## The Annals of Mathematical Statistics

### Some Theorems on Quadratic Forms Applied in the Study of Analysis of Variance Problems, I. Effect of Inequality of Variance in the One-Way Classification

G. E. P. Box

#### Abstract

This is the first of two papers describing a study of the effect of departures from assumptions, other than normality, on the null-distribution of the $F$-statistic in the analysis of variance. In this paper, certain theorems required in the study and concerning the distribution of quadratic forms in multi-normally distributed variables are first enunciated and simple approximations tested numerically. The results are then applied to determine the effect of group-to-group inequality of variance in the one-way classification. It appears that if the groups are equal, moderate inequality of variance does not seriously affect the test. However, with unequal groups, much larger discrepancies appear. In a second paper, similar methods are used to determine the effect of inequality of variance and serial correlation between errors in the two-way classification.

#### Article information

Source
Ann. Math. Statist., Volume 25, Number 2 (1954), 290-302.

Dates
First available in Project Euclid: 28 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aoms/1177728786

Digital Object Identifier
doi:10.1214/aoms/1177728786

Mathematical Reviews number (MathSciNet)
MR61787

Zentralblatt MATH identifier
0055.37305

JSTOR

#### Citation

Box, G. E. P. Some Theorems on Quadratic Forms Applied in the Study of Analysis of Variance Problems, I. Effect of Inequality of Variance in the One-Way Classification. Ann. Math. Statist. 25 (1954), no. 2, 290--302. doi:10.1214/aoms/1177728786. https://projecteuclid.org/euclid.aoms/1177728786