Campus Units

Statistics, Industrial and Manufacturing Systems Engineering

Document Type

Article

Publication Version

Published Version

Publication Date

3-2005

Journal or Book Title

Journal of Statistics Education

Volume

13

Issue

1

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.

Comments

This article is from Journal of Statistics Education 13 (2005): www.amstat.org/publications/jse/v13n1/vardeman.html

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

Language

en

File Format

application/pdf

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