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Exact One-Sided Confidence Limits For The Difference Between Two Correlated Proportions, Chris Lloyd, Max V. Moldovan
Exact One-Sided Confidence Limits For The Difference Between Two Correlated Proportions, Chris Lloyd, Max V. Moldovan
Chris J. Lloyd
We construct exact and optimal one-sided upper and lower confidence bounds for the difference between two probabilities based on matched binary pairs using well-established optimality theory of Buehler (1957). Starting with five different approximate loer and upper limits, we adjust them to have coverage probability exactly equal to the desired nominal level and then compare the resulting exact limits by their mean size. Exact limits based on the signed root likelihood ratio statistic are preferred and recommended for practical use.
Exact P-Values For Discrete Models Obtained By Estimation And Maximisation, Chris Lloyd
Exact P-Values For Discrete Models Obtained By Estimation And Maximisation, Chris Lloyd
Chris J. Lloyd
In constructing exact tests, one must deal with the possible dependence of the P-value on the nuisance parameter/s psi as well as discreteness of the sample space. A classical but heavy handed approach is to maximise over psi. We prove what has previously been understood informally, namely that maximisation produces the uinique and smallest possible P-value subject to the ordering induced by the underlying test statistic and test validity. On the other hand, allowing for the worst case will be more attractive when the P-value is less dependent on psi. We investigate the extent to which estimating psi under the …