UCLA Academic Technology Services HomeServicesClassesContactJobs
Stat Computing > SPSS > FAQ
 Search

SPSS FAQ
How can I do ANOVA contrasts in SPSS?

Let's use an example dataset, crf24, adapted from Kirk (1968, 1st Edition). 

get file 'd:\crf24.sav'.

These data are from a 2x4 factorial design but the same data can also be used for one-way ANOVA examples. The variable y is the dependent variable. The variable a is an independent variable with two levels while b is an independent variable with four levels.

Using the contrast command in a one-way ANOVA


glm y by b.
Between-Subjects Factors

N
B 1 8
2 8
3 8
4 8
Tests of Between-Subjects Effects
Dependent Variable: Y
Source Type III Sum of Squares df Mean Square F Sig.
Corrected Model 194.500(a) 3 64.833 44.276 .000
Intercept 924.500 1 924.500 631.366 .000
B 194.500 3 64.833 44.276 .000
Error 41.000 28 1.464

Total 1160.000 32


Corrected Total 235.500 31


a R Squared = .826 (Adjusted R Squared = .807) 

means tables = y by b
 / cells mean.
Case Processing Summary

Cases
Included Excluded Total
N Percent N Percent N Percent
Y * B 32 100.0% 0 .0% 32 100.0%
Report
Mean
B Y
1 2.75
2 3.50
3 6.25
4 9.00
Total 5.38

It is quite clear that there is a significant overall F for the independent variable b. Now, let's devise some contrasts that we can test: 
1) group 3 versus group 4 
2) the average of groups 1 and 2 versus the average of groups 3 and 4 
3) the average of groups 1, 2, and 3 versus group 4 


glm y by b
 /contrast(b)=special (0 0 1 -1).
Between-Subjects Factors

N
B 1 8
2 8
3 8
4 8
Tests of Between-Subjects Effects
Dependent Variable: Y
Source Type III Sum of Squares df Mean Square F Sig.
Corrected Model 194.500(a) 3 64.833 44.276 .000
Intercept 924.500 1 924.500 631.366 .000
B 194.500 3 64.833 44.276 .000
Error 41.000 28 1.464

Total 1160.000 32


Corrected Total 235.500 31


a R Squared = .826 (Adjusted R Squared = .807)
Contrast Results (K Matrix)

Dependent Variable
B Special Contrast Y
L1 Contrast Estimate -2.750
Hypothesized Value 0
Difference (Estimate - Hypothesized) -2.750
Std. Error .605
Sig. .000
95% Confidence Interval for Difference Lower Bound -3.989
Upper Bound -1.511
Test Results
Dependent Variable: Y
Source Sum of Squares df Mean Square F Sig.
Contrast 30.250 1 30.250 20.659 .000
Error 41.000 28 1.464 


glm y by b
 /contrast(b)=special (1 1 -1 -1).
Between-Subjects Factors

N
B 1 8
2 8
3 8
4 8
Tests of Between-Subjects Effects
Dependent Variable: Y
Source Type III Sum of Squares df Mean Square F Sig.
Corrected Model 194.500(a) 3 64.833 44.276 .000
Intercept 924.500 1 924.500 631.366 .000
B 194.500 3 64.833 44.276 .000
Error 41.000 28 1.464

Total 1160.000 32


Corrected Total 235.500 31


a R Squared = .826 (Adjusted R Squared = .807)
Contrast Results (K Matrix)

Dependent Variable
B Special Contrast Y
L1 Contrast Estimate -9.000
Hypothesized Value 0
Difference (Estimate - Hypothesized) -9.000
Std. Error .856
Sig. .000
95% Confidence Interval for Difference Lower Bound -10.753
Upper Bound -7.247
Test Results
Dependent Variable: Y
Source Sum of Squares df Mean Square F Sig.
Contrast 162.000 1 162.000 110.634 .000
Error 41.000 28 1.464 

glm y by b
 /contrast(b)=special (1 1 1 -3).
Between-Subjects Factors

N
B 1 8
2 8
3 8
4 8
Tests of Between-Subjects Effects
Dependent Variable: Y
Source Type III Sum of Squares df Mean Square F Sig.
Corrected Model 194.500(a) 3 64.833 44.276 .000
Intercept 924.500 1 924.500 631.366 .000
B 194.500 3 64.833 44.276 .000
Error 41.000 28 1.464

Total 1160.000 32


Corrected Total 235.500 31


a R Squared = .826 (Adjusted R Squared = .807)
Contrast Results (K Matrix)

Dependent Variable
B Special Contrast Y
L1 Contrast Estimate -14.500
Hypothesized Value 0
Difference (Estimate - Hypothesized) -14.500
Std. Error 1.482
Sig. .000
95% Confidence Interval for Difference Lower Bound -17.536
Upper Bound -11.464
Test Results
Dependent Variable: Y
Source Sum of Squares df Mean Square F Sig.
Contrast 140.167 1 140.167 95.724 .000
Error 41.000 28 1.464

