Topic 08

# Topic 08 - Topic 8 One-Way ANOVA Single Factor Analysis of...

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1 Topic 8 – One-Way ANOVA Single Factor Analysis of Variance Skim: 12.3, 17.3, 17.4

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2 Overview Note: Entire topic constitutes some review as this would be the last thing you covered in 501. We will cover it perhaps in somewhat more detail. Categorical Variables (Factors) Terminology Fixed vs. Random Effects (We’ll skip most of the random effects stuff for now and come back to it later.)
3 Overview (2) Review: Two-sample T-test ANOVA as a generalization of the two- sample T-test for categorical variables. Cell-Means and Factor-Effects ANOVA Models (same model, different form) Multiple Comparisons

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4 Terminology: The term factor is generally used to refer to a categorical predictor variable. Blood Type Gender Drug Treatment Other Examples? The term levels is used to refer to the specific categories for a factor. A / B / AB / O (could also consider +/-) Male / Female
5 Factors: Fixed or Random? A factor is fixed if the levels under consideration are the only ones of interest . The levels of the factor are selected by a non-random process and are the only levels of interest. For the time being, all factors that we will consider will be fixed. Examples?

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6 Factors: Fixed or Random? (2) A factor is random if the levels under consideration may be regarded as a sample from a larger population . Not all levels of interest are included in the study – only a random sample. We want to inferences to be applicable to the entire (larger) population of levels. Examples? Analysis is a little more complicated; we’ll save this topic for near the end of the course.
7 Example (identifying effects) To study the effect of diet on cattle, an experimenter randomly (and equally) allocates 50 cows to 5 diets (a control and 4 experimental diets). After 1 year, the cows are butchered and the amount of good meat (in pounds) is measured. Response = ______________ Cow = _______ Factor Diet = _______ Factor

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8 Notation In general, we label our factors A, B, C, etc. Factor A has levels i = 1, 2, 3, . .., a Factor B has levels j = 1, 2, 3, . .., b Factor C has levels k = 1, 2, 3, . .., c More on notation later; remember for now we are considering single factor ANOVA, so we will have only a “Factor A”.
9 Comparing Groups Suppose I want to compare heights between men and women. How would I do this?

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10 Review: Two-sample T In STAT 501 you learned to do a “Two- sample T-test” for the comparison of two sample means. We will briefly review the Two-sample T test. The reason for doing this is that ANOVA may be thought of as a direct extension of this procedure in which we make comparisons among three or more groups.
Notation for Two-Sample Settings Suppose an SRS (simple random sample) of size n 1 is selected from the 1 st population, and another SRS of size n 2 is selected from the 2 nd population. Population

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## This note was uploaded on 02/20/2012 for the course STAT 502 taught by Professor Staff during the Fall '08 term at Purdue.

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Topic 08 - Topic 8 One-Way ANOVA Single Factor Analysis of...

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