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# ch13_notes - Chapter 13 Analysis of Variance and...

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Chapter 13 Analysis of Variance and Experimental Design Outline: An Introduction to Analysis of Variance Analysis of Variance: Testing for the Equality of k Population Means Analysis of Variance (ANOVA) can be used to test for the equality of three or more population means using data obtained from observational or experimental studies. We want to use the sample results to test the following hypotheses. H 0 :   μ 1 = μ 2 = μ 3 = .  .  .  μ k H a :   Not all population means are equal Remarks: 1.If H 0 is rejected, we cannot conclude that all population means are different. 2. Rejecting H 0 means that at least two population means have different values. 1

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Assumptions for Analysis of Variance: 1. For each population, the response variable is normally distributed. 2. The variance of the response variable, denoted σ 2 , is the same for all of the populations. 3. The observations must be independent. Analysis of Variance: Testing for the equality of k population means. Notations: = value of observation i for treatment (population) j = number of observation for treatment (population) j = sample mean for treatment (population) j = sample variance for treatment (population) j = sample standard deviation for treatment (population) j Sample mean and sample variance for treatment j : Overall sample mean: where

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