chapter04_mine - Chapter 4 One-Way ANOVA Recall this chart...

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Chapter 4 One-Way ANOVA Recall this chart that showed how most of our course would be organized: Explanatory Variable(s) Response Variable Methods Categorical Categorical Contingency Tables Categorical Quantitative ANOVA Quantitative Quantitative Regression Quantitative Categorical (not discussed) When our data consists of a quantitative response variable and one or more categorical explanatory variables, we can employ a technique called analysis of variance , abbreviated as ANOVA. The material in this chapter corresponds to the first part of Chapter 14 of the textbook. Recall that a categorical explanatory variable is also called a factor . In this chapter, we’ll study the simplest form of ANOVA, one-way ANOVA, which uses one factor and one response variable. We’ll also study a more complicated setup in the next chapter, two-way ANOVA, which uses two factors instead. (In principle, we could do ANOVA with any number of factors, but in practice, people usually stick to one or two.) 4.1 Basics of One-Way ANOVA Let’s start by discussing the way we organize and label the data for one- way ANOVA. We also need to formulate the basic question that we plan to ask.
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4.1 Basics of One-Way ANOVA 55 Z Setup Typically, when we think about one-way ANOVA, we think about the factor as dividing the subjects into groups. The goal of our analysis is then to compare the means of the subjects in each group. Notation Let g represent the number of groups. Then we’ll set things up as follows: ˆ Let μ 1 2 ,...,μ g represent the true population means of the response variable for the subjects in each group. As usual, these population parameters are what we’re really interested in, but we don’t know their values. ˆ We call each observation in the sample Y ij , where i is a number from 1 to g that identifies the group number, and j identifies the individual within that group. (For example, Y 12 represents the response variable value of the second individual in the first group.) ˆ We can calculate the sample means for each group, which we’ll call ¯ Y 1 Y , ¯ Y 2 Y ,..., ¯ Y g Y . We can use these known sample means as estimates of the corresponding unknown population means. Example 4.1: Suppose we want to see if three McDonald’s locations around town tend to put the same amount of fries in a medium order, or if some locations put more fries in the container than others. We take the next 30 days on the calendar and randomly assign 10 days to each of the three locations. On each day, we go to the specified location, order a medium order of fries, take it home, and weigh it to see how many ounces of fries it contains. The categorical explanatory variable is just which location we went to, and the quantitative response variable is the number of ounces of fries. For each of the three locations (
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This note was uploaded on 01/08/2012 for the course STA 3024 taught by Professor Ta during the Summer '08 term at University of Florida.

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chapter04_mine - Chapter 4 One-Way ANOVA Recall this chart...

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