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# chapter13 - Chapter 13 Introduction to Analysis of Variance...

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Chapter 13 Introduction to Analysis of Variance PowerPoint Lecture Slides Essentials of Statistics for the Behavioral Sciences Seventh Edition by Frederick J. Gravetter and Larry B. Wallnau

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Chapter 13 Learning Outcomes
Concepts to review Variability (Chapter 4) Sum of squares Sample variance Degrees of freedom Introduction to hypothesis testing (Chapter 8) The logic of hypothesis testing Independent measures t statistic (Chapter 10)

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13.1 Introduction to Analysis of Variance Analysis of variance Used to evaluate mean differences between two or more treatments Uses sample data as basis for drawing general conclusions about populations Advantage of t test: it can be used to compare more than two treatments at a time
Figure 13.1 Typical situation in which ANOVA would be used

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Terminology Factor The independent (or quasi-independent) variable that designates the groups being compared Levels Individual conditions or values that make up a factor Factorial design A study that combines two or more factors
Figure 13.2 Research design with two factors

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Statistical hypotheses for ANOVA Null hypothesis : the level or value on the factor does not affect the dependent variable. In the population, the means of the groups do not differ from each other. 3 2 1 0 : μ = = Η
Alternate hypothesis for ANOVA • H 1 : There is at least one mean difference among the populations Several equations are possible All means are different Some means are not different, but others are

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Test statistic for ANOVA F ratio based on variance instead of sample mean differences effect treatment no with expected es) (differenc variance means sample between es) (differenc variance F =
Test statistic for ANOVA Not possible to compute a sample mean difference between more than two samples F ratio based on variance instead of sample mean difference Variance is used to define and measure the size of differences among the sample means

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chapter13 - Chapter 13 Introduction to Analysis of Variance...

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