STAT 301
March 10,
2014
Homework #7 Due Wednesday
Lab #8 Friday -
will be on Blackboard soon and
must be turned in by Friday either on Blackboard
or in lab as usual.
Gradient #2 writing is Monday 3/24

Which type of test of means is it?
One-sample, matched-pairs samples, or two-sample?
Review insurance records for
dollar amount paid after fire
damage in houses equipped with a

fire extinguisher vs. houses
without one. Was there a
difference in the average dollar
amount paid?

One-Way ANOVA:
One-Way Analysis of Variance (Chpt. 12)
© 2011 W.H. Freeman and Company

4
Introduction
The two sample
t
procedures of Chapter 7 compared the means of two
populations or the mean responses to two treatments in an
experiment.
In this chapter we’ll compare
any number
of means using
Analysis of
Variance (ANOVA)
.
Note: We are comparing
means
even though the procedure is
Analysis of
Variance.

The idea of ANOVA
A
factor
is a variable that can take one of several
levels,
one for each
treatment group.
An experiment has a
one-way
or
completely randomized design
if
several levels of one factor are being studied and the individuals are
randomly assigned to its levels. (There is only one way to group the
data
.
)
Example: Which of four advertising offers mailed to sample households produces
the highest sales?
Will a lower price in a plain mailing draw more sales on average than a higher
price in a fancy brochure? Analyzing the effect of price and layout together
requires two-way
ANOVA.
Analysis of variance
(
ANOVA
)
is the technique used to determine
whether
more than two
population means are equal.
One-way ANOVA
is used for completely randomized, one-way designs.

6
The sample means for the three samples are the same for each set.
The variation
among sample means
for (a) is identical to (b).
The variation
among the individuals
within
the three samples is much less
for (b).
CONCLUSION:
the samples in (b) contain a larger amount of variation
among the sample means
relative to
the amount of variation within the
samples, so ANOVA will find
more significant differences among the
means in (b)
–
assuming equal sample sizes here for (a) and (b).
–
Note: larger samples will find more significant differences.
The Idea of ANOVA