Exact Confidence Intervals for P sub 1 to P sub 2 in 2 by 2 Contingency Tables.
CORNELL UNIV ITHACA N Y SCHOOL OF OPERATIONS RESEARCH AND INDUSTRIAL ENGINEERING
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Consider two binomial populations Pi sub 1 and Pi sub 2 having success probabilities P sub 1 in 0,1 and P sub 2 in 0,1 respectively. This paper studies the problem of constructing exact small sample confidence intervals for the difference of the success probabilities, delta is nearly to P sub 1 to P sub 2 and their ratio the relative risk, Rho is nearly to P sub 1P sub 2 based on independent random samples of sizes N sub 1 and N sub 2 from Pi sub 1 and Pi sub 2 respectively. These are nuisance parameter problems hence the proposed intervals achieve coverage probabilities greater than or equal to their nominal 1-alpha levels. Two methods of constructing intervals are proposed. The first one is based on the well known conditional intervals for the odds ratio. The second method directly generates unconditional intervals of the desired size. An algorithm is given for producing the intervals for arbitrary N sub 1 and N sub 2. The 2x2 case is given as an illustrative example. Some comparisons are made.
- Statistics and Probability