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Ch 5 Notes

# Ch 5 Notes - Chapter 5 ANOVA Recall this chart that showed...

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Chapter 5 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 Chapter 14 of the textbook. Recall that a categorical explanatory variable is also called a factor . The simplest form of ANOVA, one-way ANOVA, uses one factor and one response variable. We’ll also study a more complicated setup, 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.) 5.1 One-Way ANOVA First we’ll consider the simplest case, one-way ANOVA. We’ll start by consid- ering the basic setup of the problem, and then we’ll see the basic hypothesis test for analyzing it, along with a methods for constructing confidence inter- vals to follow up this test.

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5.1 One-Way ANOVA 59 Basic 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: 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. 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.) We can calculate the sample means for each group, which we’ll call ¯ Y 1 , ¯ Y 2 ,..., ¯ Y g . We can use these known sample means as estimates of the corresponding unknown population means. Example 5.1 : Suppose we want to see if our three favorite 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 we got. The categorical explanatory variable is just which location we went to, and the quantitative response variable is the number of ounces of fries.
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