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# Lecture8_print - Chapter 13: Two-way Analysis of Variance...

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Unformatted text preview: Chapter 13: Two-way Analysis of Variance Readings: Chapter 13 1 Introduction • Chapter 7 : Comparison of means of two populations using the t test – One categorical variable with two categories and one quantitative variable – 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 : Comparison of means of several populations using the F test – One categorical variable with more than two categories and one quantitative variable – 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 : Comparison of means of populations that are classified in 2 ways using the F test – Two categorical variables and one quantitative variable – Example: Do brand, texture (chewy vs. crunchy), and/or their interaction make a differ- ence to the mean taste ratings (scale of 1-10) for granola bars? What’s Similar for Two-Way ANOVA? • Assume that the data are approximately normal • The groups have the same standard deviation • Pool to estimate the standard deviation • Use F test statistic for test of significance 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.) 2 Two-Way ANOVA • Notations for Two-Way ANOVA – I = number of categories for the first categorical variable/factor (call it A). – J = number of categories for the second categorical variable/factor (call it B). – n ij = number of observations for level i of factor A and level j of factor B. – N = total number of observations. – μ ij = population mean response for level i of factor A and level j of factor B – ¯ x ij = sample mean response for level i of factor A and level j of factor B – σ = common population standard deviation Example 1 : 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)....
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## This note was uploaded on 04/23/2011 for the course STAT 301 taught by Professor Staff during the Spring '08 term at Purdue.

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Lecture8_print - Chapter 13: Two-way Analysis of Variance...

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