## The Annals of Mathematical Statistics

- Ann. Math. Statist.
- Volume 28, Number 4 (1957), 902-920.

### The Comparison of the Sensitivities of Similar Experiments: Theory

D. E. W. Schumann and R. A. Bradley

#### Abstract

The comparison of the sensitivities of experiments using different scales of measurement or different experimental techniques can be effected through a comparison of noncentral variance ratios. The distribution of the ratio of two noncentral variance ratios is obtained and its properties are discussed. Based on this distribution, tests of hypotheses on the parameters on noncentrality of two noncentral variance-ratio distributions are developed. It is shown that the distribution of the ratio of two noncentral variance ratios may be approximated adequately by the distribution of the ratio of two central variance ratios with appropriately adjusted degrees of freedom. A table for use in applications of the latter distribution is given for one-sided tests at the 5% level of significance. Through the association of the distribution of the multiple correlation coefficient in regression models with that of the noncentral variance ratio, it was also possible to develop test procedures on multiple correlation coefficients. Much of the discussion in this paper is on comparisons of similar experiments in the sense that variance ratios with the same degrees of freedom are compared. However, it is shown how these results may be generalized for comparisons of dissimilar experiments.

#### Article information

**Source**

Ann. Math. Statist., Volume 28, Number 4 (1957), 902-920.

**Dates**

First available in Project Euclid: 27 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aoms/1177706792

**Digital Object Identifier**

doi:10.1214/aoms/1177706792

**Mathematical Reviews number (MathSciNet)**

MR126924

**Zentralblatt MATH identifier**

0080.12901

**JSTOR**

links.jstor.org

#### Citation

Schumann, D. E. W.; Bradley, R. A. The Comparison of the Sensitivities of Similar Experiments: Theory. Ann. Math. Statist. 28 (1957), no. 4, 902--920. doi:10.1214/aoms/1177706792. https://projecteuclid.org/euclid.aoms/1177706792