Abstract
This paper deals with testing the equality of several homoscedastic normal population means. We introduce a newly developed computational approach test (CAT), which is essentially a parametric bootstrap method, and discuss its merits and demerits. In the process of studying the CAT’s usefulness, we compare it with the traditional one-way ANOVA’s F test as well as the analysis of means (ANOM) method. Further, the model robustness of the above three methods have been studied under the ‘t-model’. The motivation behind the proposed CAT is to provide the applied researchers a statistical tool to carry out a comparison of several population means, in a parametric setup, without worrying about the sampling distribution of the inherent test statistic. The CAT can be used to test the equality of several means when the populations are assumed to be heteroscedastic t-distributions.
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References
Bartlett MS: The use of transformations. Biometrics 3, 39–52 (1947). doi:10.2307/3001536
Berg BA: Markov Chain Monte Carlo simulations and their statistical analysis. World Scientific, Singapore (2004)
Casella G, George EI: Explaining the Gibbs sampler. Am Stat 46, 167–174 (1992). doi:10.2307/2685208
Efron B (1982) The Jackknife, the Bootstrap, and other resampling plans (CBMS-NSF Regional Conference Series in Applied Mathematics (Monographs, 38)). SIAM (Society for Industrial and Applied Mathematics), Philadelphia
Erdman LW: Studies to determine if antibiosis occurs among Rhizobia. J Am Soc Agron 38, 251–258 (1946)
Fisher RA: Statistical methods for research workers. Oliver & Boyd, Edinburg (1925)
Foa EB, Rothbaum BO, Riggs DS, Murdock TB: Treatment of post- traumatic stress disorder in rape victims: a comparison between cognitive behavioral procedures and counselling. J Consult Clin Psychol 59, 715–723 (1991). doi:10.1037/0022-006X.59.5.715
Hjorth UJS: Computer intensive statistical methods: validation, model selection and Bootstrap. Chapman and Hall, London (1994)
La Place PS (1827) Memoirs sur le flux et reflux lunaire atmospheric. In: Connaissance des Temps pour l’an 1830, pp 3–18
Levene H: Robust tests for equality of variance. In: Olkin, Z(eds) Contributions to probability and statistics, pp. 278–292. Stanford University Press, Paolo Alto (1960)
Lin JJ, Pal N: A note on robustness of normal variance estimators under t-distributions. Comm Stat Theory Methods 34, 1117–1126 (2005). doi:10.1081/STA-200056812
Nelson PR, Wludyka PS, Copeland KAF (2005) The analysis of means: a graphical method for comparing means, rates and proportions. SIAM (Society for Industrial and Applied Mathematics), Philadelphia
Nelson PR: Multiple comparisons of means using simultaneous confidence intervals. J Qual Technol 21, 232–241 (1989)
Pal N, Lim WK, Ling CH: A computational approach to statistical inferences. J Appl Probab Stat 2(1), 13–35 (2007)
Shapiro SS, Wilk MB: An analysis of variance test for normality (complete samples). Biometrika 52, 591–611 (1965)
Steel RGD, Torrie JH: Principles and procedures of statistics: a biometrical approach. McGraw-Hill, New York (1980)
Tsui KW, Weerahandi S: Generalized p-values in significance testing of hypotheses in the presence of nuisance parameters. J Am Stat Assoc 84, 602–607 (1989). doi:10.2307/2289949
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Chang, CH., Pal, N., Lim, W.K. et al. Comparing several population means: a parametric bootstrap method, and its comparison with usual ANOVA F test as well as ANOM. Comput Stat 25, 71–95 (2010). https://doi.org/10.1007/s00180-009-0162-z
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DOI: https://doi.org/10.1007/s00180-009-0162-z