### SPSS Series 1: ANOVA and Factorial ANOVA

```By Hui Bian
Office for Faculty Excellence
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 Repeated measures ANOVA with SPSS
 One-way within-subjects ANOVA with SPSS
 One between and one within mixed design with
SPSS
 Repeated measures MANOVA with SPSS
 How to interpret SPSS outputs
 How to report results
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 When the same measurement is made several
times on each subject or case, such as
 Same group of people are pretested and post-tested
on a dependent variable.
 Comparing the same subjects under several
different treatments.
 Interested in the performance trends over time: is it
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 Between and within factors
 Between factors: a grouping or classification variables
such as sex, age, grade levels, treatment conditions etc.
 Within factors: is the one with multiple measures from a
group of people such as time.
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 Assumptions
 Independence of the observations
 Violation is serious
 Multivariate normality
 Fairly robust against violation
 Sphericity
 Not necessary for the multivariate approach
 The variance-covariance matrices are the same across
the cells formed by the between-subjects effects.
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 A simplest design
 One within-subjects factor
 One dependent variable
 A group of subjects measured at different points in time
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 Example: sample is from high school students.
 Research questions:
 1. whether there is a significant change on frequency of
drinking over time (3 months) before and after treatment;
 2. whether the relationship between the within factor (time)
and frequency of drinking is linear, quadratic, or cubic.
 Within-subjects factor: time.
 Dependent variable: frequency of drinking (a28 and
b28).
 Two-time points data: a28 means baseline and b28
means 3-month posttest
 Two conditions: before treatment and after treatment
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 The design
Conditions
Subjects
Before treatment
After treatment
1
2
3
4
.
.
.
n
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 Select Intervention group as our sample
 Go to Data
Select Cases
 Check If conditions…
 Then click If
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 Let Conditions = 1
 Then click Continue
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 Run Repeated Measures analysis
 Analyze
General Linear Model
Repeated
Measures
 Type Time as Within-Subject Factor Name, type 2 as
Number of Levels, then click Add
 Type dv1 as Measure Name (dv means dependent
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 Then click Define
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 After Define you should get this window
 Move a28 to (1, dv1)
 Move b28 to (2, dv2)
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 We don’t have any between-subjects factors
 Click Options to get this
Check Compare main effects
even we have two levels for
within-subjects factor. I just
want to show the pair
comparison function.
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 Click Plots to get this window
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 SPSS outputs
 Descriptive statistic results
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 SPSS outputs
 Within-subjects effect: results of two tables are same.
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Correction options include Geenhouse-Geisser, Huyn-Feldt, and Lower-bound
when sphericity is not assumed. They produce more conservative estimates.
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 SPSS outputs
 Within-subjects effect: if there is no homogeneity of
dependent variable covariance matrix, the Sphericity is
not assumed. We should use the correction options.
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 SPSS outputs
 The mathematical properties underlying the
relationship between within-subjects factor and
dependent variable.
Test linear component of
Time effect
The linear component is
not significant
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 SPSS outputs
 Plot
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Cubic
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 SPSS outputs
 Pairwise comparisons: the within-subjects factor only
has two levels. So we get the same results as multivariate
tests table shows.
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 Results
 One-way within-subjects ANOVA was performed to test
whether there was a difference of frequency of drinking
between before-treatment and after-treatment
conditions. The observed F value was not statistically
significant, F(1, 136) = .42, p = .52, partial η2 = .003, which
indicated no difference of frequency of drinking over
time.
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 Two-way mixed design
 Two independent factors: one is a between-subjects
factor and one is a within-subjects factor
 One dependent variable.
 Tests null hypotheses about the effects of both the
between-subjects factor and within-subjects factor.
 Tests the effect of interactions between factors.
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 Example:
 Research questions:
 whether there is a significant change on frequency of
drinking over time (3 months) between intervention and
control group.
 Within-subjects factor: time.
 Between-subjects factor: conditions (intervention vs.
control).
 Dependent variable: frequency of drinking (a28 and
b28).
 Two-time points data: a28 means baseline and b28
means 3-month posttest
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 The design
Conditions
Intervention
Subjects
Time 1
Time 2
Control
Time 1
Time 2
1
2
3
4
.
.
.
n
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 Run repeated measures analysis
 Select all cases
 Go to Analyze
General Linear Model
Repeated
Measures
 The same procedure to define the within-subjects factor
and dependent variable.
 Move Conditions to…
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 Click Options
 Click Plots
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 SPSS outputs
 Multivariate tests
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 SPSS outputs
 Estimated marginal means
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 SPSS outputs
 Plots
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 Results
 The intervention effect was analyzed using repeated
measures ANOVA. There was no statically significant
difference between intervention and control group over
time on frequency of drinking, F(1,285) = .90, p = .34,
partial η2 = .003.
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 Example
 Research questions:
 whether there is a significant change on drinking behaviors
over time (3 months) between intervention and control
groups; or whether there is an intervention effect on drinking
behaviors.
 Within-subjects factor: time.
 Between-subjects factor: conditions (two levels)
 Dependent variables: frequency of drinking (a28 and
b28), quantity of drinking (a31 and b31), and heavy
drinking (a34 and b34).
 Two-time points data: baseline and posttest
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 Run repeated measures analysis
 Go to Analyze
General Linear Model
Repeated
Measures
 We have three dependent variables
 Still one within-subjects factor
 Click Define
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 Move a28/b28, a31/b31, and a34/b34 to…
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 Options and Plots
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 SPSS outputs
 Multivariate tests
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 SPSS outputs
 Within-subjects effects
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 SPSS outputs
 Univariate tests
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 SPSS outputs
 Estimated marginal means
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 SPSS outputs
 Plots: dv1 (frequency of drinking)
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 SPSS outputs
 Plots: dv2 (quantity of drinking)
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 SPSS outputs
 Plots: dv3 (heavy drinking)
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 Results
 Repeated measures MANOVA test was conducted to test
intervention effect on drinking behaviors. The results
showed there was no difference between intervention
and control group on frequency, quantity, and heavy
drinking over time, F(3, 283) = 1.18, p = .32, η2 = .01.
Univariate tests also indicated there was no intervention
effect on individual drinking behavior, F(1, 285) = .90, p
= .34, η2 = .003 for frequency, F(1, 285) = .67, p = .41, η2 =
.002 for quantity, and F(1, 285) = .39, p = .53, η2 = .001 for
heavy drinking.
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 Example (planned comparisons)
 One within-subjects factor: time
 One between-subjects factor: living condition (11r)
 One dependent variable: frequency of drinking (a28 and
b28)
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 Contrasts are used to test for differences among the
levels of a between-subjects factor.
 Go to Analyze
General Linear Model
Repeated Measures
 The same procedure to define within-subjects factor
and dependent variable
 Click Contrasts
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 You should get the left window
 Choose Simple (simple means compares the mean of
each level to the mean of a reference).
Pull
down
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 Decide which category of between-subjects factor is a
reference category.
 The between-subjects factor is a11r: 1= Mother and
father; 2 = Mother and stepfather; 3 = Mother; 4 =
Others.
 Use 1 = Mother and father as a reference.
Check First, then
click Change
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 SPSS outputs
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Meyers, L. S., Gamst, G., & Guarino, A. J. (2006).
Applied multivariate research: design and
interpretation. Thousand Oaks, CA: Sage Publications,
Inc.
Stevens, J. P. (2002). Applied multivariate statistics for
the social sciences. Mahwah, NJ: Lawrence Erlbaum
Associates, Inc.
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