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March, 1961 Tables for Unbiased Tests on the Variance of a Normal Population
James Pachares
Ann. Math. Statist. 32(1): 84-87 (March, 1961). DOI: 10.1214/aoms/1177705141


Tables of critical values defining an unbiased test are given for testing the null hypothesis $\sigma^2 = \sigma^2_0$ against the two-sided alternative hypothesis $\sigma^2 \neq \sigma^2_0$ where $\sigma^2$ is the variance of a normal population. Use of the tabulated values leads to the logarithmically shortest confidence limits for $\sigma^k, k > 0$. The critical values have been found to five significant figures for $\alpha = .01, .05, .10$ where $\alpha$ is the size of the critical region and for $\nu = 1(1)20, 24, 30, 40, 60, 120$ where $\nu$ equals the degrees of freedom of the chi-square distribution. A least squares equation is given which may be used to find the critical values when $\nu \geqq 10$ for $\alpha = .01, .05, .10$. Since submitting a revision of the present paper for publication, the article by Tate and Klett [6] appeared necessitating a second revision. An explanation of the overlap of the present paper with [6] is included in Section 5. In addition, a brief discussion of [2], which was called to the writer's attention by the editor, has been added in Section 5.


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James Pachares. "Tables for Unbiased Tests on the Variance of a Normal Population." Ann. Math. Statist. 32 (1) 84 - 87, March, 1961.


Published: March, 1961
First available in Project Euclid: 27 April 2007

zbMATH: 0124.10003
MathSciNet: MR119298
Digital Object Identifier: 10.1214/aoms/1177705141

Rights: Copyright © 1961 Institute of Mathematical Statistics

Vol.32 • No. 1 • March, 1961
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