10.3102/10769986019002091.
   Google Scholar
• Asiribo, O, and J. Gurland. 1990. Coping with variance heterogeneity. Communications in Statistics - Theory and Methods 19 (11):4029–48. doi:10.1080/03610929008830427.
   Web of Science ®Google Scholar
• Aspin, A. A. 1948. Interval estimates for linear combinations of means. Biometrika 35 (1):276–85.
   Google Scholar
• Bailey, B. J. R. 1980. Accurate normalizing transformations of Student's t variate. Applied Statistics 29, 304–6.
   Google Scholar
• Bhattacharya, B, and D. Habtzghi. 2002. Median of the p-value under the alternative hypothesis. The American Statistician 56 (3):202–6. doi:10.1198/000313002146.
   Web of Science ®Google Scholar
• Blanca, M. J., R. Alarcón, J. Arnau, R. Bono, and R. Bendayan. 2018. Effect of variance ratio on ANOVA robustness: Might 1.5 be the limit? Behavior Research Methods 50 (3):937–62. doi:10.3758/s13428-017-0918-2.
   PubMed Web of Science ®Google Scholar
• Brown, M. B, and A. B. Forsythe. 1974. Robust tests for the equality of variances. Journal of the American Statistical Association 69 (346):364–7. doi:10.1080/01621459.1974.10482955.
   Web of Science ®Google Scholar
• Cavus, M, and B. Yazici. 2020. Testing the equality of normal distributed and independent groups’ means under unequal variances by doex package. The R Journal 12 (2):134–54. doi:10.32614/RJ-2021-008.
   Google Scholar
• Cavus, M., B. Yazici, and A. Sezer. 2021. Penalized power approach to compare the power of the tests when Type I error probabilities are different. Communications in Statistics – Simulation and Computation 50 (7):1912–26. doi:10.1080/03610918.2019.1588310.
   Web of Science ®Google Scholar
• Dag, O., A. Dolgun, and N. M. Konar. 2018. onewaytests: An r package for one-way tests in independent groups designs. The R Journal 10 (1):175–99. doi:10.32614/RJ-2018-022.
   Google Scholar
• Dempster, A, and M. Schatzoff. 1965. Expected significance level as a sensitivity index for test statistics. Journal of the American Statistical Association 60 (310):420–36. doi:10.2307/2282680.
   Web of Science ®Google Scholar
• García-Pérez, A. 2014. The p value line: A way to choose the tuning constant in tests based on the Huber M-estimator. TEST 23 (3):536–55. doi:10.1007/s11749-014-0361-y.
   Web of Science ®Google Scholar
• Gokpinar, E, and F. Gokpinar. 2012. A test based on the computational approach for equality of means under the unequal variance assumption. Hacettepe Journal of Mathematics and Statistics 41 (4):605–13.
   Web of Science ®Google Scholar
• Hartung, J., D. Argac, and K. H. Makambi. 2002. Small sample properties of tests on homogeneity in one-way ANOVA and meta-analysis. Statistical Papers 43 (2):197–1145. doi:10.1007/s00362-002-0097-8.
   Web of Science ®Google Scholar
• Johansen, S. 1980. The Welch-James approximation to the distribution of the residual sum of squares in a weighted linear regression. Biometrika 67 (1):85–92. doi:10.1093/biomet/67.1.85.
   Web of Science ®Google Scholar
• Krishnamoorthy, K., F. Lu, and T. Mathew. 2007. A parametric bootstrap approach for anova with unequal variances: Fixed and random models. Computational Statistics & Data Analysis 51 (12):5731–42. doi:10.1016/j.csda.2006.09.039.
   Web of Science ®Google Scholar
• Lehmann, E. L. 1986. Testing Statistical Hypotheses. New York: Wiley.
   Google Scholar
• Mbah, A. K, and A. Paothong. 2015. Shapiro–Francia test compared to other normality test using expected p-value. Journal of Statistical Computation and Simulation 85 (15):3002–16. doi:10.1080/00949655.2014.947986.
   Web of Science ®Google Scholar
• Mehrotra, D. V. 1997. Improving the Brown-Forsythe solution to the generalized Behrens-Fisher problem. Communications in Statistics - Simulation and Computation 26 (3):1139–45. doi:10.1080/03610919708813431.
   Web of Science ®Google Scholar
• Murdoch, D. J., Y. L. Tsai, and J. Adcock. 2008. P-values are random variables. The American Statistician 62 (3):242–5. doi:10.1198/000313008X332421.
   Web of Science ®Google Scholar
• Ozdemir, A. F, and S. Kurt. 2006. One-way fixed effect analysis of variance under variance heterogeneity and a solution proposal. Selcuk Journal of Applied Mathematics 7 (2):81–90.
   Google Scholar
• Sackrowitz, H, and E. Samuel-Cahn. 1999. values as random variables-expected p values. The American Statistician 53 (4):326–31. doi:10.1080/00031305.1999.10474484.
   Web of Science ®Google Scholar
• Uhm, T, and S. Yi. 2021. A comparison of normality testing methods by empirical power and distribution of P-values. Communications in Statistics – Simulation and Computation. doi:10.1080/03610918.2021.1963450.
   Web of Science ®Google Scholar
• Weerahandi, S. 1995. ANOVA under unequal error variances. Biometrics 51 (2):589–99. doi:10.2307/2532947.
   Web of Science ®Google Scholar
• Welch, B. L. 1951. On the comparison of several mean values. Biometrika 38 (3-4):330–6. doi:10.1093/biomet/38.3-4.330.
   Web of Science ®Google Scholar