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Volume 10, Pages 865-878
Methods Paper

Exact Probabilities and Confidence Limits for Binomial Samples: Applied to the Difference between Two Proportions

1Department of Chemistry, Technical University of Cluj-Napoca, Romania
2Department of Medical Informatics and Biostatistics, “Iuliu Hatieganu” University of Medicine and Pharmacy Cluj-Napoca, Romania

Received 5 March 2010; Revised 7 April 2010; Accepted 7 April 2010

Academic Editor: Richard Brown

Copyright © 2010 Lorentz Jäntschi and Sorana D. Bolboacă.


An exact probabilities method is proposed for computing the confidence limits of medical binomial parameters obtained based on the 2×2 contingency table. The developed algorithm was described and assessed for the difference between two binomial proportions (a bidimensional parameter). The behavior of the proposed method was analyzed and compared to four previously defined methods: Wald and Wilson, with and without continuity corrections. The exact probabilities method proved to be monotonic in computing the confidence limits. The experimental errors of the exact probabilities method applied to the difference between two proportions has never exceeded the imposed significance level of 5%.