# 36 - Chapter 14: Comparing Groups: Analysis of Variance...

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1 Chapter 14: Comparing Groups: Analysis of Variance Methods Section 14.1 How Can We Compare Several Means? ANOVA

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2 Learning Objectives 1. Analysis of Variance 2. Hypotheses and Assumptions for the ANOVA Test 3. Variability Between Groups and Within Groups 4. ANOVA F- Test Statistic 5. ANOVA F- test for Comparing Population Means of Several Groups 6. The Variance Estimates and the ANOVA Table 7. Assumptions for the ANOVA F- Test and the Effects of Violating Them 8. Why Not Use Multiple t -tests?
3 Learning Objective 1 : Analysis of Variance The analysis of variance method compares means of several groups Let g denote the number of groups Each group has a corresponding population of subjects The means of the response variable for the g populations are denoted by µ 1 , µ 2 , … µ g

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4 Learning Objective 2: Hypotheses and Assumptions for the ANOVA Test The analysis of variance is a significance test of the null hypothesis of equal population means: H 0 : µ 1 = µ 2 = …= µ g The alternative hypothesis is: H a : At least two of the population means are unequal
5 Learning Objective 2: Hypotheses and Assumptions for the ANOVA Test The assumptions for the ANOVA test comparing population means are as follows: 1. The population distributions of the response variable for the g groups are normal with the same standard deviation for each group

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6 Learning Objective 2 : Hypotheses and Assumptions for the ANOVA Test 1. Randomization: In a survey sample, independent random samples are selected from the g populations In an experiment, subjects are randomly assigned separately to the g groups
7 Learning Objective 2: Example: How Long Will You Tolerate Being Put on Hold? An airline has a toll-free telephone number for reservations The airline hopes a caller remains on hold until the call is answered, so as not to lose a potential customer

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8 The airline recently conducted a randomized experiment to analyze whether callers would remain on hold longer, on the average, if they heard: An advertisement about the airline and its current promotion Muzak (“elevator music”) Classical music Learning Objective 2: Example: How Long Will You Tolerate Being Put on Hold?
9 The company randomly selected one out of every 1000 calls in a week For each call, they randomly selected one of the three recorded messages They measured the number of minutes that the caller stayed on hold before hanging up (these calls were purposely not answered) Learning Objective 2: Example: How Long Will You Tolerate Being Put on Hold?

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10 Learning Objective 2: Example: How Long Will You Tolerate Being Put on Hold?
11 Denote the holding time means for the populations that these three random samples represent by: µ 1 = mean for the advertisement µ 2 = mean for the Muzak µ 3 = mean for the classical music Learning Objective 2: Example: How Long Will You Tolerate Being Put on Hold?

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12 The hypotheses for the ANOVA test are:
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## This note was uploaded on 08/01/2011 for the course STAT 101 taught by Professor Thomas during the Spring '11 term at Pennsylvania State University, University Park.

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36 - Chapter 14: Comparing Groups: Analysis of Variance...

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