# Factorial repeated-measures ANOVA The data will be arranged in a

```Factorial repeated-measures ANOVA
The data will be arranged in a manner similar to a one-factor repeated-measures design: one subject per row and one
column per observation. However, for multi-factor designs, each column represents a combination of conditions, and
you should (but don't have to) organize columns systematically, like this (where the as are for one factor and its levels
and the bs for another factor and its levels):
a1b1
a1b2
a1b3
a2b1
a2b2
a2b3
a3b1
a3b2
a3b3
This will help when you execute the ANOVA. Notice that the a factor changes "slowly" from column to column and the b
factor changes "rapidly". Knowing which factors change quickly and slowly can help execute the ANOVA. An example
appears below. This is from a design in which subjects see faces of three types (normal/original; with the eyes and
mouth upside-down; or negative versions, as in photographic film) and in three orientations (upright/0 degrees;
sideways/90 degrees; or flipped/180 degrees):
To carry out the ANOVA, follow these commands (which are illustrated in part at right):




click on Analyze > General Linear Model > Repeated Measures
name both of within-subjects factors and enter the number of levels
of each factor; I recommend naming the slow-changing factor first
(although this isn't required); then Define them
move the variable names to the Within-Subjects Variables box;
order matters, which is why SPSS provides the indices in
parentheses; make sure the levels of the different factors match up
with the indices!
click on Plots, Options, etc., for
descriptive statistics and other good
stuff, then click OK
Exercise #1
Perform the omnibus ANOVA on the SAB.sav
data and put the Test of Within-Subjects
Effects table into an email or a Word
document to send my way
([email protected]).
Mixed-factor ANOVA
The data will be arranged in a manner similar to a one-factor RM design: one subject per row and one column per
observation. However, in addition to variables for each level of the repeated-measures factor(s), there must be a column
for each between-subjects factor to identify which level of this factor the subject is nested within. An example of the
layout of a two-factor (one between, one within) design appears at left below. And the analysis, which proceeds via
Analyze > GLM > Repeated Measures > Define, name factor, Number of Levels, Add > Define, should end up looking like
the image at right below, just before clicking OK (and maybe you should consider adding plots or asking for descriptive
statistics and effect-sizes, too).
The output looks like that at below right.
Tests of Withi n-Subjects Effects
Measure: MEASUR E_1
Exercise #2
Open the mixed-factor.sav file and delete
day3. Now carry out the omnibus ANOVA
and put the Test of Within-Subjects Effects
and the Tests of Between-Subject Effects
into the email or Word document from
Exercise #1.
Sourc e
day
Sphericity Assumed
Greenhouse-Geisser
Huy nh-Feldt
Lower-bound
day * display Sphericity Assumed
Greenhouse-Geisser
Huy nh-Feldt
Lower-bound
Error(day )
Sphericity Assumed
Greenhouse-Geisser
Huy nh-Feldt
Lower-bound
Ty pe III Sum
of Squares
752.889
752.889
752.889
752.889
113.778
113.778
113.778
113.778
77. 333
77. 333
77. 333
77. 333
df
2
1. 427
1. 997
1. 000
4
2. 854
3. 994
2. 000
18
12. 842
17. 973
9. 000
Mean Square
376.444
527.627
377.015
752.889
28. 444
39. 868
28. 488
56. 889
4. 296
6. 022
4. 303
8. 593
F
87. 621
87. 621
87. 621
87. 621
6. 621
6. 621
6. 621
6. 621
Sig.
.000
.000
.000
.000
.002
.007
.002
.017
Tests of Between-Subjects Effects
Measure: MEASURE_1
Transf ormed Variable: Av erage
Sourc e
Interc ept
display
Error
Ty pe III Sum
of Squares
25175. 111
270.222
56. 667
df
1
2
9
Mean Square
25175. 111
135.111
6. 296
F
3998.400
21. 459
Sig.
.000
.000
```