The Emperor's New Tests

In the past two decades, striking examples of allegedly inferior likelihood ratio tests (LRT) have appeared in the statistical literature. These examples, which arise in multiparameter hypothesis testing problems, have several common features. In each case the null hypothesis is composite, the size...

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Bibliographic Details
Published in:Statistical science 1999-11, Vol.14 (4), p.355-369
Main Authors: Perlman, Michael D., Wu, Lang
Format: Article
Language:English
Subjects:
a-admissibility
bioequivalence problem
Biometrics
Clinical trials
d-admissibility
Emperors
Fisher-Neyman debate
Hypothesis test
Hypothesis testing
Inference
likelihood ratio test
Mathematics
multiple endpoints in clinical trials
multivariate one-sided alternatives
Null hypothesis
order-restricted hypotheses
power
Ratio test
significance test
size test
Statistics
test for qualitative interactions
Therapeutic equivalency
unbiased test
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Summary:In the past two decades, striking examples of allegedly inferior likelihood ratio tests (LRT) have appeared in the statistical literature. These examples, which arise in multiparameter hypothesis testing problems, have several common features. In each case the null hypothesis is composite, the size α LRT is not similar and hence biased, and competing size α tests can be constructed that are less biased, or even unbiased, and that dominate the LRT in the sense of being everywhere more powerful. It is therefore asserted that in these examples and, by implication, many other testing problems, the LR criterion produces "inferior," "deficient," "undesirable," or "flawed" statistical procedures. This message, which appears to be proliferating, is wrong. In each example it is the allegedly superior test that is flawed, not the LRT. At worst, the "superior" tests provide unwarranted and inappropriate inferences and have been deemed scientifically unacceptable by applied statisticians. This reinforces the well-documented but oft-neglected fact that the Neyman-Pearson theory desideratum of a more (or most) powerful size α test may be scientifically inappropriate; the same is true for the criteria of unbiasedness and α-admissibility. Although the LR criterion is not infallible, we believe that it remains a generally reasonable first option for non-Bayesian parametric hypothesis-testing problems.
ISSN:0883-4237
2168-8745
DOI:10.1214/ss/1009212517