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

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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
http://projecteuclid.org/euclid.aoms/1177728786

JSTOR
links.jstor.org

Digital Object Identifier
doi:10.1214/aoms/1177728786

Mathematical Reviews number (MathSciNet)
MR61787

Zentralblatt MATH identifier
0055.37305

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. The Annals of Mathematical Statistics 25 (1954), no. 2, 290--302. doi:10.1214/aoms/1177728786. http://projecteuclid.org/euclid.aoms/1177728786.


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See also

  • 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.