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Hypothesis estimates for contingency tables

The contingency table arises in nearly every application of statistics. However, even the basic problem of testing independence is not totally resolved. More than thirty- five years ago, Lancaster(1961) proposed using the mid p-value for testing independence in a contingency table. The mid p-value is defined as half the condition probability of the observed statistic plus the conditional probability of more extreme values, given the marginal totals. Recently there seems to be recognition that the mid p-value is quite an attractive procedure. It tends to be less conservative than the p-value derived from Fisher's exact test. However, the procedure is considered to be some what ad-hoc. We provide theory to justify mid p-values and apply the Neyman-Pearson fundamental lemma and the estimated truth approach, to derive optimal procedures, named expected p-values. The estimated truth approach views p-values as estimators of the truth function which is one or zero depending on whether the null hypothesis holds or not. A decision theory approach is taken to compare the traditional p-value with the mid p-value. For the two-sided case, the expected p-value is a new procedure that can be constructed numerically. In a contingency table of two independent binomial samplings with balanced sample sizes, the expected p-value reduces to a two-sided mid p-value . Further, numerical evidence shows that the expected p-values lead to tests which have type one error very close to the nominal level. Our theory provides strong support for mid p-value.

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Selected Publications:

1. An empirical investigation of some effects of spareness in constingency tables, Computational Statistics and Data Analysis�]with Alan Agresti�^5, 9-21 (1987).(SCI) .

2. Simultaneous estimation of Poisson means under entropy loss (with Malay Ghosh), Ann. Stat. 16, 278-291 (1988).(SCI) .

3. Ridge estimation of independent Poisson means under entropy loss, Statistics & Decisions, 10, 1-23 (1992).

4. Simultaneous estimation of Poisson means under relative squared error loss (with Y. H. Lin), Statistics & Decisions, 11, 357-375 (1993).

5. Bounded risk conditions in simultaneous estimation of independent Poisson means (with Y. H. Liu) , Journal of Statistical Planning and Inference, 47, 319-331 (1995).(SCI) .

6. Noninformative priors for the two sample normal problem (with M. Ghosh), TEST, V5, #1, 145-157 (1996).(SCI) .

7. Posterior robustness in simulataneous estimation problem with exchangeable contaminated priors (with Y. H. Liu), Journal of Statistical Planning and Inference, 65, 129-143 (1997).(SCI) .

8. An optimality theory for mid p-values in 2×2 contingency tables (with J. T. Gene Hwang), Statistica Sinica, 11, 807-826 (2001).(SCI) .

9. The Equivalence of the mid p-value and the expected p-value for testing equality of two balanced binomial proportions (with D. W. Lee J. T. Gene Hwang), Journal of statistical planning and Inference, 126, 273-280 (2004).(SCI) .

10. Improved exact confidence intervals for the odds ratio in two independent binomial samples (with Lin, C. Y.), Biometrical Journal, 48, 1008-1019 (2006).(SCI) .

11. Improved p-values for testing marginal homogeneity in 2x2 contingency tables (with Lee-Shen Chen), Communications in Statistics-Theory and Methods, 38, 1649-1663 (2009).(SCI).

12. Improved p-value tests for comparing two independent binomial proportions (with Che-Yang Lin), Communications in Statistics-Simulation and Computation, 38, 78-91(2009).(SCI).

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