Extending Edwards likelihood ratios to simple one sided hypothesis tests. (English) Zbl 1306.62061

Summary: With regard to the one sided hypothesis test, we propose a likelihood ratio that might be viewed as a Bayes/Non-Bayes compromise in the spirit of I. J. Good [Good thinking. The foundations of probability and its applications. Minneapolis: University of Minnesota Press (1983; Zbl 0583.60001)] The influence of A. W. F. Edwards [Likelihood. An account of the statistical concept of likelihood and its application to scientific inference. Cambridge: At the University Press (1972; Zbl 0231.62005)] will also be apparent. Although we will develop some general ideas, most of our effort will focus on tests of a single unknown mean and the specific case of a sample from a normal population with unknown mean and known variance.


62F03 Parametric hypothesis testing
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[1] G. Casella and R. Berger, Reconciling Bayesian and frequentist evidence in the one-sided testing problem , Journal of the American Statistical Association, 82.397 (1987), 106-111. · Zbl 0612.62021 · doi:10.2307/2289130
[2] R. Christensen, Testing, Fisher, Neyman, Pearson, and Bayes , The American Statistician, 59.2 (2005), 121-126. · doi:10.1198/000313005X20871
[3] M. H. DeGroot and M. J. Schervish, Probability and Statistics , 3rd ed., Addison-Wesley, 2002.
[4] A. W. F. Edwards, Likelihood , Cambridge University Press, Cambridge (expanded edition, 1992, Johns Hopkins University Press, Baltimore), 1972.
[5] I. J. Good, Good Reasoning: The Foundations of Probability and Its Applications , University of Minnesota Press, 1983. · Zbl 0583.60001
[6] I. J. Good, The Bayes/non-Bayes compromise: a brief review , Journal of the American Statistical Association, 87.419 (1992), 576-606. · doi:10.1080/01621459.1992.10475256
[7] R. E. Kass and A. E. Raftery, Bayes factors , Journal of the American Statistical Association, 90.430 (1995), 791. · Zbl 0846.62028
[8] F. L. Ramsey and D. W. Schafer, The Statistical Sleuth , Brooks/Cole, 1953. · Zbl 1329.62005
[9] P. R. Rosenbaum, Observational Studies , 2nd ed., Springer, New York, 2002. · Zbl 0985.62091
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