SPSS Series 3 Repeated Measure ANOVA and MANOVA PDF

7/30/2019 SPSS Series 3 Repeated Measure ANOVA and MANOVA PDF

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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 withSPSS

Repeated measures MANOVA with SPSS

How to interpret SPSS outputs

How to report results

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When the same measurement is made severaltimes 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 severaldifferent treatments.

Interested in the performance trends over time: is itlinear, quadratic, or cubic?

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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 ofdrinking 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 b28means 3-month posttest Two conditions: before treatment and after treatment

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The design

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Conditions

Subjects Before treatment After treatment

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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 clickAdd Type dv1 as Measure Name (dv means dependent

variable), then clickAdd

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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 dont have any between-subjects factors

Click Options to get this

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Check Compare main effectseven we have two levels forwithin-subjects factor. I justwant to show the paircomparison 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-boundwhen 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 isnot assumed. We should use the correction options.

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SPSS outputs The mathematical properties underlying the

relationship between within-subjects factor anddependent variable.

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Test linear component ofTime effect

The linear component isnot significant


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SPSS outputs Plot

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Quadratic Cubic


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SPSS outputs Pairwise comparisons: the within-subjects factor only

has two levels. So we get the same results as multivariatetests table shows.

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Results One-way within-subjects ANOVA was performed to test

whether there was a difference of frequency of drinkingbetween before-treatment and after-treatment

conditions. The observed Fvalue was not statisticallysignificant, F(1, 136) = .42,p = .52, partial 2= .003, whichindicated no difference of frequency of drinking overtime.

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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 thebetween-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 ofdrinking over time (3 months) between intervention andcontrol 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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Conditions

Intervention Control

Subjects Time 1 Time 2 Time 1 Time 2

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Run repeated measures analysis Select all cases

Go toAnalyze General Linear Model RepeatedMeasures

The same procedure to define the within-subjects factorand dependent variable.

Move Conditionsto

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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 significantdifference between intervention and control group over

time on frequency of drinking, F(1,285) = .90,p = .34,partial 2 = .003.

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Example Research questions:

whether there is a significant change on drinking behaviorsover time (3 months) between intervention and control

groups; or whether there is an intervention effect on drinkingbehaviors.

Within-subjects factor: time.

Between-subjects factor: conditions (two levels)

Dependent variables: frequency of drinking (a28 andb28), quantity of drinking (a31 and b31), and heavydrinking (a34 and b34).

Two-time points data: baseline and posttest

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Run repeated measures analysis

Go to Analyze General Linear Model RepeatedMeasures

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 resultsshowed there was no difference between intervention

and control group on frequency, quantity, and heavydrinking over time, F(3, 283) = 1.18,p = .32, 2 = .01.Univariate tests also indicated there was no interventioneffect on individual drinking behavior, F(1, 285) = .90,p

= .34, 2

= .003 for frequency, F(1, 285) = .67,p = .41, 2

=.002 for quantity, and F(1, 285) = .39,p = .53, 2 = .001 forheavy 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 thelevels of a between-subjects factor.

Go to Analyze General Linear ModelRepeated Measures

The same procedure to define within-subjects factorand 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).

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Pulldown


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Decide which category of between-subjects factor is areference category.

The between-subjects factor is a11r: 1= Mother andfather; 2 = Mother and stepfather; 3 = Mother; 4 =Others.

Use 1 = Mother and father as a reference.

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Check First, thenclick Change


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SPSS outputs

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Meyers, L. S., Gamst, G., & Guarino, A. J. (2006).Applied multivariate research: design andinterpretation. Thousand Oaks, CA: Sage Publications,Inc.

Stevens, J. P. (2002).Applied multivariate statistics forthe social sciences. Mahwah, NJ: Lawrence ErlbaumAssociates, Inc.

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SPSS Series 3 Repeated Measure ANOVA and MANOVA PDF

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