# Topic 13 - Topic 13 Random Effects Background Reading:...

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1 Topic 13 – Random Effects Background Reading: Parts of Chapters 17 and 19

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2 Reading Summary Section 17.1 (particularly page 422) Section 17.6 (pages 438-440) Section 19.7 (pages 538-541)
3 Random Effects So far we have really only dealt with fixed effects – we set the levels (or they are at least predetermined) and are only interested in those particular levels. Often we have factors with lots of levels, and to get observations at all of them would be inconvenient if we could do it at all. So we take a random sample of levels – hence random effects.

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4 Fixed vs. Random Recall: A factor is fixed if the levels under consideration are the only ones of interest . Selected by a non- random process. (e.g. gender, hair color) A factor is random if the levels under consideration may be regarded as a sample from a larger population . Want to draw inference on this larger population of levels. (e.g. subject / person)
5 Why care about fixed/random? Affects the “expected mean squares” on which F-tests are based. No major differences for 1-way ANOVA. For ANOVA with multiple factors and interactions, we will see that different ratios of mean squares will be needed for the significance tests. The denominator will no longer always be the MSE. Affects interpretations as well (we wouldn’t do multiple comparisons for a random factor).

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6 CLG Discussion For each of three examples: 1. Identify the response variable and factors involved in each study. 2. Identify a “research question of interest”. 3. Determine the number of levels for each factor, and decide whether each factor is fixed or random.
7 Example 1 Auto manufacturer wants to study the effects of differences between drivers (A) and differences between cars (B) on gasoline consumption. Four drivers were selected at random, and additionally five cars of the same model with manual transmissions were randomly taken from the assembly line. Each driver drove each car twice over a 40-mile test course and the MPG were recorded.

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8 Example 1 Response: Research Question: Factor Levels Fixed/Random
9 Example 2 A researcher studied the sodium content of six brands of U.S. beers sold in a metropolitan area. For each beer, both the regular and light versions were examined.

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10 Example 2 Response: Research Question: Factor Levels Fixed/Random
11 Example 3 Twelve job applicants were rated by each of the three personnel officers for a company. Each applicant was rated by each officer. We want to explore whether there are differences among the personnel officers.

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12 Example 3 Response: Research Question: Factor Levels Fixed/Random
13 Random Effects - Variances When we have random effects, we have multiple variances: Variance associated with the effect itself (e.g. subject – there is a variance associated to

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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 University-West Lafayette.

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Topic 13 - Topic 13 Random Effects Background Reading:...

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