Transcript Variations of ANOVA

Repeated Measures ANOVA
• Used when the research
design contains one factor
on which participants are
measured more than twice
(dependent, or withingroups design).
• Similar to the pairedsamples 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 Output
Descriptive Statistics
No Alcohol
Three Beers
Six Beers
Mean
18.8000
16.4667
12.6000
Std. Deviation
2.42605
2.66905
3.77586
N
15
15
15
The descriptive statistics box
provides the mean, standard
deviation, and number of participants
for each measurement time.
Multivariate Testsb
Effect
BEER
Pillai's Trace
Wilks ' Lambda
Hotelling's Trace
Roy's Larges t Root
Value
.821
.179
4.572
4.572
a. Exact statistic
b.
Des ign: Intercept
Within Subjects Design: BEER
F
Hypothesis df
a
29.715
2.000
29.715a
2.000
29.715a
2.000
29.715a
2.000
Error df
13.000
13.000
13.000
13.000
Sig.
.000
.000
.000
.000
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
Tests of Within-Subjects Effects
Measure: MEASURE_1
Source
beer
Error(beer)
Sphericity Assumed
Greenhouse-Geisser
Huynh-Feldt
Lower-bound
Sphericity Assumed
Greenhouse-Geisser
Huynh-Feldt
Lower-bound
Type III Sum
of Squares
294.178
294.178
294.178
294.178
87.156
87.156
87.156
87.156
df
2
1.409
1.520
1.000
28
19.730
21.282
14.000
Mean Square
147.089
208.741
193.523
294.178
3.113
4.417
4.095
6.225
F
47.254
47.254
47.254
47.254
Sig.
.000
.000
.000
.000
Partial Eta
Squared
.771
.771
.771
.771
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.
Post Hoc Tests
Pairwise Comparisons
Meas ure: MEASURE_1
(I) BEER
1
2
3
(J) BEER
2
3
1
3
1
2
Mean
Difference
(I-J)
2.333*
6.200*
-2.333*
3.867*
-6.200*
-3.867*
Std. Error
.410
.794
.410
.668
.794
.668
a
Sig.
.000
.000
.000
.000
.000
.000
95% Confidence Interval for
a
Difference
Lower Bound Upper Bound
1.454
3.213
4.497
7.903
-3.213
-1.454
2.434
5.300
-7.903
-4.497
-5.300
-2.434
Bas ed on es timated marginal means
*. The mean difference is significant at the .05 level.
a. Adjus tment for multiple comparisons : Leas t Significant Difference (equivalent to no
adjus tments ).
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!
Low
Male Mod
High
Low
Female Mod
High
M
X
X
X
X
X
X
X
F
X
X
X
X
X
X
X
A
X
X
X
X
X
X
X
U
X
X
X
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 withinsubjects 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 Output
Descriptive Statistics
Dependent Variable: PLAYTIME
Social Condition
Alone
Parents
Total
AGE
4 years
6 years
Total
4 years
6 years
Total
4 years
6 years
Total
Mean
5.0000
10.0000
7.5000
15.0000
35.0000
25.0000
10.0000
22.5000
16.2500
Std. Deviation
1.22474
1.22474
2.87711
3.67423
3.93700
11.13553
5.86894
13.45982
11.96871
N
a
Le vene's Test of Equa lity of Error Variances
Dependent Variable: playtime
F
2.469
df1
df2
3
16
Sig.
.099
Tests t he null hypothes is that the error variance of the
dependent variable is equal across groups.
a. Design: Int ercept+s occond+ age+soc cond * age
5
5
10
5
5
10
10
10
20
The descriptive statistics
box provides the means,
standard deviations, and
Ns for each main effect,
as well as all interactions.
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
Tests of Between-Subjects Effects
Dependent Variable: playtime
Source
Corrected Model
Intercept
soccond
age
soccond * age
Error
Total
Corrected Total
Type III Sum
of Squares
2593.750a
5281.250
1531.250
781.250
281.250
128.000
8003.000
2721.750
df
3
1
1
1
1
16
20
19
Mean Square
864.583
5281.250
1531.250
781.250
281.250
8.000
F
108.073
660.156
191.406
97.656
35.156
Sig.
.000
.000
.000
.000
.000
Partial Eta
Squared
.953
.976
.923
.859
.687
a. R Squared = .953 (Adjus ted R Squared = .944)
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.