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This article is an attempt to throw more light on the problem of choosing plotting positions for the frequencies related to ordered sample values. The problem is particularly pertinent where special-scale graph paper is used such that a straight line indicates conformance of data to type of distribution assumed to apply. Such graph paper is often briefly referred to as “probability paper.” The types of distributions here considered are the normal and the extreme-value distribution of Type I, with the accent on the extreme-value case. Various methods of determining plotting positions have been put forward and there is confusion of thought in judging what plotting convention is optimum. An optimum criterion proposed by Chernoff and Lieberman has received wide attention. Blom in a recent book develops further criteria [2]. To clarify the problem the author has analyzed the purposes to be served in plotting data on probability paper. With a specific concept of the purpose to be served in mind, it bec...

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 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 ar...