Two and More Factors ANOVA - Agricultural Statistical Data Analysis Using Stata - page 125

Predictive Margins of Nitro#Var with 95% Cls

1000

Var = 1
Var = 3

Var = 2

8000

6000

4000

0 50

Nitrogen Rate: 0-140 kg/ha

80 110 140

Figure 6.9 Graphic output from the marginsplot command following margins
nitro#var command.

fertilizer with management, management with variety, or a three-way
interaction of nitrogen fertilizer, management, and variety.
The fertilizer by variety interaction can be further examined with
the following commands:

margins nitro# var
marginsplot

Both varieties 1 and 2 (var) increase in yield with increasing fertil-
izer application. Variety 3, on the other hand, increases yield up to
80 kg/ha at which point the yield decreases (Figure 6.9).

Covariance Analysis

Covariance analysis is a type of ANOVA that combines categori-
cal and continuous factors to more accurately predict the effects of
the categorical independent variable. This analysis of covariance that
includes both categorical and continuous factors has as an underlying
premise that there is a known relationship between the covariate and
the independent variable. There are several conditions that should be
met before using covariance analysis. The first is that the covariate
is fixed and the covariate will not affect the treatments. Second, the
regression of the covariate on the dependent variable is linear and
independent of the treatments. Finally, the residuals are normally and
independently distributed.