03-anova-part1-handout

03-anova-part1-handout - STA 3024: ANOVA Douglas Whitaker...

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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. Weve 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 t-tests? Douglas Whitaker (Statistics Department) STA 3024: ANOVA 3 February 2012 2 / 34 Analysis of Variance Doing a bunch of t-tests 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 were analyzing the variability (variance), we call this Analysis of Variance (or ANOVA for short) Before we talk about ANOVA, why isnt doing a bunch of t-tests the answer to comparing more than 2 groups? Douglas Whitaker (Statistics Department) STA 3024: ANOVA 3 February 2012 3 / 34 Using a bunch of t-tests When we conduct a single t-test, what is our probability of committing a Type I Error? Right, . Lets take = 0 . 05 for this example. So our probability that we dont make a Type I Error is 0.95. If we do three t-tests at = 0 . 05 , what is the probability that we dont 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 t-tests Using three t-tests at = 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 level is 1-0.857=0.143. This. Isnt. Good. Using ANOVA takes into account this problem and eliminates it for us. (But well 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 nitty-gritty details of Analysis of Variance, lets talk about some terminology. ANOVA is used when we have categorical explanatory variables and quantitative response variables. This is very specific; we cant 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 isnt a topic well 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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This note was uploaded on 02/14/2012 for the course STA 3024 taught by Professor Ta during the Spring '08 term at University of Florida.

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03-anova-part1-handout - STA 3024: ANOVA Douglas Whitaker...

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