Note that you can enter multiple contrasts in a single statement, as shown below. Each contrast must be separated by a comma. While you get the significance for each individual test, you do not get the t-value. To obtain the t-value, you will have to divide the contrast estimate by the std. error in the Contrast Results (K Matrix) table. 

glm y by b
 /contrast(b)=special (0 0 1 -1, 1 1 -1 -1,  1 1 1 -3).
Between-Subjects Factors

N
B 1 8
2 8
3 8
4 8
Tests of Between-Subjects Effects
Dependent Variable: Y
Source Type III Sum of Squares df Mean Square F Sig.
Corrected Model 194.500(a) 3 64.833 44.276 .000
Intercept 924.500 1 924.500 631.366 .000
B 194.500 3 64.833 44.276 .000
Error 41.000 28 1.464

Total 1160.000 32


Corrected Total 235.500 31


a R Squared = .826 (Adjusted R Squared = .807)
Contrast Results (K Matrix)

Dependent Variable
B Special Contrast Y
L1 Contrast Estimate -2.750
Hypothesized Value 0
Difference (Estimate - Hypothesized) -2.750
Std. Error .605
Sig. .000
95% Confidence Interval for Difference Lower Bound -3.989
Upper Bound -1.511
L2 Contrast Estimate -9.000
Hypothesized Value 0
Difference (Estimate - Hypothesized) -9.000
Std. Error .856
Sig. .000
95% Confidence Interval for Difference Lower Bound -10.753
Upper Bound -7.247
L3 Contrast Estimate -14.500
Hypothesized Value 0
Difference (Estimate - Hypothesized) -14.500
Std. Error 1.482
Sig. .000
95% Confidence Interval for Difference Lower Bound -17.536
Upper Bound -11.464
Test Results
Dependent Variable: Y
Source Sum of Squares df Mean Square F Sig.
Contrast 192.250 2 96.125 65.646 .000
Error 41.000 28 1.464

 

Using the contrast command in a two-way ANOVA

Now let's try the same contrasts on b but in a two-way ANOVA. 
glm y by a b.
Between-Subjects Factors

N
A 1 16
2 16
B 1 8
2 8
3 8
4 8
Tests of Between-Subjects Effects
Dependent Variable: Y
Source Type III Sum of Squares df Mean Square F Sig.
Corrected Model 217.000(a) 7 31.000 40.216 .000
Intercept 924.500 1 924.500 1199.351 .000
A 3.125 1 3.125 4.054 .055
B 194.500 3 64.833 84.108 .000
A * B 19.375 3 6.458 8.378 .001
Error 18.500 24 .771

Total 1160.000 32


Corrected Total 235.500 31


a R Squared = .921 (Adjusted R Squared = .899) 

glm y by a b
/contrast(b)=special (0 0 1 -1).
Between-Subjects Factors

N
A 1 16
2 16
B 1 8
2 8
3 8
4 8
Tests of Between-Subjects Effects
Dependent Variable: Y
Source Type III Sum of Squares df Mean Square F Sig.
Corrected Model 217.000(a) 7 31.000 40.216 .000
Intercept 924.500 1 924.500 1199.351 .000
A 3.125 1 3.125 4.054 .055
B 194.500 3 64.833 84.108 .000
A * B 19.375 3 6.458 8.378 .001
Error 18.500 24 .771

Total 1160.000 32


Corrected Total 235.500 31


a R Squared = .921 (Adjusted R Squared = .899)
Contrast Results (K Matrix)

Dependent Variable
B Special Contrast Y
L1 Contrast Estimate -2.750
Hypothesized Value 0
Difference (Estimate - Hypothesized) -2.750
Std. Error .439
Sig. .000
95% Confidence Interval for Difference Lower Bound -3.656
Upper Bound -1.844
Test Results
Dependent Variable: Y
Source Sum of Squares df Mean Square F Sig.
Contrast 30.250 1 30.250 39.243 .000
Error 18.500 24 .771 

glm y by a b
 /contrast(b)=special (1 1 -1 -1).
Between-Subjects Factors

N
A 1 16
2 16
B 1 8
2 8
3 8
4 8
Tests of Between-Subjects Effects
Dependent Variable: Y
Source Type III Sum of Squares df Mean Square F Sig.
Corrected Model 217.000(a) 7 31.000 40.216 .000
Intercept 924.500 1 924.500 1199.351 .000
A 3.125 1 3.125 4.054 .055
B 194.500 3 64.833 84.108 .000
A * B 19.375 3 6.458 8.378 .001
Error 18.500 24 .771

