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Seminars

## General Departmental Seminar Series

### Dealing with Discreteness: Making 'Exact' Confidence Intervals for Proportions, Differences of Proportions, and Odds Ratios More Exact

Alan Agresti, Department of Statistics
University of Florida

Friday, May 4, 2001, 12:00-1:00 pm

3285 Medical Sciences Center
1300 University Avenue

ABSTRACT

`Exact' methods for categorical data are exact in term of using probability distributions that do not depend on unknown parameters. However, they are conservative inferentially, having actual error probabilities for tests and confidence intervals that are bounded above by the nominal level. We examine the conservatism for interval estimation and suggest ways of reducing it. We illustrate for several parameters of interest with contingency tables, including the binomial parameter, the difference between two binomial parameters, the odds ratio and relative risk in a $2\times 2$ table, and the common odds ratio for several such tables. Less conservative behavior results from devices such as (1) inverting tests using statistics that are "less discrete," (2) inverting a single two-sided test rather than two separate one-sided tests of half the nominal level each, (3) using unconditional rather than conditional methods (where appropriate) and (4) inverting tests using alternative P-values. We also summarize simple ways of adjusting some large-sample methods to improve their small-sample performance.

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