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Comparing Variances of Correlated Variables

Published online by Cambridge University Press:  01 January 2025

Ayala Cohen
Ayala Cohen*
Affiliation:
Faculty of Industrial Engineering and Management Technion, Haifa
*
Requests for reprints should be sent to Ayala Cohen, Faculty of Industrial Engineering and Management, Technion, Haifa, ISRAEL 32000.
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Abstract

A test is proposed for the equality of the variances of k ≥ 2 correlated variables. Pitman's test for k = 2 reduces the null hypothesis to zero correlation between their sum and their difference. Its extension, eliminating nuisance parameters by a bootstrap procedure, is valid for any correlation structure between the k normally distributed variables. A Monte Carlo study for several combinations of sample sizes and number of variables is presented, comparing the level and power of the new method with previously published tests. Some nonnormal data are included, for which the empirical level tends to be slightly higher than the nominal one. The results show that our method is close in power to the asymptotic tests which are extremely sensitive to nonnormality, yet it is robust and much more powerful than other robust tests.

Keywords

variancescorrelated variablesbootstrapFisher's z-transformrobustness

Information

Type
Original Paper
Information
Psychometrika , Volume 51 , Issue 3 , September 1986, pp. 379 - 391
Copyright
Copyright © 1986 The Psychometric Society

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Footnotes

This research was supported by the fund for the promotion of research at the Technion.

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