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One-Way ANOVA

  • Ronald Christensen
Chapter
Part of the Springer Texts in Statistics book series (STS)

Abstract

In this and the following chapters, we apply the general theory of linear models to various special cases. This chapter considers the analysis of one-way ANOVA models. A one-way ANOVA model can be written
$$y_{ij} = \mu + \alpha_{i} + e_{ij}, \quad i = 1, \cdots, t, \quad j = 1, \cdots, N_i,$$
where \({\rm E}(e_{ij}) = 0, {\rm Var}(e_{ij}) = \sigma^2, {\rm and \ Cov}(e_{ij}, e_{j^{\prime}}, e_{{i^\prime j^\prime}}) = 0 {\rm when} (i, j) \neq (j^\prime, j^\prime)\). For finding tests and confidence intervals, the e ij s are assumed to have a multivariate normal distribution. Here α i is an effect for y ij belonging to the ith group of observations. Group effects are often called treatment effects because one-way ANOVA models are used to analyze completely randomized experimental designs.

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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Department of Mathematics and Statistics MSC01 11151 University of New MexicoAlbuquerqueUSA

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