Lab Topic: Using SPSS Special Contrasts
Part 1: Repeated Measures ANOVA
Picking up on last week’s RM ANOVA, we ran a two-way repeated measures ANOVA
where subjects rated a course they liked on four dimensions and a course they disliked on
four dimensions. We found that the two-way interaction evidently had something to do
with more variability for courses that were disliked, across dimensions (simple main
effects analysis). Picking up from here, we can use SPSS syntax, specifically the
MMATRIX subcommand, to help further isolate the source of the interaction. Looking
at the graph below (and legend denoting which numbers on the x-axis correspond to
which dimensions), we might first want to test whether, for disliked courses, course value
is significantly different from the other three dimensions. The contrast (null hypothesis)
would look something like this:
Dvalue*3 drapport*-1 dgrading*-1 dorganize*-1 = 0.
If this were significant, we might want to also test rapport vs. grading, rapport vs.
organization, and grading vs. organization to find out whether the three means previously
grouped together differ significantly among one another. Using the MMATRIX
subcommand in SPSS, we can test these directly by adding the following syntax (just
above the WSDESIGN subcommand)
/MMATRIX = 'd-value v othr' dvalue 3 drapport -1 dgrading -1 dorganize -1;
'd-rapport v grade' drapport 1 dgrading -1;
'd-rapport v org' drapport 1 dorganize -1;
'd-grade v org' dgrading 1 dorganize -1
Note that each hypothesis contains a brief label (in tick marks) and each contrast is
separated by a semi-colon. The full syntax will run the overall ANOVA.
TITLE 'SETE Dimension by Course - Two-Way RM ANOVA'.
GLM
rapport drapport grading dgrading organize dorganize value dvalue
/WSFACTOR = dimens 4 Polynomial course 2 Polynomial
/METHOD = SSTYPE(3)
/PLOT = PROFILE( dimens*course )
/EMMEANS = TABLES(OVERALL)
/EMMEANS = TABLES(dimens)
/EMMEANS = TABLES(course)
/EMMEANS = TABLES(dimens*course)
/PRINT = DESCRIPTIVE ETASQ OPOWER
/CRITERIA = ALPHA(.05)
/MMATRIX = 'd-value v othr' dvalue 3 drapport -1 dgrading -1 dorganize -1;
'd-rapport v grade' drapport 1 dgrading -1;
'd-rapport v org' drapport 1 dorganize -1;
'd-grade v org' dgrading 1 dorganize -1
/WSDESIGN = dimens course dimens*course .
Estimated Marginal Means of MEASURE_1
course
1
2
Estimated Marginal Means
5
4
3
2
1
2
3
4
dimension
Within-Subjects Factors
Measure: MEASURE_1
course
1
2
dimension
1
Dependent
Variable
rapport
2
grading
3
value
4
organize
1
drapport
2
dgrading
3
dvalue
4
dorganize
Part 2: Groups x Trials (Randomized x Repeated, Split Plot Factorial, etc.):
Now we’ll use an example taken from class. This is where people are assigned to read
one of three types (genre) of books, and the number of books read over three months
serves as the DV. The data yield a significant genre*time interaction, which can be seen
in the plot below. It appears that the pattern for science fiction is much different than the
one for mystery and romance, which seem very similar. Thus, let’s check to see whether
science fiction differs from mystery and romance combined, for each of the three months.
To do this, we need to incorporate a between subjects matrix, which in SPSS is the “L”
matrix (M Matrix is for repeated measures designs). The easiest way to do this is to
specify the GLM the way you want it, requesting all the options you wish, then pasting
and adding “GEF” to the /PRINT subcommand. This prints the “general estimable
function”, which gives you a clue as to how SPSS is treating the between subjects
variable.
Estimated Marginal Means of MEASURE_1
genre
7.00
science fiction
mystery
romance
Estimated Marginal Means
6.00
5.00
4.00
3.00
2.00
1.00
1
2
3
month
The output for GEF gives us a number of things we don’t care about, but the following
table is important as it tells us that genre=1 (science fiction) is in the first position in the
LMATRIX, genre=2 (mystery) is in the second, etc.
General Estimable Function(a)
Contrast
Parameter
Intercept
L1
L2
L3
1
0
0
[genre=1.00]
0
1
0
[genre=2.00]
0
0
1
[genre=3.00]
1
-1
-1
a Design: Intercept+genre
Within Subjects Design: month
We now have what we need to construct our contrast. We’ll begin with month one. We
use the following two lines of syntax to construct our contrast.
/LMATRIX = "genre @ m1" genre 2 -1 -1
/MMATRIX = 'w-in m1' month1 1 month2 0 month3 0;
This tells SPSS that we want to contrast science fiction (coefficient of 2) against mystery
and romance together (each getting a coefficient of -1). The second part, MMATRIX
tells it that we want to do it for month1, and that month2 and 3 are to be left out of the
test (because they get coefficients of zeros). Hopefully people will recognize that we
could do something more complicated here, by, say comparing science fiction to the
other two genres for months 1 & 2 combined, if we so desired. Once we have done this,
we can run it and go back and change the MMATRIX line to read:
/MMATRIX = 'w-in m1' month1 0 month2 1 month3 0;
And again to…
/MMATRIX = 'w-in m1' month1 0 month2 0 month3 1;
To test both the 2nd and third months respectively. Since the first month isn’t significant,
we would likely just test the third month and be finished. The main point here is that the
LMATRIX and MMATRIX commands work together to perform the contrast we are
looking for.
