Comparing the Variances of Two Dependent Groups

Rand R. Wilcox

Journal of Educational and Behavioral Statistics, 1990, vol. 15, issue 3, 237-247

Abstract: Let X and Y be dependent random variables with variances σ 2 x and σ 2 y . Recently, McCulloch (1987) suggested a modification of the Morgan-Pitman test of H o : σ 2 x =σ 2 y But, as this paper describes, there are situations where McCulloch’s procedure is not robust. A subsample approach, similar to the Box-Scheffe test, is also considered and found to give conservative results, in terms of Type I errors, for all situations considered, but it yields relatively low power. New results on the Sandvik-Olsson procedure are also described, but the procedure is found to be nonrobust in situations not previously considered, and its power can be low relative to the two other techniques considered here. A modification of the Morgan-Pitman test based on the modified maximum likelihood estimate of a correlation is also considered. This last procedure appears to be robust in situations where the Sandvik-Olsson (1982) and McCulloch procedures are robust, and it can have more power than the Sandvik-Olsson. But it too gives unsatisfactory results in certain situations. Thus, in terms of power, McCulloch’s procedure is found to be best, with the advantage of being simple to use. But, it is concluded that, in terms of controlling both Type I and Type II errors, a satisfactory solution does not yet exist.

Keywords: Morgan-Pitman test; Box-Scheffe test; modified maximum likelihood estimator (search for similar items in EconPapers)
Date: 1990
References: Add references at CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
https://journals.sagepub.com/doi/10.3102/10769986015003237 (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:sae:jedbes:v:15:y:1990:i:3:p:237-247

DOI: 10.3102/10769986015003237

Access Statistics for this article

More articles in Journal of Educational and Behavioral Statistics
Bibliographic data for series maintained by SAGE Publications ().