Levene tests of homogeneity of variance for general block and treatment designs

ONeill, Michael E. and Mathews, Ky L. (2002) Levene tests of homogeneity of variance for general block and treatment designs. Biometrics, 58 1: 216-224. doi:10.1111/j.0006-341X.2002.00216.x

Author ONeill, Michael E.
Mathews, Ky L.
Title Levene tests of homogeneity of variance for general block and treatment designs
Journal name Biometrics   Check publisher's open access policy
ISSN 0006-341X
Publication date 2002-03
Sub-type Article (original research)
DOI 10.1111/j.0006-341X.2002.00216.x
Volume 58
Issue 1
Start page 216
End page 224
Total pages 9
Editor D. Commenges
B. Cullis
Place of publication Washington, D.C. USA
Publisher Blackwell Publishing
Collection year 2002
Language eng
Subject C1
230204 Applied Statistics
780101 Mathematical sciences
Abstract This article develops a weighted least squares version of Levene's test of homogeneity of variance for a general design, available both for univariate and multivariate situations. When the design is balanced, the univariate and two common multivariate test statistics turn out to be proportional to the corresponding ordinary least squares test statistics obtained from an analysis of variance of the absolute values of the standardized mean-based residuals from the original analysis of the data. The constant of proportionality is simply a design-dependent multiplier (which does not necessarily tend to unity). Explicit results are presented for randomized block and Latin square designs and are illustrated for factorial treatment designs and split-plot experiments. The distribution of the univariate test statistic is close to a standard F-distribution, although it can be slightly underdispersed. For a complex design, the test assesses homogeneity of variance across blocks, treatments, or treatment factors and offers an objective interpretation of residual plot.
Keyword Mathematics, Interdisciplinary Applications
Statistics & Probability
Factorial Treatment Designs
General Linear Model
Homogeneity Of Variance
Levene's Test
Multivariate Analysis Of Variance
Weighted Least Squares
Q-Index Code C1

Document type: Journal Article
Sub-type: Article (original research)
Collection: School of Agriculture and Food Sciences
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Created: Tue, 14 Aug 2007, 18:32:42 EST