How can I do ANOVA contrasts in SPSS?

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How can I do ANOVA contrasts in SPSS?

By stats writer / June 30, 2024

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ANOVA contrasts in SPSS refer to a statistical analysis method used to compare the means of three or more groups. This technique allows researchers to determine if there are significant differences between the means of the groups being studied. To perform ANOVA contrasts in SPSS, one must first input the data into the software and specify the groups to be compared. Next, the appropriate ANOVA test must be selected and the desired contrast options must be specified. SPSS will then calculate the contrast values and provide the necessary statistical output for interpretation. This process can be useful in various research settings, such as comparing the effectiveness of different treatments or identifying significant differences between demographic groups. Overall, ANOVA contrasts in SPSS are a valuable tool for understanding and analyzing group differences in a systematic and rigorous manner.

How can I do ANOVA contrasts in SPSS? | SPSS FAQ

Let’s use an example dataset, crf24.sav, adapted from Kirk (1968, First Edition).

get file 'c:tempcrf24.sav'.

These data are from a 2×4 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
(F(3, 28) = 44.276, p = .000). 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

This contrast is statistically significant
(F(1, 28) = 20.659, p = .000).

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

This contrast is also statistically significant (F(1, 28) = 110.634, p =
.000).

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

This contrast is also statistically significant (F(1, 28) = 95.724, p =
.000).

Note that you can enter multiple contrasts in
a single subcommand, as shown below. Each contrast must be separated by a comma. While you get the significance
tests 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
contrast 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

For more information on coding contrasts,
please see How can I use the lmatrix subcommand to understand a three-way interaction
in ANOVA? .

References

Kirk, Roger E. (1968) Experimental Design: Procedures for the Behavioral Sciences.
Monterey, California: Brooks/Cole Publishing.

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stats writer (2024). How can I do ANOVA contrasts in SPSS?. PSYCHOLOGICAL SCALES. Retrieved from https://scales.arabpsychology.com/stats/how-can-i-do-anova-contrasts-in-spss/

stats writer. "How can I do ANOVA contrasts in SPSS?." PSYCHOLOGICAL SCALES, 30 Jun. 2024, https://scales.arabpsychology.com/stats/how-can-i-do-anova-contrasts-in-spss/.

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How can I do ANOVA contrasts in SPSS?

How can I do ANOVA contrasts in SPSS? | SPSS FAQ

Using the contrast command in a one-way ANOVA

Using the contrast command in a two-way ANOVA

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Using the contrast command in a one-way ANOVA

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