Repeated Measures ANOVA

• Used when the research design contains one factor on which participants are measured more than twice (dependent, or within-groups design).

• Similar to the paired-samples t-test

Computing Repeated Measures ANOVA in SPSS

• Go to Analyze General Linear Model Repeated Measures

• In the repeated measures define factor(s) window, name the factor and enter the number of levels click Add click Define

• In the Repeated Measures dialog box, click on the first level of your variable and move it to the __?__(1) space in the within-subjects variables window continue to do this for all of the remaining levels of the variable

• Click Options Move factor 1 to the Display Means for window and select Compare Main Effects also select Descriptive Statistics and Estimates of Effect Size.

• Click Continue Click OK

Interpreting the OutputDescriptive Statistics

18.8000 2.42605 15

16.4667 2.66905 15

12.6000 3.77586 15

No Alcohol

Three Beers

Six Beers

Mean Std. Deviation N

Multivariate Testsb

.821 29.715a 2.000 13.000 .000

.179 29.715a 2.000 13.000 .000

4.572 29.715a 2.000 13.000 .000

4.572 29.715a 2.000 13.000 .000

Pillai's Trace

Wilks' Lambda

Hotelling's Trace

Roy's Largest Root

EffectBEER

Value F Hypothesis df Error df Sig.

Exact statistica.

Design: Intercept Within Subjects Design: BEER

b.

The descriptive statistics box provides the mean, standard deviation, and number of participants for each measurement time.

This box is generated because three (or more) columns of measurements are being compared. This only needs to be interpreted when those columns of measurements correspond to separate variables (multivariate designs).

Main Analysis

The row you are interested in is the row which has the name of your variable in it. The between df appear in this row; the within degrees of freedom appear in the error row. F is your test statistic, and Sig is its probability. Partial eta squared is the effect size statistic for the F-ratio.

Tests of Within-Subjects Effects

Measure: MEASURE_1

294.178 2 147.089 47.254 .000 .771

294.178 1.409 208.741 47.254 .000 .771

294.178 1.520 193.523 47.254 .000 .771

294.178 1.000 294.178 47.254 .000 .771

87.156 28 3.113

87.156 19.730 4.417

87.156 21.282 4.095

87.156 14.000 6.225

Sphericity Assumed

Greenhouse-Geisser

Huynh-Feldt

Lower-bound

Sphericity Assumed

Greenhouse-Geisser

Huynh-Feldt

Lower-bound

Sourcebeer

Error(beer)

Type III Sumof Squares df Mean Square F Sig.

Partial EtaSquared

Post Hoc TestsPairwise Comparisons

Measure: MEASURE_1

2.333* .410 .000 1.454 3.213

6.200* .794 .000 4.497 7.903

-2.333* .410 .000 -3.213 -1.454

3.867* .668 .000 2.434 5.300

-6.200* .794 .000 -7.903 -4.497

-3.867* .668 .000 -5.300 -2.434

(J) BEER2

3

1

3

1

2

(I) BEER1

2

3

MeanDifference

(I-J) Std. Error Sig.a

Lower Bound Upper Bound

95% Confidence Interval forDifference

a

Based on estimated marginal means

The mean difference is significant at the .05 level.*.

Adjustment for multiple comparisons: Least Significant Difference (equivalent to noadjustments).

a.

Pairwise Comparisons provide the mean difference between each measurement time and its significance.

Factorial ANOVA

• A special case of ANOVA in which there is more than one independent variable (IV) being explored.

• Because there are multiple IVs, factorial designs have multiple hypotheses which are analyzed by multiple F tests: one for each main effect (IV); and one for each possible interaction between the IVs.

Looking for Main Effects

• Main Effect: the action of a single IV in an experiment

Looking for Interactions

• Interaction: the effect of one IV changes across the levels of another IV

• Higher-Order Interaction: an interaction effect involving more than two IVs

Laying Out a Factorial Design• Design Matrix: a visual representation of the research

design• Hint: If you can’t draw it, you can’t interpret it!

M F A ULow X X X X

Male Mod X X X X X XHigh X X X XLow X X X X X

Female Mod X X X X XHigh X X X X X

X X X X

Describing the Design

• Shorthand Notation: a system that uses numbers to describe the design of a factorial study

Within-Subjects Factorial Designs

• Within-Subjects Factorial Design: a factorial design in which subjects receive all conditions in the experiment

Mixed Designs

• Mixed Design: a factorial design that combines within-subjects and between-subjects factors

Computing Factorial ANOVA in SPSS• Analyze General Linear Model Univariate• Move the independent variables to the Fixed Factor(s) box

Move the dependent variable to the Dependent Variable box

• Click Options highlight the independent variables and the interaction term in the Factor(s) box and move it to the Display Means for box Under Display, check descriptive statistics, homogeneity tests, and estimates of effect size. Note that the significance level is already set at 0.05. Click Continue.

• Click OK.

Interpreting the OutputDescriptive Statistics

Dependent Variable: PLAYTIME

5.0000 1.22474 5

10.0000 1.22474 5

7.5000 2.87711 10

15.0000 3.67423 5

35.0000 3.93700 5

25.0000 11.13553 10

10.0000 5.86894 10

22.5000 13.45982 10

16.2500 11.96871 20

AGE4 years

6 years

Total

4 years

6 years

Total

4 years

6 years

Total

Social ConditionAlone

Parents

Total

Mean Std. Deviation N

The descriptive statistics box provides the means, standard deviations, and Ns for each main effect, as well as all interactions.

Levene's Test of Equality of Error Variancesa

Dependent Variable: playtime

2.469 3 16 .099F df1 df2 Sig.

Tests the null hypothesis that the error variance of thedependent variable is equal across groups.

Design: Intercept+soccond+age+soccond * agea.

Levene’s test is designed to compare the error variance of the dependent variable across groups. We do not want this result to be significant.

Main Analysis

There are three hypotheses being tested here (one for each main effect and one for the interaction). Thus, there are three separate F-tests conducted. The between degrees of freedom, as well as the F-ratio, its significance, and associated effect size, are located on the rows with the variable names. The within degrees of freedom is located with the error term.

Tests of Between-Subjects Effects

Dependent Variable: playtime

2593.750a 3 864.583 108.073 .000 .953

5281.250 1 5281.250 660.156 .000 .976

1531.250 1 1531.250 191.406 .000 .923

781.250 1 781.250 97.656 .000 .859

281.250 1 281.250 35.156 .000 .687

128.000 16 8.000

8003.000 20

2721.750 19

SourceCorrected Model

Intercept

soccond

age

soccond * age

Error

Total

Corrected Total

Type III Sumof Squares df Mean Square F Sig.

Partial EtaSquared

R Squared = .953 (Adjusted R Squared = .944)a.