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Pairwise comparisons were introduced in Stata 12.
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Stata 12 has two new commands for performing all pairwise comparisons of means and other margins across the levels of categorical variables. The pwmean command provides a simple syntax for computing all pairwise comparisons of means. After fitting a model with almost any estimation command, the pwcompare command can perform pairwise comparisons of estimated marginal means and other types of marginal linear predictions. In addition, the margins command now allows for performing all pairwise comparisons of linear and nonlinear predictions, such as marginal probabilities. With each of these commands, p-values and confidence intervals can be adjusted for multiple comparisons.
To obtain all pairwise differences of the mean of y across the levels of a treatment and adjust the p-values and confidence intervals for multiple comparisons using Tukey’s HSD, we can type
| Number of | ||
| Comparisons | ||
| treatment | 10 | |
| Tukey Tukey | ||
| y | Contrast Std. Err. t P>|t| [95% Conf. Interval] | |
| treatment | ||
| 2 vs 1 | 3.62272 1.589997 2.28 0.156 -.7552913 8.000731 | |
| 3 vs 1 | .4906299 1.589997 0.31 0.998 -3.887381 4.868641 | |
| 4 vs 1 | 4.922803 1.589997 3.10 0.019 .5447922 9.300815 | |
| 5 vs 1 | -1.238328 1.589997 -0.78 0.936 -5.616339 3.139683 | |
| 3 vs 2 | -3.13209 1.589997 -1.97 0.285 -7.510101 1.245921 | |
| 4 vs 2 | 1.300083 1.589997 0.82 0.925 -3.077928 5.678095 | |
| 5 vs 2 | -4.861048 1.589997 -3.06 0.021 -9.239059 -.4830368 | |
| 4 vs 3 | 4.432173 1.589997 2.79 0.046 .0541623 8.810185 | |
| 5 vs 3 | -1.728958 1.589997 -1.09 0.813 -6.106969 2.649053 | |
| 5 vs 4 | -6.161132 1.589997 -3.87 0.001 -10.53914 -1.78312 | |
If treatment=1 is a control and the other levels represent treatments, we may want to use Dunnett’s method for making comparisons.
| Number of | ||
| Comparisons | ||
| treatment | 4 | |
| Dunnett Dunnett | ||
| y | Contrast Std. Err. t P>|t| [95% Conf. Interval] | |
| treatment | ||
| 2 vs 1 | 3.62272 1.589997 2.28 0.079 -.2918331 7.537273 | |
| 3 vs 1 | .4906299 1.589997 0.31 0.994 -3.423923 4.405183 | |
| 4 vs 1 | 4.922803 1.589997 3.10 0.008 1.00825 8.837356 | |
| 5 vs 1 | -1.238328 1.589997 -0.78 0.852 -5.152881 2.676225 | |
After fitting a model, we can use pwcompare to make pairwise comparisons of the margins. We could fit the fully interacted model
and obtain pairwise comparisons of all the cell means for the interaction.
| Unadjusted | ||
| Margin Std. Err. Groups | ||
| treatment#grp | ||
| 1 0 | 36.91257 1.116571 A | |
| 1 1 | 45.81229 1.116571 B | |
| 2 0 | 38.79482 1.116571 A C | |
| 2 1 | 51.17547 1.116571 E | |
| 3 0 | 36.34383 1.116571 A | |
| 3 1 | 47.36229 1.116571 B | |
| 4 0 | 41.81757 1.116571 CD | |
| 4 1 | 50.7529 1.116571 E | |
| 5 0 | 35.69507 1.116571 A | |
| 5 1 | 44.55313 1.116571 B D | |
Because there are many pairwise comparisons, we obtain the results of the tests symbolically. Two means that have the same letter are not significantly different from each other at a 5% significance level.
See New in Stata 18 to learn about what was added in Stata 18.
