Chapter 12

# Chapter 12 - Chapter 12 Introduction to Analysis of...

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Chapter 12 Introduction to Analysis of Variance PowerPoint Lecture Slides Essentials of Statistics for the Behavioral Sciences Eighth Edition by Frederick J. Gravetter and Larry B. Wallnau

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Chapter 12 Learning Outcomes
Tools You Will Need 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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12.1 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 Clear advantage over a t test: it can be used to compare more than two treatments at the same time
Figure 12.1 Typical Situation for Using ANOVA

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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 12.2 Two-Factor Research Design

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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, this is equivalent to saying that the means of the groups do not differ from each other 3 2 1 0 : H
Alternate Hypothesis for ANOVA H1 : There is at least one mean difference among the populations (Acceptable shorthand is “Not H0 ”) Issue: how many ways can H0 be wrong? All means are different from every other mean Some means are not different from some others, but other means do differ from some means

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Test statistic for ANOVA F -ratio is 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 used to define and measure the size of differences among sample means (numerator) Variance in the denominator measures the mean differences that would be expected if there is no treatment effect

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Type I Errors and Multiple-Hypothesis tests Why ANOVA (if t can compare two means)?
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