The Annals of Mathematical Statistics

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

G. E. P. Box

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Abstract

Theorems already enunciated in a previous paper on quadratic forms are used to determine the effects of inequality of variance and first order serial correlation of errors in the two-way classification on the analysis of variance. It is found that when the appropriate null hypothesis is true, inequality of variance from column to column results in an increased chance of exceeding the significance point for the test on homogeneity of column means, and a decreased chance for the corresponding test on row means. For moderate differences in variance neither effect is large. First order serial correlation within rows produces a large effect on the "between rows" comparisons, but little effect on the "between columns" comparisons.

Article information

Source
Ann. Math. Statist. Volume 25, Number 3 (1954), 484-498.

Dates
First available in Project Euclid: 28 April 2007

Permanent link to this document
http://projecteuclid.org/euclid.aoms/1177728717

JSTOR
links.jstor.org

Digital Object Identifier
doi:10.1214/aoms/1177728717

Mathematical Reviews number (MathSciNet)
MR64361

Zentralblatt MATH identifier
0056.36604

Citation

Box, G. E. P. 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. 25 (1954), no. 3, 484--498. doi:10.1214/aoms/1177728717. http://projecteuclid.org/euclid.aoms/1177728717.


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See also

  • Part I: G. E. P. Box. 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., Volume 25, Number 2 (1954), 290--302.