Abstract
In this paper, we propose a multiple decision procedure for testing the homogeneity of normal means when the sample sizes and unknown variances are unequal. When there is a substantial departure from the null hypothesis we reject the null hypothesis and also identify the levels that contributed most towards the departure from homogeneity.
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References
Basu, D. (1995). On statistics independent of a complete sufficient statistic, Sankhyā, 15, 377–380.
Graybill, F. A. (1976). Theory and Application of the Linear Model, Boston, MA: Duxbury Press.
Gupta, S. S., Huang, D. Y. and Panchapakesan, S. (1995). Multiple decision procedures in analysis of variance and regression analysis, Technical Report No. 95–44C, Center for Statistical Decision Sciences and Department of Statistics, Purdue University, West Lafayette, Indiana.
Huang, D. Y. (1996). Selection procedures in linear models, Journal of Statistical Planning and Inference, 54, 271–277.
Lee, A. F. S. (1992). Optimal sample sizes determined by two-sample Welch’s t test, Communications in Statistics—Simulation and Computation, 21, 689–696.
Ott, R. L. (1993). An Introduction to Statistical Methods and Data Analysis, Belmont, CA: Wadsworth Publishing Company, Inc.
Scheffé, H. (1970). Practical solutions of the Behrens-Fisher problem, Journal of the American Statistical Association, 65, 1501–1508.
Welch, B. L. (1937). The significance between the difference between two means when the population variances are unequal, Biometrika, 29, 350–362.
Welch, B. L. (1947). The generalization of “Student’s” problem when several different population variances are involved, Biometrika, 34 28–35.
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© 1997 Birkhäuser Boston
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Huang, DY., Lin, CC. (1997). Multiple Decision Procedures for Testing Homogeneity of Normal Means With Unequal Unknown Variances. In: Panchapakesan, S., Balakrishnan, N. (eds) Advances in Statistical Decision Theory and Applications. Statistics for Industry and Technology. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-2308-5_17
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DOI: https://doi.org/10.1007/978-1-4612-2308-5_17
Publisher Name: Birkhäuser Boston
Print ISBN: 978-1-4612-7495-7
Online ISBN: 978-1-4612-2308-5
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