# Anova 3 - STA 3024 ANOVA Douglas Whitaker Statistics...

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Unformatted text preview: STA 3024: ANOVA Douglas Whitaker Statistics Department 17 February 2012 Douglas Whitaker (Statistics Department) STA 3024: ANOVA 17 February 2012 1 / 18 Analysis of Variance ANOVA are a class of models to explain the variability in the data. Essentially, all models are wrong, but some are useful. –George Box (famous statistician) There isn’t always just one correct way to model the data. Douglas Whitaker (Statistics Department) STA 3024: ANOVA 17 February 2012 2 / 18 One-Way ANOVA We’ve talked about the “theory” bits of one-way ANOVA a fair amount. For given response in group i (let’s say the j th one), we think that Y ij = μ i + e ij Basically, the value each Y ij (each response) is based on the mean of the group it is in, plus some random bit. We could also think of this same model as Y ij = μ + τ i + e ij where μ is some overall mean and τ i is the effect due to being in group i . This is usually known as a treatment effect. Douglas Whitaker (Statistics Department) STA 3024: ANOVA 17 February 2012 3 / 18 One-Way ANOVA These two models are different ways of thinking about the same type of variability. Y ij = μ i + e ij Y ij = μ + τ i + e ij Both are right, and both are wrong. They are both simplifications of some real phenomenon, but they both can yield important results. Also, the math works out the same for both of them. Douglas Whitaker (Statistics Department) STA 3024: ANOVA 17 February 2012 4 / 18 Blocking We talked about blocking on Wednesday. Blocking is essentially the matched pairs version of one-way ANOVA.version of one-way ANOVA....
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Anova 3 - STA 3024 ANOVA Douglas Whitaker Statistics...

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