Two and More Factors ANOVA - Agricultural Statistical Data Analysis Using Stata - page 113

The results are essentially the same, but now we can use the margins
and marginsplot commands to examine the var#fert interaction.
Enter the following command and see the results:
margins var#fert
Predictive margins Number of obs = 54
Expression : Linear prediction, predict()
------------------------------------------------------------------
| Delta-method
| Margin Std. Err. z P>|z| [95% Conf. Interval]
--------+---------------------------------------------------------
var#fert|
1 0 |3571.667 370.4258 9.64 0.000 2845.645 4297.688
1 60 | 5132 370.4258 13.85 0.000 4405.979 5858.021
1 120 | 7548 370.4258 20.38 0.000 6821.979 8274.021
2 0 |4934.333 370.4258 13.32 0.000 4208.312 5660.355
2 60 |6713.667 370.4258 18.12 0.000 5987.645 7439.688
2 120 |7211.333 370.4258 19.47 0.000 6485.312 7937.355
3 0 |4249.667 370.4258 11.47 0.000 3523.645 4975.688
3 60 |6122.333 370.4258 16.53 0.000 5396.312 6848.355
3 120 |7868.333 370.4258 21.24 0.000 7142.312 8594.355
4 0 | 4059 370.4258 10.96 0.000 3332.979 4785.021
4 60 |5553.667 370.4258 14.99 0.000 4827.645 6279.688
4 120 |7094.333 370.4258 19.15 0.000 6368.312 7820.355
5 0 |4101.667 370.4258 11.07 0.000 3375.645 4827.688
5 60 |5633.333 370.4258 15.21 0.000 4907.312 6359.355
5 120 | 6012 370.4258 16.23 0.000 5285.979 6738.021
6 0 |3207.333 370.4258 8.66 0.000 2481.312 3933.355
6 60 |3714.333 370.4258 10.03 0.000 2988.312 4440.355
6 120 | 2492 370.4258 6.73 0.000 1765.979 3218.021
------------------------------------------------------------------
If you examine the Margin column, which contains the means
sorted by variety and then fertilizer rate, you may begin to see the
interaction. All the variety yields increase with increasing fertilizer
application except for variety 6. To see this more clearly, enter the
margins command as margins fert#var (this is in reverse order
from above—results not shown) and then enter the marginsplot
command. The results of the marginsplot are seen in Figure 6.5
and graphically show the differences between the varieties.
Another approach to see this interaction effect is to calculate a
separate ANOVA for each variety. One way to do this is to examine
the fertilizer rates effect for each variety. The following command will
calculate an ANOVA for each variety:
by var, sort: anova yield fert rep