The full syntax looks as follows (depending upon which options were chosen):
GLM
month1 month2 month3 BY genre
/WSFACTOR = month 3 Polynomial
/METHOD = SSTYPE(3)
/PLOT = PROFILE( month*genre )
/EMMEANS = TABLES(OVERALL)
/EMMEANS = TABLES(genre)
/EMMEANS = TABLES(month)
/EMMEANS = TABLES(genre*month)
/PRINT = PARAMETER GEF
/CRITERIA = ALPHA(.05)
/WSDESIGN = month
/LMATRIX = "genre @ m1" genre 2 -1 -1
/MMATRIX = 'w-in m1' month1 1 month2 0 month3 0;
/DESIGN = genre .
Note, I have not figured out a way to test all three contrasts in one run. It only uses the
final one each time, but I am sure there is a way and I just didn’t crack the code yet.
Part 3: Between Subjects Contrasts
We will now return to the drug interaction example from a few weeks ago in lab. For this
example, we had drug A and drug B, with three levels each, and we were testing to see
whether there was an interaction between the two. The plot of the resultant interaction
follows.
Again, we have to use the LMATRIX subcommand and we can add a statement to the
/PRINT subcommand to get some basic information. Adding “TEST(LMATRIX)” to the
end of the existing /PRINT statement gives us several additional tables. We are
interested in three matrices, FACTORA, FACTORB, and FACTORA x FACTORB.
Factor A and Factor B matrices are straight forward, they have three elements, 1, 2 & 3,
each which correspond to how our data are entered (three levels of each drug). The
interaction matrix is more important and is pasted below.
Estimated Marginal Means
Estimated Marginal Means of anxiety
20.00
FactorB
18.00
1.00
2.00
3.00
16.00
14.00
12.00
10.00
8.00
6.00
1.00
2.00
3.00
FactorA
FactorA * FactorB
Contrast
Parameter
Intercept
L8
L9
L11
L12
0
0
0
0
[FactorA=1.00]
0
0
0
0
[FactorA=2.00]
0
0
0
0
[FactorA=3.00]
0
0
0
0
[FactorB=1.00]
0
0
0
0
[FactorB=2.00]
0
0
0
0
[FactorB=3.00]
0
0
0
0
[FactorA=1.00] *
[FactorB=1.00]
1
0
0
0
[FactorA=1.00] *
[FactorB=2.00]
0
1
0
0
[FactorA=1.00] *
[FactorB=3.00]
-1
-1
0
0
[FactorA=2.00] *
[FactorB=1.00]
0
0
1
0
[FactorA=2.00] *
[FactorB=2.00]
0
0
0
1
[FactorA=2.00] *
[FactorB=3.00]
0
0
-1
-1
[FactorA=3.00] *
[FactorB=1.00]
-1
0
-1
0
[FactorA=3.00] *
[FactorB=2.00]
0
-1
0
-1
[FactorA=3.00] *
[FactorB=3.00]
1
1
1
1
The default display of this matrix is the transpose of the corresponding L matrix.
Based on Type III Sums of Squares.
We aren’t interested in the contrasts L8, L9, etc. We are interested in the elements with
asterisk signs (which actually appear in the SPSS output). Because we have a 3x3
design, we have 9 elements in this matrix, one for each cell. The entries with asterisks
tell us the order. The first element is Factor AB11, followed by AB12, then AB13.
Looking at the graph, we probably want to look at contrasts involving level 3 of A and all
levels of B (within A3). Thus, with our first contrast, let’s compare level 1 & 3 of factor
B (the two points furthest apart) with each other, ignoring AB23 for now. The following
/LMATRIX subcommand accomplishes this.
/LMATRIX = "B1 vs B3 at A3"
FactorB 1 0 -1
FactorA*FactorB 0 0 0 0 0 0 1 0 -1;
Note that with the first line I provide a label, with the second line I tell it we are
contrasting level 1 & 3 of FactorB, and with the third line, I further tell it that this
contrast is limited to level 3 of FactorA. To understand this, note that the first six entries
are zeros. Consulting the AxB table above (looking at entries with asterisks), we see that
the first six entries of the LMATRIX for AxB correspond to levels 1 & 2 of FactorA.
The last three entries correspond to B1, B2, & B3 for A3, or AB31, AB32, and AB33.
Since AB31 is assigned a 1, and AB33 a -1, and AB32 a zero, we are contrasting just AB31
vs. AB33. The result is that all three means are significantly different from each other at
the highest dose of FactorA. As an exercise here, one might wish to compare the next
biggest difference, AB12, versus AB13 & AB11 combined to see if that difference is
significant.
The full syntax for this particular run is as follows:
TITLE 'two-way anova for drug interaction with LMATRIX Contrasts'.
UNIANOVA
anxiety BY FactorA FactorB
/LMATRIX = "B1 vs B3 at A3"
FactorB 1 0 -1
FactorA*FactorB 0 0 0 0 0 0 1 0 -1;
/LMATRIX "B1 vs B2 at A3"
FactorB 1 -1 0
FactorA*FactorB 0 0 0 0 0 0 1 -1 0;
/LMATRIX "B2 vs B3 at A3"
FactorB 0 1 -1
FactorA*FactorB 0 0 0 0 0 0 0 1 -1;
/METHOD = SSTYPE(3)
/INTERCEPT = INCLUDE
/POSTHOC = FactorA FactorB ( QREGW )
/PLOT = PROFILE( FactorA*FactorB )
/EMMEANS = TABLES(OVERALL)
/EMMEANS = TABLES(FactorA)
/EMMEANS = TABLES(FactorB)
/EMMEANS = TABLES(FactorA*FactorB)
/PRINT = DESCRIPTIVE ETASQ OPOWER HOMOGENEITY TEST(LMATRIX)
/CRITERIA = ALPHA(.05)
/DESIGN = FactorA FactorB FactorA*FactorB .