計量生物学
Online ISSN : 2185-6494
Print ISSN : 0918-4430
原著
Bayesian Indexes of Superiority and Equivalence and the p-value of the F-test for the Variances of Normal Distributions
Masaaki DoiKazuki IdeYohei Kawasaki
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ジャーナル フリー

2017 年 38 巻 1 号 p. 1-16

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抄録

We here consider the problem of comparing the variances of two normal populations. To make a more efficient decision than that made with the conventional F-test, we propose using the Bayesian index of the superiority of the variance of one group to the other θ=Pr12 > σ22 | x1, x2). We express this index according to the hypergeometric series and the cumulative distribution functions of well-known distributions. Furthermore, we investigate the relationship between the Bayesian index and the p-value of the F-test. In addition, we propose another index, the Bayesian index of equivalence of two groups, e(Δ) = Pr(Δ < σ12 < 1/Δ | x1, x2) for 0 < Δ < 1, which is also expressed according to the hypergeometric series and the cumulative distribution functions of well-known distributions. Finally, we evaluate the properties of the Bayesian index of equivalence using simulation, and illustrate the application of the Bayesian indexes with data from actual clinical trials.

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© 2017 The Biometric Society of Japan
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