![](https://d3ilqtpdwi981i.cloudfront.net/3w2vgFUkn_4OsuGTr3oYROB2bPY=/425x550/smart/https://bepress-attached-resources.s3.amazonaws.com/uploads/b1/f3/2b/b1f32b30-2a0e-460d-b2ce-a62c229951ea/thumbnail_664d6582-0a9b-4bd9-a6b7-68c395691c68.jpg)
Article
The Expected Sample Variance of Uncorrelated Random Variables with a Common Mean and Some Applications in Unbalanced Random Effects Models
Journal of Statistics Education
Document Type
Article
Disciplines
Publication Version
Published Version
Publication Date
3-1-2005
DOI
10.17877/DE290R-7656
Abstract
There is a little-known but very simple generalization of the standard result that for uncorrelated random variables with common mean µ and variance 2 σ , the expected value of the sample variance is 2 σ . The generalization justifies the use of the usual standard error of the sample mean in possibly heteroscedastic situations, and motivates elementary estimators in even unbalanced linear random effects models. The latter both provides nontrivial examples and exercises concerning method-of-moments estimation, and also helps "demystify" the whole matter of variance component estimation. This is illustrated in general for the simple one-way context and for a specific unbalanced two-factor hierarchical data structure.
Rights
This text may be freely shared among individuals, but it may not be republished in any medium without express written consent from the authors and advance notification of the editor.
Copyright Owner
Stephen B. Vardeman and Joanne R. Wendelberger
Copyright Date
2005
Language
en
File Format
application/pdf
Citation Information
Stephen B. Vardeman and Joanne Wendelberger. "The Expected Sample Variance of Uncorrelated Random Variables with a Common Mean and Some Applications in Unbalanced Random Effects Models" Journal of Statistics Education Vol. 13 Iss. 1 (2005) Available at: http://works.bepress.com/stephen_vardeman/11/
This article is from Journal of Statistics Education 13 (2005): www.amstat.org/publications/jse/v13n1/vardeman.html