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Unformatted text preview: STA 3024: ANOVA Douglas Whitaker Statistics Department 3 February 2012 Douglas Whitaker (Statistics Department) STA 3024: ANOVA 3 February 2012 1 / 34 Analysis of Variance We spent the last few weeks reviewing old material, and we introduced some new material related to comparing two groups. We’ve talked a lot about how to compare two groups... But what about comparing more than two groups? What should we do? Should we just do a bunch of ttests? Douglas Whitaker (Statistics Department) STA 3024: ANOVA 3 February 2012 2 / 34 Analysis of Variance Doing a bunch of ttests is not the answer. What we will do is examine the variability between each group and compare it to the variability within the groups. Because we’re analyzing the variability (variance), we call this “Analysis of Variance” (or ANOVA for short) Before we talk about ANOVA, why isn’t doing a bunch of ttests the answer to comparing more than 2 groups? Douglas Whitaker (Statistics Department) STA 3024: ANOVA 3 February 2012 3 / 34 Using a bunch of ttests When we conduct a single ttest, what is our probability of committing a Type I Error? Right, α . Let’s take α = 0 . 05 for this example. So our probability that we don’t make a Type I Error is 0.95. If we do three ttests at α = 0 . 05 , what is the probability that we don’t make a Type I Error in any of them? . 95 × . 95 × . 95 = 0 . 95 3 = 0 . 857 Douglas Whitaker (Statistics Department) STA 3024: ANOVA 3 February 2012 4 / 34 Using a bunch of ttests Using three ttests at α = 0 . 05 , our true probability of not making any Type I Errors is 0.857 and not 0.95 like we would think it is. (So, essentially our real α level is 10.857=0.143. This. Isn’t. Good. Using ANOVA takes into account this problem and eliminates it for us. (But we’ll come back to this multiple testing issue in a little while.) Douglas Whitaker (Statistics Department) STA 3024: ANOVA 3 February 2012 5 / 34 ANOVA Before we jump into the nittygritty details of Analysis of Variance, let’s talk about some terminology. ANOVA is used when we have categorical explanatory variables and quantitative response variables. This is very specific; we can’t do ANOVA if we have any other arrangement of categorical/quantitative. Douglas Whitaker (Statistics Department) STA 3024: ANOVA 3 February 2012 6 / 34 ANOVA Explanatory Variable Response Variable Method Categorical Quantitative ANOVA Quantitative Quantitative Regression Categorical Categorical Contingency Tables Quantitative Categorical Logistic Regression* *Logistic regression isn’t a topic we’ll cover in depth, but I may discuss it briefly with other material. Douglas Whitaker (Statistics Department) STA 3024: ANOVA 3 February 2012 7 / 34 ANOVA (some terms) Definition A factor is a term for a categorical explanatory variable in the context of ANOVA....
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 Spring '08
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 Statistics, Variance, Douglas Whitaker, (Statistics Department)

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