An Interactive Tutorial for SPSS 10.0 for Windows©
Analysis of Covariance
(GLM Approach)
by
Julia Hartman
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© Copyright 2000, Julia Hartman
1
ANCOVA (GLM):
Introduction
Analysis of Covariance (ANCOVA) is used:
• To assess the joint significance of predictors on a
continuous outcome (GLM approach)
• To generate prediction equations for various levels
of a categorical predictor (regression approach)
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2
ANCOVA (GLM):
Introduction
This tutorial uses the General Linear Model
(GLM) approach to ANCOVA to determine
whether MCAT scores are significantly different
among medical students who had different types
of undergraduate majors, when adjusted for year
of matriculation.
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3
ANCOVA (GLM):
Introduction
• Dependent variable
 nmtot1: MCAT total (most recent)
• Fixed factor
 bmaj2: Undergraduate major
1 = Biology/Chemistry
2 = Other science/health
3 = Other
• Covariate
 matyr: Year of matriculation
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4
ANCOVA (GLM):
Starting the Procedure
• In the menu, click
Analyze
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5
ANCOVA (GLM):
Starting the Procedure
• In the menu, click on
Analyze
• Point to
General Linear Model
© Copyright 2000, Julia Hartman
6
ANCOVA (GLM):
Starting the Procedure
• In the menu, click on
Analyze
• Point to
General Linear Model
• Point to Univariate…
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7
ANCOVA (GLM):
Starting the Procedure
• In the menu, click on
Analyze
• Point to
General Linear Model
• Point to Univariate…
… and click.
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8
ANCOVA (GLM):
Selecting Variables
Choose the variables for
analysis from the list in
the variable box.
For this tutorial,
begin by scrolling
down the variable list.
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9
ANCOVA (GLM):
Selecting Variables
Point to the variable
labeled Undergraduate
Major [bmaj2]
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10
ANCOVA (GLM):
Selecting Variables
Point to the variable
labeled Undergraduate
Major [bmaj2]
…and click.
© Copyright 2000, Julia Hartman
11
ANCOVA (GLM):
Selecting Variables
Move bmaj2, a
categorical variable, to
the box labeled
Fixed Factor(s) by
clicking the arrow.
© Copyright 2000, Julia Hartman
12
ANCOVA (GLM):
Selecting Variables
Scroll back up the list,
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13
ANCOVA (GLM):
Selecting Variables
Scroll back up the list,
point to the variable
nmtot1, which is
labeled MCAT TOTAL
1992-PRESENT, MOST
RECENT
© Copyright 2000, Julia Hartman
14
ANCOVA (GLM):
Selecting Variables
Scroll back up the list,
point to the variable
nmtot1, which is
labeled MCAT TOTAL
1992-PRESENT, MOST
RECENT
…and click.
© Copyright 2000, Julia Hartman
15
ANCOVA (GLM):
Selecting Variables
Move nmtot1, a
continuous variable,
to the box labeled
Dependent Variable
by clicking the
arrow.
© Copyright 2000, Julia Hartman
16
ANCOVA (GLM):
Selecting Variables
Scroll to the top of
the list
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17
ANCOVA (GLM):
Selecting Variables
Scroll to the top of the
list, and click the
variable matyr, which
is labeled
MATRICULATION DATE.
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18
ANCOVA (GLM):
Selecting Variables
Move matyr, another
continuous variable, to
the box labeled
Covariate(s) by
clicking the arrow.
© Copyright 2000, Julia Hartman
19
ANCOVA (GLM):
Profile Plots
Request profile plots
of estimated marginal
means by clicking the
button labeled
Plots…
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20
ANCOVA (GLM):
Profile Plots
This tutorial requests a
profile plot of
matyr*bmaj2.
Click matyr in the
Factors box.
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21
ANCOVA (GLM):
Profile Plots
Move matyr to the
Horizontal Axis box by
clicking the arrow.
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22
ANCOVA (GLM):
Profile Plots
Now click bmaj2 in
the Factors box …
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23
ANCOVA (GLM):
Profile Plots
and move it to the
Separate Lines box
by clicking the arrow.
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24
ANCOVA (GLM):
Profile Plots
Click the Add button
to request the plot.
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25
ANCOVA (GLM):
Profile Plots
Click the Continue
button.
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26
ANCOVA (GLM):
Post Hoc Multiple Comparisons
To request post hoc
tests for pairwise
multiple comparisons,
click the Post Hoc…
button.
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27
ANCOVA (GLM):
Post Hoc Multiple Comparisons
Comparisons are
available for the
categorical variable
bmaj2 only.
Click bmaj2 in the
Factor(s) box.
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28
ANCOVA (GLM):
Post Hoc Multiple Comparisons
Move bmaj2 to the
Post Hoc Tests for:
box by clicking the
arrow.
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29
ANCOVA (GLM):
Post Hoc Multiple Comparisons
Request multiple
comparison test(s)
by clicking in the
corresponding
checkbox.
For this tutorial,
click Bonferroni.
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30
ANCOVA (GLM):
Post Hoc Multiple Comparisons
In SPSS, you can
request as many
multiple comparison
tests as you want.
To continue the
tutorial, click the
Continue button.
© Copyright 2000, Julia Hartman
31
ANCOVA (GLM):
Optional Descriptive Statistics
To display estimated
marginal means,
parameter estimates, and
descriptive and diagnostic
statistics, or to change the
alpha level, click the
Options… button.
© Copyright 2000, Julia Hartman
32
ANCOVA (GLM):
Options: Estimated Marginal Means
You can request an overall
(grand) marginal mean, as
well as marginal means
for the factors and the
interaction(s).
For this tutorial, click
bmaj2.
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33
ANCOVA (GLM):
Options: Estimated Marginal Means
Click the arrow to
move bmaj2 to the
Display Means for:
box.
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34
ANCOVA (GLM):
Selecting Options
Request other options by
clicking the appropriate
checkbox.
In the Display area, click
the checkbox for
Descriptive statistics…
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35
ANCOVA (GLM):
Selecting Options
…and the one for
Homogeneity tests.
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36
ANCOVA (GLM):
Selecting Options
This tutorial uses no more
options, so click the
Continue button.
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37
ANCOVA (GLM):
Run the analysis
Click the OK button
to run the ANCOVA
(GLM).
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38
ANCOVA (GLM) Output:
General Information
The labels and format
of your output may be
somewhat different.
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39
ANCOVA (GLM) Output: :
Descriptive Statistics
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40
ANCOVA (GLM) Output: :
Descriptive Statistics (continued)
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ANCOVA (GLM) Output:
Test of Equality of Error Variances
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42
ANCOVA (GLM) Output:
Tests of Between-Subjects Effects
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43
ANCOVA (GLM) Output:
Expected Mean Squares
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44
ANCOVA (GLM):
Estimated Marginal Means:
Undergraduate Major
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45
ANCOVA (GLM):
Post Hoc Tests:
Undergraduate Major
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46
ANCOVA (GLM):
Profile Plot: Gender*Resloc
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An Interactive Tutorial for
SPSS 10.0 for Windows©:
ANCOVA (GLM)
Click one of the following:
• Repeat this tutorial
• Return to the list of tutorials
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