The Annals of Mathematical Statistics
- Ann. Math. Statist.
- Volume 25, Number 2 (1954), 290-302.
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
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.
Ann. Math. Statist., Volume 25, Number 2 (1954), 290-302.
First available in Project Euclid: 28 April 2007
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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
- Part II: G. E. P. Box. Some Theorems on Quadratic Forms Applied in the Study of Analysis of Variance Problems, II. Effects of Inequality of Variance and of Correlation Between Errors in the Two-Way Classification. Ann. Math. Statist., Volume 25, Number 3 (1954), 484--498.