Stata does not have a built-in contrast command; however, ATS has developed a program that will do ANOVA contrasts. You can download the program anovacontrast.ado by typing search anovacontrast (see How can I use the search command to search for programs and get additional help? for more information about using search).
Now, let’s read in an example dataset, crf24, adapted from Kirk (1968, First Edition).
use https://stats.idre.ucla.edu/stat/stata/faq/crf24
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 anovacontrast command in a one-way ANOVA
anova y b
Number of obs = 32 R-squared = 0.8259
Root MSE = 1.21008 Adj R-squared = 0.8072
Source | Partial SS df MS F Prob > F
-----------+----------------------------------------------------
Model | 194.50 3 64.8333333 44.28 0.0000
|
b | 194.50 3 64.8333333 44.28 0.0000
|
Residual | 41.00 28 1.46428571
-----------+----------------------------------------------------
Total | 235.50 31 7.59677419
table b, contents(mean y)
----------+-----------
b | mean(y)
----------+-----------
1 | 2.75
2 | 3.5
3 | 6.25
4 | 9
----------+-----------
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
anovacontrast b, values(0 0 1 -1) Contrast variable b (0 0 1 -1) Dep Var = y source SS df MS N of obs = 32 ---------+--------------------------------- F = 20.66 contrast | 30.25 1 30.2500 Prob > F = 0.0001 error | 41 28 1.4643 ---------+--------------------------------- anovacontrast b, values(1 1 -1 -1) Contrast variable b (1 1 -1 -1) Dep Var = y source SS df MS N of obs = 32 ---------+--------------------------------- F = 110.63 contrast | 162 1 162.0000 Prob > F = 0.0000 error | 41 28 1.4643 ---------+--------------------------------- anovacontrast b, values(1 1 1 -3) Contrast variable b (1 1 1 -3) Dep Var = y source SS df MS N of obs = 32 ---------+--------------------------------- F = 95.72 contrast | 140.166667 1 140.1667 Prob > F = 0.0000 error | 41 28 1.4643 ---------+---------------------------------
Using the anovacontrast command in a two-way ANOVA
Now let’s try the same contrasts on b but in a two-way ANOVA.
anova y a b a*b
Number of obs = 32 R-squared = 0.9214
Root MSE = .877971 Adj R-squared = 0.8985
Source | Partial SS df MS F Prob > F
-----------+----------------------------------------------------
Model | 217.00 7 31.00 40.22 0.0000
|
a | 3.125 1 3.125 4.05 0.0554
b | 194.50 3 64.8333333 84.11 0.0000
a*b | 19.375 3 6.45833333 8.38 0.0006
|
Residual | 18.50 24 .770833333
-----------+----------------------------------------------------
Total | 235.50 31 7.59677419
anovacontrast b, values(0 0 1 -1)
Contrast variable b (0 0 1 -1) Dep Var = y
source SS df MS N of obs = 32
---------+--------------------------------- F = 39.24
contrast | 30.25 1 30.2500 Prob > F = 0.0000
error | 18.5 24 0.7708
---------+---------------------------------
anovacontrast b, values(1 1 -1 -1)
Contrast variable b (1 1 -1 -1) Dep Var = y
source SS df MS N of obs = 32
---------+--------------------------------- F = 210.16
contrast | 162 1 162.0000 Prob > F = 0.0000
error | 18.5 24 0.7708
---------+---------------------------------
anovacontrast b, values(1 1 1 -3)
Contrast variable b (1 1 1 -3) Dep Var = y
source SS df MS N of obs = 32
---------+--------------------------------- F = 181.84
contrast | 140.166667 1 140.1667 Prob > F = 0.0000
error | 18.5 24 0.7708
---------+---------------------------------
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.