1
Chapter 13:
TwoWay Analysis of Variance
Chapter 7
:
Twosample comparison of means t tests (
1 categorical and 1 quantitative
variables)
Example:
Are the mean taste ratings of chewy granola bars the same as those for crunchy granola
bars if you conduct a taste test?
Chapter 12
:
F tests compare the means of several populations (
1 categorical and 1 quantitative
variables)
Example:
Are the mean taste ratings of Quaker, Kellogg’s, and Nature Valley granola bars the
same if you conduct a taste test?
Chapter 13
:
F tests compare the means of populations that are classified in 2 ways (
2 categorical and 1
quantitative
variables)
Example:
Do brand, texture (chewy vs. crunchy), and/or their interaction make a difference to the
mean taste ratings for granola bars?
What’s similar for Two
Way ANOVA?
Just as in Oneway ANOVA we still:
We still assume the data are approximately normal.
The groups must have the same standard deviation (even if the means may be different).
We pool to estimate the standard deviation.
F statistics are used for the significance tests.
What’s different for Two
Way ANOVA?
We can look it each categorical variable separately, and we can look at their interaction.
(With one
way ANOVA it was impossible to look at interaction.)
Example (from 4
th
edition of M&M):
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).
a)
A study of smoking classifies subjects as nonsmokers, moderate smokers, or heavy smokers.
Samples of 80 men and 80 women are drawn from each group.
Each person reports the
number of hours of sleep he or she gets on a typical night.
b)
The strength of concrete depends upon the formula used to prepare it.
An experiment
compares 6 different mixtures.
Nine specimens of concrete are poured from each mixture.
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 Spring '08
 Staff
 Standard Deviation, Variance, DFE, main effect, mean taste ratings

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