ECONOMETRICS: USING COMPUTER PROGRAMS TO COMPUTE EXACT BINOMIAL PROPORTION CONFIDENCE INTERVALS BY THE CLOPPER – PEARSON METHOD

Abstract

The article cites several methods of computing confidence intervals for the probability of an event (or a parameter of the binomial distribution), which are based on the global form of the de Moivre – Laplace theorem and therefore assume a sufficiently large sample size, namely Wald interval, Wilson score interval, Agresti – Coull interval, and the arcsine transformation. The advantages of using the exact Clopper – Pearson method, which does not rely on approximating the binomial distribution with the normal distribution, are formulated and substantiated. Reservations about the Clopper – Pearson method expressed by some authors, who used Bayesian inference and therefore actually considered credible intervals instead of confidence intervals, are cited. The relationship between the Clopper – Pearson method of computing one-sided confidence intervals for the binomial distribution parameter and the exact solution (using the Neyman – Pearson lemma) to the problem oftesting a hypothesis about a probability value, is given. The Clopper – Pearson equations are solved using a well-knownrelationship between the binomial and the beta distribution functions. Calculating one-sided and two-sided Clopper – Pearson confidence intervals using the inverse beta function in the free and open-source application LibreOffice Calc, is detailed. For arbitrary sample size, the inverse beta function is computed with high accuracy in this application, which confirms the generality of the approach proposed in the article.