The Uses and Usefulness of Binomial Probability Paper

Abstract This article describes certain uses of Binomial Probability Paper. This graph paper was designed to facilitate the employment of R. A. Fisher's inverse sine transformation for proportions. The transformation itself is designed to adjust binomially distributed data so that the variance will not depend on the true value of the proportion p, but only on the sample size n. In addition, binomial data so transformed more closely approximate normality than the raw data. The usefulness of plotting binomial data in rectangular coordinates, using a square-root scale for the number observed in each category, was first pointed out by Fisher and Mather 10. The graph paper under discussion 1 I Available from the Codex Book Company, 74 Broadway, Norwood, Mass. No. 31,298 on thin paper, No. 32,298 on thick paper. is specially ruled to make this mode of plotting both simple and rapid. A graduated quadrant makes the angular transformation (p = cos2 φ or p = sin2 φ) easily available at the same time. Most tests of counted data can be made quickly, easily and with what is usually adequate accuracy with this paper. Some 22 examples are given.