The distribution of the variance ratio, F = S 1 2 /S 2 2

Pierre Jolicoeur
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Pierre Jolicoeur: University of Montreal, Department of Biological Science

Chapter Chapter 8 in Introduction to Biometry, 1999, pp 40-41 from Springer

Abstract: Abstract The theoretical foundations of the distribution of the variance ratio were established by the British biometrician Ronald Aylmer Fisher (1890–1962), but it is the American statistician George W. Snedecor (1881-1974) who expressed that distribution with respect to the ratio of two variances and paved the way for the convenient tables available today. Snedecor denoted the ratio of two observed variances, by an upper case Fin honor of Fisher.The Fdistribution is the probability distribution of the ratio of two independent variance estimates, of which each is obtained by dividing a sum of squares of standardized normal deviations, which follows aχ 2 distribution, by the corresponding number of degrees of freedom. The variance ratio distribution is continuous and asymmetrical and ranges from 0 to + ∞ like the χ 2 distribution, but it differs from the latter by having two numbers of degrees of freedom instead of only one. The variance ratio distribution is useful not only to test the hypothesis that two normal statistical populations have equal individual variabilities (chapter 11) but also in many kinds of analyses of variance (chapters 12, 21, 26, 27, 28, etc.) where the numerator of F may reflect the possible presence of differences between the means or the estimation (regression) lines of several groups of data.

Date: 1999
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DOI: 10.1007/978-1-4615-4777-8_9

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