Chapter 4
OneWay 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, oneway ANOVA,
which uses one factor and one response variable. We’ll also study a more
complicated setup in the next chapter, twoway 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 OneWay 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 OneWay ANOVA
55
Setup
Typically, when we think about oneway 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
,μ
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 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.
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 Summer '08
 TA
 Statistics, Normal Distribution, Statistical hypothesis testing

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