Chapter 13
TwoWay Analysis of Variance
To recap: ……………….
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 (scale of 110)?
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 (scale of 110)?
Chapter 13
: F tests compare the means of populations that are classified in 2 ways (
2
categorical and 1 quantitative
variables) We will use Twoway ANOVAcompares the
means of populations that are classified two ways or the mean responses in twofactor
experiments.
Example:
Do brand (Quaker, Kellogg’s, and Nature Valley), texture (chewy vs. crunchy),
and/or their interaction make a difference to the mean taste ratings (scale of 110) for granola
bars?
What’s similar for TwoWay ANOVA? Just as in Oneway ANOVA we still:
1
• assume the data are approximately normal
2
• the groups have the same standard deviation (even if the means may be different)
3
• pool to estimate the standard deviation
4
• use F statistics for significance tests.
What’s different for TwoWay ANOVA?
We can look at each categorical variable separately, and we can look at their interaction.
(With oneway ANOVA it was impossible to look at interaction.)
Examples 1 & 2:
For the two examples below, identify the response variable and both
factors, and state the number of levels for each factor (I and J) and total number of
observations (N).
1.
The strength of concrete depends upon the formula used to prepare it.
An experiment
compares six different mixtures.
Nine specimens of concrete are poured from each
mixture.
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 Spring '08
 Staff
 Standard Deviation, Variance, GPi, twoway anova

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