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Erschienen in:
2011 | OriginalPaper | Buchkapitel
One-Way ANOVA
verfasst von : Ronald Christensen
Erschienen in: Plane Answers to Complex Questions
Verlag: Springer New York
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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
i
th group of observations. Group effects are often called
treatment effects
because one-way ANOVA models are used to analyze completely randomized experimental designs.