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Tables of the Freeman-Tukey Transformations for the Binomial and Poisson Distributions

Frederick Mosteller and Cleo Youtz
Biometrika
Vol. 48, No. 3/4 (Dec., 1961), pp. 433-440
Published by: Oxford University Press on behalf of Biometrika Trust
DOI: 10.2307/2332765
Stable URL: http://www.jstor.org/stable/2332765
Page Count: 8
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Tables of the Freeman-Tukey Transformations for the Binomial and Poisson Distributions
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Abstract

We present a table of the Freeman-Tukey variance stabilizing arc-sine transformation for the binomial distribution together with properties of the transformation. Entries in the table are $\theta = \frac{1}{2} \{\arc \sin \sqrt \big(\frac{x}{n +1}\big) + \arc \sin \sqrt \big(\frac{x +1}{n +1}\big)\},$ where n is the sample size and x is the number of successes observed in a binomial experiment. Values of θ are given in degrees, to two decimal places, for n = 1 [1] 50 and x = 0[1] n. In addition, for completeness, we give a table of the corresponding square-root transformation to two decimal places for use with Poisson counts. The observed count is x (x = 0 [1] 50) and the transformed values are $g = \sqrt x + \sqrt (x + 1)$; the squares of the transformed values are also given for use in analysis of variance computations.

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