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Spring 2012 Chap 13

# Spring 2012 Chap 13 - Chapter 13 Two-Way Analysis of...

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Chapter 13 Two-Way Analysis of Variance To recap: ………………. Chapter 7 : Two-sample comparison of means t tests ( 1 categorical and 1 quantitative variables) 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 and 1 quantitative variables) 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 and 1 quantitative variables) We will use Two-way ANOVA--compares the means of populations that are classified two ways or the mean responses in two-factor experiments. Example: Do brand (Quaker, Kellogg’s, and Nature Valley), texture (chewy vs. crunchy), and/or their interaction make a difference to the mean taste ratings (scale of 1-10) for granola bars? What’s similar for Two-Way ANOVA? Just as in One-way ANOVA we still: 1 • assume the data are approximately normal 2 • the groups have the same standard deviation (even if the means may be different) 3 • pool to estimate the standard deviation 4 • use F statistics for significance tests. What’s different for Two-Way ANOVA? We can look at each categorical variable separately, and we can look at their interaction. (With one-way ANOVA it was impossible to look at interaction.) Examples 1 & 2: For the two examples below, identify the response variable and both factors, and state the number of levels for each factor (I and J) and total number of observations (N). 1. The strength of concrete depends upon the formula used to prepare it. An experiment compares six different mixtures. Nine specimens of concrete are poured from each mixture.

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