This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Chapter 13: Twoway 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 110)? • 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 110)? • 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 110) for granola bars? What’s Similar for TwoWay 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 TwoWay ANOVA? • We can look at each categorical variable separately, and we can look at their interaction. (With oneway ANOVA it was impossible to look at interaction.) 2 TwoWay ANOVA • Notations for TwoWay 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 2way 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)....
View
Full
Document
This note was uploaded on 04/23/2011 for the course STAT 301 taught by Professor Staff during the Spring '08 term at Purdue.
 Spring '08
 Staff

Click to edit the document details