Two and More Factors ANOVA - Agricultural Statistical Data Analysis Using Stata - page 128

33.98727). The fourth command calculates the analysis of covariance
as shown above and the last command, matrix list e(b), which
must be entered immediately after the anova estimation command,
shows the regression matrix for the analysis of covariance. The error
regression coefficient is shown as part of this matrix below cov with a
value of -3.1320175. Entering the values in the adjusted mean equa-
tion results in the adjusted mean for the first variety of 92.58733.
92.58733 = 88.1 - (-3.1320175)(35.42 - 33.98727)
This is a long way to go and rather tedious to calculate these means.
Fortunately, Stata has a command that calculates the adjusted or mar-
ginal means. Enter the following command:
margins var
This results in the following output:
Predictive margins Number of obs = 55
Expression : Linear prediction, predict()
------------------------------------------------------------
| Delta-method
| Margin Std. Err. z P>|z| [95% Conf. Interval]
-------+----------------------------------------------------
var |
1 |92.58733 3.406412 27.18 0.000 85.91088 99.26377
2 |79.11642 6.275393 12.61 0.000 66.81688 91.41597
3 |78.10311 3.508606 22.26 0.000 71.22637 84.97985
4 |84.53012 3.950303 21.40 0.000 76.78767 92.27257
5 |95.98305 4.967951 19.32 0.000 86.24605 105.7201
6 |97.50684 3.588881 27.17 0.000 90.47277 104.5409
7 |99.97868 3.379806 29.58 0.000 93.35438 106.603
8 |72.04475 3.364251 21.41 0.000 65.45094 78.63856
9 |81.14672 3.390371 23.93 0.000 74.50171 87.79172
10 |122.7838 5.140306 23.89 0.000 112.709 132.8587
11 |74.31913 3.365915 22.08 0.000 67.72206 80.91621
------------------------------------------------------------
The Margin column lists the marginal or adjusted means. You will
note that the rank ordering of these means will differ considerably
from the observed means. Previously when we used the margins
command, the means were the arithmetic means because there was no
covariate involved.