1
Chapter 12
Inference for OneWay ANOVA and Comparing the Means
Learning goals for this chapter:
Know how oneway ANOVA and 2sample comparison of means techniques are
related.
Test the standard deviations to see if it is appropriate to pool the variances.
Understand why it is important to pool the variances in oneway ANOVA.
Explain and check the assumptions for doing oneway ANOVA.
Calculate
2
R
and the estimate for
.
Write the correct hypotheses (includ
ing the words “population mean”) for one

way ANOVA.
Use the F test statistic and Pvalue from SPSS to perform the oneway ANOVA
test.
State the conclusion to a oneway ANOVA test in terms of the story.
Know when to use a Bonferroni multiple comparisons test.
Use SPSS to perform the Bonferroni multiple comparisons test and interpret the
output (both Pvalues and confidence intervals).
State the conclusions to a Bonferroni multiple comparisons test in terms of the
story.
Interpret sidebyside boxplots and means plots in terms of the story.
Recognize the response variable, factors, number of levels for each factor, and the
total number of observations for a story.
Identify from reading a story whether the scenario is oneway ANOVA.
Use OneWay ANOVA when you have
one categorical
and
one quantitative
variable
and you want to compare the means.
If the categorical variable has 2 groups (gender = male or female, for example), use Ch. 7
twosample comparison of means ttest.
If the categorical variable has more than 2 groups (eye color = blue, brown, black, green,
hazel, other), then use Ch 12 oneway ANOVA.
ANOVA
:
ANalysis Of Variance:
the method for comparing several means
Oneway ANOVA:
F test
for
H
0
:
1
=
2
=. . . =
I
(all
the population means are equal)
H
a
:
not all the population means are equal (at least one is different)
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Is there at least one population mean that is statistically significantly different from the
others?
When you first approach a problem which involves comparing more than 2 groups, here
is what you should do:
1.
Find the size (
n
), sample mean, and sample standard deviation of each group.
You
can then plot the means on a graph.
Do histograms of each group to look for
outliers and overall shape.
2.
Find the 5number summary (Min, Q1, Median, Q3, Max) for each group, and do
sidebyside box plots to see how much overlap there is between the groups.
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 Spring '08
 Staff
 Normal Distribution, Standard Deviation, Variance, ANOVA SPSS

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