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Chapter 13:
TwoWay Analysis of Variance
Learning goals for this chapter:
Know how twoway ANOVA is related to oneway ANOVA and 2sample
comparison of means techniques.
Test the standard deviations to see if it is OK to pool the variances.
Understand why it is important to be able to pool the variances for twoway
ANOVA.
Explain and check the assumptions that must be met for doing twoway ANOVA.
Calculate
2
R
and the estimate for
.
Write the 3 sets of hypotheses for twoway ANOVA.
Use the F test statistics and Pvalues from SPSS to do twoway ANOVA
hypothesis tests.
Write conclusions to twoway ANOVA tests in terms of the story, including using
the words “population mean.”
Interpret means plots in terms of the two main effects and potential interaction.
Understand that summary statistics and graphs refer to the sample data, and
hypothesis tests give us information about the population parameter.
Recognize the response variable, factors, number of levels for each factor, and the
total number of observations.
Identify whether the best statistical technique for a story is:
1sample mean,
matched pairs, 2sample comparison of means, oneway ANOVA, twoway
ANOVA, or summary statistics.
Chapter 7
:
Twosample comparison of means t tests (
1 categorical variable for sorting
and 1 quantitative
variable
for measurement
)
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 variable
for sorting and 1 quantitative
variable
for measurement
)
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 variables for sorting and 1 quantitative
variable
for measurement
)
Example:
Do brand, texture (chewy vs. crunchy), and/or their interaction make a
difference to the mean taste ratings (scale of 110) for granola bars?
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What’s similar for TwoWay ANOVA?
Just as in Oneway ANOVA we still:
assume the data are approximately normal
the groups have the same standard deviation (even if the means may be different)
pool to estimate the standard deviation
use F statistics for significance tests.
What’s different for TwoWay ANOVA?
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 Spring '08
 Staff
 Standard Deviation, Variance, main effect, twoway anova

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