@article{mehrotra_chan_berger_2003, title={A cautionary note on exact unconditional inference for a difference between two independent binomial proportions}, volume={59}, ISSN={["0006-341X"]}, DOI={10.1111/1541-0420.00051}, abstractNote={Fisher's exact test for comparing response proportions in a randomized experiment can be overly conservative when the group sizes are small or when the response proportions are close to zero or one. This is primarily because the null distribution of the test statistic becomes too discrete, a partial consequence of the inference being conditional on the total number of responders. Accordingly, exact unconditional procedures have gained in popularity, on the premise that power will increase because the null distribution of the test statistic will presumably be less discrete. However, we caution researchers that a poor choice of test statistic for exact unconditional inference can actually result in a substantially less powerful analysis than Fisher's conditional test. To illustrate, we study a real example and provide exact test size and power results for several competing tests, for both balanced and unbalanced designs. Our results reveal that Fisher's test generally outperforms exact unconditional tests based on using as the test statistic either the observed difference in proportions, or the observed difference divided by its estimated standard error under the alternative hypothesis, the latter for unbalanced designs only. On the other hand, the exact unconditional test based on the observed difference divided by its estimated standard error under the null hypothesis (score statistic) outperforms Fisher's test, and is recommended. Boschloo's test, in which the p-value from Fisher's test is used as the test statistic in an exact unconditional test, is uniformly more powerful than Fisher's test, and is also recommended.}, number={2}, journal={BIOMETRICS}, author={Mehrotra, DV and Chan, ISF and Berger, RL}, year={2003}, month={Jun}, pages={441–450} }
@article{berger_sidik_2003, title={Exact unconditional tests for a 2 x 2 matched-pairs design}, volume={12}, ISSN={["0962-2802"]}, DOI={10.1191/0962280203sm312ra}, abstractNote={The problem of comparing two proportions in a 2 × 2 matched-pairs design with binary responses is considered. We consider one-sided null and alternative hypotheses. The problem has two nuisance parameters. Using the monotonicity of the multinomial distribution, four exact unconditional tests based on p-values are proposed by reducing the dimension of the nuisance parameter space from two to one in computation. The size and power of the four exact tests and two other tests, the exact conditional binomial test and the asymptotic McNemar’s test, are considered. It is shown that the tests based on the confidence interval p-value are more powerful than the tests based on the standard p-value. In addition, it is found that the exact conditional binomial test is conservative and not powerful for testing the hypothesis. Moreover, the asymptotic McNemar’s test is shown to have incorrect size; that is, its size is larger than the nominal level of the test. Overall, the test based on McNemar’s statistic and the confidence interval p-value is found to be the most powerful test with the correct size among the tests in this comparison.}, number={2}, journal={STATISTICAL METHODS IN MEDICAL RESEARCH}, author={Berger, RL and Sidik, K}, year={2003}, month={Mar}, pages={91–108} }
@article{saikali_berger_2002, title={More powerful tests for the sign testing problem}, volume={107}, ISSN={["1873-1171"]}, DOI={10.1016/S0378-3758(02)00252-5}, abstractNote={For i=1,…,p, let Xi1,…,Xini denote independent random samples from normal populations. The ith population has unknown mean μi and unknown variance σi2. We consider the sign testing problem of testing H0:μi⩽ai, for some i=1,…,p, versus H1:μi>ai, for all i=1,…,p, where a1,…,ap are fixed constants. Here, H1 might represent p different standards that a product must meet before it is considered acceptable. For 0<α<12, we first derive the size-α likelihood ratio test (LRT) for this problem, and then we describe an intersection–union test (IUT) that is uniformly more powerful than the likelihood ratio test if the sample sizes are not all equal. For a more general model than the normal, we describe two intersection–union tests that maximize the size of the rejection region formed by intersection. Applying these tests to the normal problem yields two tests that are uniformly more powerful than both the LRT and IUT described above. A small power comparison of these tests is given.}, number={1-2}, journal={JOURNAL OF STATISTICAL PLANNING AND INFERENCE}, author={Saikali, KG and Berger, RL}, year={2002}, month={Sep}, pages={187–205} }
@misc{berger_doi_2001, title={Lehr, R. G. (2000), Letter to the editor, The American Statistician, 54,325: Comment by Berger and Doi}, volume={55}, number={4}, journal={American Statistician}, author={Berger, R. L. and Doi, J.}, year={2001}, pages={373–374} }
@misc{berger_coutant_2001, title={Wardell, D. G. (1997), "Small-sample interval estimation of Bernoulli and Poisson parameters," The American Statistician, 51, 321-325: Comment by Berger and Coutant}, volume={55}, number={1}, journal={American Statistician}, author={Berger, R. L. and Coutant, B. W.}, year={2001}, pages={85} }
@article{berger_boos_1999, title={Confidence limits for the onset and duration of treatment effect}, volume={41}, ISSN={["0323-3847"]}, DOI={10.1002/(SICI)1521-4036(199909)41:5<517::AID-BIMJ517>3.3.CO;2-V}, abstractNote={Studies of biological variables such as those based on blood chemistry often have measurements taken over time at closely spaced intervals for groups of individuals. Natural scientific questions may then relate to the first time that the underlying population curve crosses a threshold (onset) and to how long it stays above the threshold (duration). In this paper we give general confidence regions for these population quantities. The regions are based on the intersection-union principle and may be applied to totally nonparametric, semiparametric, or fully parametric models where level-α tests exist pointwise at each time point. A key advantage of the approach is that no modeling of the correlation over time is required.}, number={5}, journal={BIOMETRICAL JOURNAL}, author={Berger, RL and Boos, DD}, year={1999}, pages={517–531} }
@article{hsu_berger_1999, title={Stepwise confidence intervals without multiplicity adjustment for dose-response and toxicity studies}, volume={94}, number={446}, journal={Journal of the American Statistical Association}, author={Hsu, J. C. and Berger, R. L.}, year={1999}, pages={468–482} }
@article{berger_1999, title={The emperor's new tests - Comment}, volume={14}, ISSN={["0883-4237"]}, DOI={10.1214/ss/1009212518}, number={4}, journal={STATISTICAL SCIENCE}, author={Berger, RL}, year={1999}, month={Nov}, pages={370–381} }
@inproceedings{berger_1998, title={Using computer algebra systems to teach graduate mathematical statistics: potential and pitfalls}, volume={1}, number={1998}, booktitle={Statistical education: Expanding the Network. Proceedings of the Fifth International Conference on Teaching of Statistics. International Statistical Institute, 1998.}, author={Berger, R. L.}, year={1998}, pages={189–195} }
@inbook{berger_1997, title={Likelihood ratio tests and intersection-union tests}, booktitle={Advances in statistical decision theory and applications}, publisher={Boston: Birkhauser}, author={Berger, R. L.}, editor={S. Panchapakesan and Balakrishnan, N.Editors}, year={1997}, pages={225–237} }