Abstract
This work studies the performance of certain information theoretic techniques and two classical hypothesis testing procedures in identifying the correct models for population means in one factor ANOVA. A simulation study is used, and data samples are generated to conform to assumptions of the one factor fixed effects analysis of variance. Data sets with three data samples in each set are generated for different combinations of population means and sample sizes with equal variances for the samples. The sizes of the three samples are specified both equal and unequal. Three different specifications of population means are studied, all three means equal, two means equal and one mean different, and all three means different. The effectiveness of each statistical technique is measured by the empirical probabilities of selecting the correct model for the population means.
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References
Akaike, H. (1974). A New Look at the Statistical Model Identification. IEEE Transactions on Automatic Control, AC-19, 716–723.
Bozdogan, H. (1981). Multiple Sample Cluster Analysis and Approaches to Validity Studies in Clustering Individuals. Doctoral Dissertation, University of Illinois at Chicago Circle.
Bozdogan, H. & Sclove, S.L. (1984). Multi-sample Cluster Analysis Using Akaike’s Information Criterion. Annals of the Institute of Statistical Mathematics, Vol.36, 134–180.
Bozdogan, H. (1987). Model Selection and Akaike’s Information Criterion: The General Theory and its Analytical Extensions. Psychometrica, Vol.52, No.3, Special Section, 345–370.
Geweke, J. and Meese, R. (1981) Estimating Regression Models of Finite but Unknown Order, International Economic Review, Vol.22, 55–70.
Kotz, D., et.al. (1991) Latex and the GNUPLOT Plotting Program. GNUPLOT, MS-DOS Version 3.0, Dartmouth.
IMSL-International Mathematics and Statistical Library. (1985) IMSL,Inc., Houston.
Kirk, R.E. (1982). Experimental Design, Second Edition. Brooks/Cole Publishing Co., Belmont.
Mood, A.M., Graybill, F.A. & Boes, D.C. (1974). Introduction to the Theory of Statistics, Third Edition. McGraw-Hill Book Company, New York.
Rosenblum, E.P. (1985) A Simulation Study of Information Theoretic Techniques and F Tests in One Factor Analysis of Variance. Doctoral Dissertation, University of Virginia, Charlottesville.
Schwarz, G. (1978). Estimating the Dimension of a Model. The Annals of Statistics, Vol.6, No.2, 461–464.
Sclove, S. L. (1987). Application of Model-Selection Criteria to Some Problems in Multivariate Analysis, Psychometrika, Vol.52, No.3, Special Section, 333–343.
Stoica, P., et.al. (1986) Model-Structure Selection. Int. J. Control, Vol.43, No.6, 1841–1878.
Sugiura, N. (1979). Comparison of Information Criteria in the Selection of Regressor Variables. International Conference in Statistics in Tokyo.
Terasvirta, T. and Mellin, I. (1986). Model Selection Criteria and Model Selection Tests in Regression Models, Scand J Statist, Vol.13, 159–171.
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© 1994 Springer Science+Business Media Dordrecht
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Rosenblum, E.P. (1994). A Simulation Study of Information Theoretic Techniques and Classical Hypothesis Tests in One Factor Anova. In: Bozdogan, H., et al. Proceedings of the First US/Japan Conference on the Frontiers of Statistical Modeling: An Informational Approach. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-0800-3_13
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DOI: https://doi.org/10.1007/978-94-011-0800-3_13
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-4344-1
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