## The Annals of Mathematical Statistics

- Ann. Math. Statist.
- Volume 35, Number 1 (1964), 206-208.

### Monotonicity of the Power Functions of Some Tests of Independence between Two Sets of Variates

T. W. Anderson and S. Das Gupta

#### Abstract

For testing independence between two sets of normally distributed variates we consider the class of test procedures which are invariant under certain groups of transformations and depend only on the sample canonical correlation coefficients [1]. The power function of such a test depends only on the population canonical correlation coefficients as parameters, which may be regarded as measures of deviation from the hypothesis. In this paper sufficient conditions on the invariant procedure for the power function to be a monotonically increasing function of each of the parameters are obtained. The likelihood-ratio test [1] and Roy's maximum root test [5] satisfy these conditions. In [4] only the unbiasedness of the maximum root test was proved, although the authors claimed to prove the monotonicity property.

#### Article information

**Source**

Ann. Math. Statist., Volume 35, Number 1 (1964), 206-208.

**Dates**

First available in Project Euclid: 27 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aoms/1177703743

**Digital Object Identifier**

doi:10.1214/aoms/1177703743

**Mathematical Reviews number (MathSciNet)**

MR158475

**Zentralblatt MATH identifier**

0212.22702

**JSTOR**

links.jstor.org

#### Citation

Anderson, T. W.; Gupta, S. Das. Monotonicity of the Power Functions of Some Tests of Independence between Two Sets of Variates. Ann. Math. Statist. 35 (1964), no. 1, 206--208. doi:10.1214/aoms/1177703743. https://projecteuclid.org/euclid.aoms/1177703743