Chapter 13 - Chapter 13: Two-Way Analysis of Variance...

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1 Chapter 13: Two-Way Analysis of Variance 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? 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? Chapter 13 : F tests compare the means of populations that are classified in 2 ways ( 2 categorical and 1 quantitative variables) Example: Do brand, texture (chewy vs. crunchy), and/or their interaction make a difference to the mean taste ratings for granola bars? What’s similar for Two-Way ANOVA? Just as in One-way ANOVA we still: We still assume the data are approximately normal. The groups must have the same standard deviation (even if the means may be different). We pool to estimate the standard deviation. F statistics are used for the significance tests. What’s different for Two-Way ANOVA? We can look it each categorical variable separately, and we can look at their interaction. (With one- way ANOVA it was impossible to look at interaction.) Example (from 4 th edition of M&M): Each of the following situations is a 2-way study design. For each case, identify the response variable and both factors, and state the number of levels for each factor (I and J) and the total number of observations (N). a) A study of smoking classifies subjects as nonsmokers, moderate smokers, or heavy smokers. Samples of 80 men and 80 women are drawn from each group. Each person reports the number of hours of sleep he or she gets on a typical night. b) The strength of concrete depends upon the formula used to prepare it. An experiment compares 6 different mixtures. Nine specimens of concrete are poured from each mixture.
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This note was uploaded on 02/28/2012 for the course STAT 301 taught by Professor Staff during the Spring '08 term at Purdue University-West Lafayette.

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Chapter 13 - Chapter 13: Two-Way Analysis of Variance...

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