By Hui BianOffice for Faculty Excellence

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Repeated measures ANOVA with SPSSOne-way within-subjects ANOVA with SPSSOne between and one within mixed design

with SPSSRepeated measures MANOVA with

SPSSHow 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 asSame 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 linear, quadratic, or cubic?

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Between and within factorsBetween 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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AssumptionsIndependence of the observations

Violation is seriousMultivariate normality

Fairly robust against violationSphericity

Not necessary for the multivariate approachThe variance-covariance matrices are the

same across the cells formed by the between-subjects effects.

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A simplest designOne within-subjects factorOne dependent variableA 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 posttestTwo conditions: before treatment and after

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The design

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Select Intervention group as our sampleGo to Data Select Cases Check If conditions…Then click If

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Let Conditions = 1Then click Continue

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Run Repeated Measures analysisAnalyze General Linear Model

Repeated MeasuresType Time as Within-Subject Factor Name,

type 2 as Number of Levels, then click AddType dv1 as Measure Name (dv means

dependent variable), then click Add

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Then click Define

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After Define you should get this windowMove a28 to (1, dv1)Move b28 to (2, dv2)

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We don’t have any between-subjects factorsClick Options to get this

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Check Compare main effects even we have two levels for within-subjects factor. I just want to show the pair comparison function.

Click Plots to get this window

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SPSS outputsDescriptive statistic results

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SPSS outputsWithin-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.

SPSS outputsWithin-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 outputsThe mathematical properties underlying the

relationship between within-subjects factor and dependent variable.

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Test linear component of Time

effect The linear component is not significant

SPSS outputsPlot

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Quadratic

Cubic

SPSS outputsPairwise comparisons: the within-subjects

factor only has two levels. So we get the same results as multivariate tests table shows.

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ResultsOne-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 designTwo 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

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Run repeated measures analysisSelect all casesGo to Analyze General Linear Model

Repeated MeasuresThe same procedure to define the within-

subjects factor and dependent variable.Move Conditions to…

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Click OptionsClick Plots

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SPSS outputsMultivariate tests

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SPSS outputsEstimated marginal means

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SPSS outputsPlots

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ResultsThe 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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ExampleResearch 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 analysisGo to Analyze General Linear Model

Repeated MeasuresWe have three dependent variablesStill one within-subjects factorClick 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 outputsMultivariate tests

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SPSS outputsWithin-subjects effects

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SPSS outputsUnivariate tests

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SPSS outputsEstimated marginal means

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SPSS outputsPlots: dv1 (frequency of drinking)

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SPSS outputsPlots: dv2 (quantity of drinking)

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SPSS outputsPlots: dv3 (heavy drinking)

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ResultsRepeated 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: timeOne 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 windowChoose Simple (simple means compares the

mean of each level to the mean of a reference).

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Pull down

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.

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Check First, then click Change

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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