Stata FAQ: How can I do post-hoc pairwise comparisons of adjusted means in Stata? This FAQ will cover doing pairwise comparisons for adjusted means and will make use of the margins and pwcompare commands.
We will demonstrate the pairwise comparisons of adjusted means using the hsbdemo dataset with prog (program type) as the categorical variable and read as the continuous covariate.
We will begin by running a model without the covariate so that we can see the differences in the unadjusted means.
use https://stats.idre.ucla.edu/stat/data/hsbdemo, clear
tabstat write, by(prog) stat(n mean sd)
Summary for variables: write
by categories of: prog (type of program)
prog | N mean sd
---------+------------------------------
general | 45 51.33333 9.397775
academic | 105 56.25714 7.943343
vocation | 50 46.76 9.318754
---------+------------------------------
Total | 200 52.775 9.478586
----------------------------------------
anova write prog
Number of obs = 200 R-squared = 0.1776
Root MSE = 8.63918 Adj R-squared = 0.1693
Source | Partial SS df MS F Prob > F
-----------+----------------------------------------------------
Model | 3175.69786 2 1587.84893 21.27 0.0000
|
prog | 3175.69786 2 1587.84893 21.27 0.0000
|
Residual | 14703.1771 197 74.635417
-----------+----------------------------------------------------
Total | 17878.875 199 89.843593
margins prog // view cell means
Adjusted predictions Number of obs = 200
Expression : Linear prediction, predict()
------------------------------------------------------------------------------
| Delta-method
| Margin Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
prog |
1 | 51.33333 1.287853 39.86 0.000 48.80919 53.85748
2 | 56.25714 .8430976 66.73 0.000 54.6047 57.90958
3 | 46.76 1.221764 38.27 0.000 44.36539 49.15461
------------------------------------------------------------------------------
pwcompare prog, mcompare(tukey) effects // pairwise comparisons
Pairwise comparisons of marginal linear predictions
Margins : asbalanced
---------------------------
| Number of
| Comparisons
-------------+-------------
prog | 3
---------------------------
------------------------------------------------------------------------------
| Tukey Tukey
| Contrast Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
prog |
2 vs 1 | 4.92381 1.539279 3.20 0.005 1.288703 8.558916
3 vs 1 | -4.573333 1.775183 -2.58 0.029 -8.765543 -.3811241
3 vs 2 | -9.497143 1.484426 -6.40 0.000 -13.00271 -5.991573
------------------------------------------------------------------------------
Note: The tukey method requires balanced data for proper level coverage. A
factor was found to be unbalanced.
With unbalanced data the tukey option in pwcompare produces the Tukey-Kramer solution.
Next, we add the covariate to the model. The margins and pwcompare commands take into account the covariate in the model to produces the cell means and the pairwise differences.
anova write prog c.read
Number of obs = 200 R-squared = 0.3925
Root MSE = 7.44408 Adj R-squared = 0.3832
Source | Partial SS df MS F Prob > F
-----------+----------------------------------------------------
Model | 7017.68123 3 2339.22708 42.21 0.0000
|
prog | 650.259965 2 325.129983 5.87 0.0034
read | 3841.98338 1 3841.98338 69.33 0.0000
|
Residual | 10861.1938 196 55.4142539
-----------+----------------------------------------------------
Total | 17878.875 199 89.843593
margins prog, asbalanced
Predictive margins Number of obs = 200
Expression : Linear prediction, predict()
------------------------------------------------------------------------------
| Delta-method
| Margin Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
prog |
1 | 52.50272 1.118549 46.94 0.000 50.31041 54.69504
2 | 54.39898 .7599706 71.58 0.000 52.90946 55.88849
3 | 49.6097 1.106984 44.82 0.000 47.44005 51.77934
------------------------------------------------------------------------------
pwcompare prog, mcompare(tukey) effects
Pairwise comparisons of marginal linear predictions
Margins : asbalanced
---------------------------
| Number of
| Comparisons
-------------+-------------
prog | 3
---------------------------
------------------------------------------------------------------------------
| Tukey Tukey
| Contrast Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
prog |
2 vs 1 | 1.896256 1.375278 1.38 0.354 -1.351677 5.14419
3 vs 1 | -2.893026 1.542866 -1.88 0.149 -6.536747 .7506945
3 vs 2 | -4.789282 1.39847 -3.42 0.002 -8.091988 -1.486576
------------------------------------------------------------------------------
Note: The tukey method requires balanced data for proper level coverage. A
factor was found to be unbalanced.
Once again, with unbalanced data the tukey option in pwcompare produces the Tukey-Kramer solution.