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Chapter13

# Chapter13 - Chapter 13 Two-Way Analysis of Variance...

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1 Chapter 13: Two-Way Analysis of Variance Learning goals for this chapter: Know how two-way ANOVA is related to one-way ANOVA and 2-sample comparison of means techniques. Test the standard deviations to see if it is OK to pool the variances. Understand why it is important to be able to pool the variances for two-way ANOVA. Explain and check the assumptions that must be met for doing two-way ANOVA. Calculate 2 R and the estimate for . Write the 3 sets of hypotheses for two-way ANOVA. Use the F test statistics and P-values from SPSS to do two-way ANOVA hypothesis tests. Write conclusions to two-way ANOVA tests in terms of the story, including using the words “population mean.” Interpret means plots in terms of the two main effects and potential interaction. Understand that summary statistics and graphs refer to the sample data, and hypothesis tests give us information about the population parameter. Recognize the response variable, factors, number of levels for each factor, and the total number of observations. Identify whether the best statistical technique for a story is: 1-sample mean, matched pairs, 2-sample comparison of means, one-way ANOVA, two-way ANOVA, or summary statistics. Chapter 7 : Two-sample comparison of means t tests ( 1 categorical variable for sorting and 1 quantitative variable for measurement ) Example: Are the mean taste ratings of chewy granola bars the same as those for crunchy granola bars if you conduct a taste test (scale of 1-10)? Chapter 12 : F tests compare the means of several populations ( 1 categorical variable for sorting and 1 quantitative variable for measurement ) Example: Are the mean taste ratings of Quaker, Kellogg’s, and Nature Valley granola bars the same if you conduct a taste test (scale of 1-10)? Chapter 13 : F tests compare the means of populations that are classified in 2 ways ( 2 categorical variables for sorting and 1 quantitative variable for measurement ) Example: Do brand, texture (chewy vs. crunchy), and/or their interaction make a difference to the mean taste ratings (scale of 1-10) for granola bars?

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2 What’s similar for Two-Way ANOVA? Just as in One-way ANOVA we still: assume the data are approximately normal the groups have the same standard deviation (even if the means may be different) pool to estimate the standard deviation use F statistics for significance tests. What’s different for Two-Way ANOVA?
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Chapter13 - Chapter 13 Two-Way Analysis of Variance...

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