Total 1160.000 32


Corrected Total 235.500 31


a R Squared = .921 (Adjusted R Squared = .899)
Contrast Results (K Matrix)

Dependent Variable
B Special Contrast Y
L1 Contrast Estimate -9.000
Hypothesized Value 0
Difference (Estimate - Hypothesized) -9.000
Std. Error .621
Sig. .000
95% Confidence Interval for Difference Lower Bound -10.281
Upper Bound -7.719
Test Results
Dependent Variable: Y
Source Sum of Squares df Mean Square F Sig.
Contrast 162.000 1 162.000 210.162 .000
Error 18.500 24 .771 

glm y by a b
 /contrast(b)=special (1 1 1 -3).
Between-Subjects Factors

N
A 1 16
2 16
B 1 8
2 8
3 8
4 8
Tests of Between-Subjects Effects
Dependent Variable: Y
Source Type III Sum of Squares df Mean Square F Sig.
Corrected Model 217.000(a) 7 31.000 40.216 .000
Intercept 924.500 1 924.500 1199.351 .000
A 3.125 1 3.125 4.054 .055
B 194.500 3 64.833 84.108 .000
A * B 19.375 3 6.458 8.378 .001
Error 18.500 24 .771

Total 1160.000 32


Corrected Total 235.500 31


a R Squared = .921 (Adjusted R Squared = .899)
Contrast Results (K Matrix)

Dependent Variable
B Special Contrast Y
L1 Contrast Estimate -14.500
Hypothesized Value 0
Difference (Estimate - Hypothesized) -14.500
Std. Error 1.075
Sig. .000
95% Confidence Interval for Difference Lower Bound -16.719
Upper Bound -12.281
Test Results
Dependent Variable: Y
Source Sum of Squares df Mean Square F Sig.
Contrast 140.167 1 140.167 181.838 .000
Error 18.500 24 .771

Note that the F-ratios in these contrasts are larger than the F-ratios in the one-way ANOVA example. This is because the two-way ANOVA has a smaller mean square residual than the one-way ANOVA.

SPSS has a number of "built-in" contrasts that you can use, of which special (used in the above examples) is only one. Below is a table listing those contrasts with an explanation of the contrasts that they make and an example of how the syntax works. The repeated comparison compares group 1 with 2, 2 with 3, and 3 with 4 as shown in the Contrast Results (K Matrix) table in the results.

Name of contrast Comparison made
Simple Compares each level of a variable to the last level (or whichever level is specified).
Deviation Compares deviations from the grand mean.
Difference Compares levels of a variable with the mean of the previous levels of the variable.
Helmert Compare levels of a variable with the mean of the subsequent levels of the variable.
Polynomial Orthogonal polynomial contrasts.
Repeated Adjacent levels of a variable.
Special User-defined contrast. 
glm y by a b
 /contrast(b)=repeated.
Between-Subjects Factors

N
A 1 16
2 16
B 1 8
2 8
3 8
4 8
Tests of Between-Subjects Effects
Dependent Variable: Y
Source Type III Sum of Squares df Mean Square F Sig.
Corrected Model 217.000(a) 7 31.000 40.216 .000
Intercept 924.500 1 924.500 1199.351 .000
A 3.125 1 3.125 4.054 .055
B 194.500 3 64.833 84.108 .000
A * B 19.375 3 6.458 8.378 .001
Error 18.500 24 .771

Total 1160.000 32


Corrected Total 235.500 31


a R Squared = .921 (Adjusted R Squared = .899)
Contrast Results (K Matrix)

Dependent Variable
B Repeated Contrast Y
Level 1 vs. Level 2 Contrast Estimate -.750
Hypothesized Value 0
Difference (Estimate - Hypothesized) -.750
Std. Error .439
Sig. .100
95% Confidence Interval for Difference Lower Bound -1.656
Upper Bound .156
Level 2 vs. Level 3 Contrast Estimate -2.750
Hypothesized Value 0
Difference (Estimate - Hypothesized) -2.750
Std. Error .439
Sig. .000
95% Confidence Interval for Difference Lower Bound -3.656
Upper Bound -1.844
Level 3 vs. Level 4 Contrast Estimate -2.750
Hypothesized Value 0
Difference (Estimate - Hypothesized) -2.750
Std. Error .439
Sig. .000
95% Confidence Interval for Difference Lower Bound -3.656
Upper Bound -1.844
Test Results
Dependent Variable: Y
Source Sum of Squares df Mean Square F Sig.
Contrast 194.500 3 64.833 84.108 .000
Error 18.500 24 .771

How to cite this page

Report an error on this page

UCLA Researchers are invited to our Statistical Consulting Services
We recommend others to our list of Other Resources for Statistical Computing Help
These pages are Copyrighted (c) by UCLA Academic Technology Services

The content of this web site should not be construed as an endorsement of any particular web site, book, or software product by the University of California