Two and More Factors ANOVA - Agricultural Statistical Data Analysis Using Stata - page 118

-------+----------------------------------------------------
year#var | 1191.44855 14 85.103468 1.26 0.2432
rep#var|year | 7076.74621 105 67.397583
--------+----------------------------------------------------
|
Residual | 0 0
--------+----------------------------------------------------
Total | 10961.7903 143 76.6558764
The results of this analysis indicate there are no treatment effects
and the treatment by year also is not significant. The important idea
to recognize in analyzing data over seasons or years is that seasons are
considered fixed effects and years are considered random effects. This
is evident in the selection of the denominator for calculating the F
value. In the former case, the pooled error will have a larger degrees of
freedom, which will result in a smaller denominator value. This means
that finding differences between treatments will generally occur more
often. In the latter case, the denominator degrees of freedom for treat-
ment effects is the year-by-treatment interaction, which will have a
smaller degrees of freedom and result in a larger denominator value
for the F calculation and less chance of finding differences.
hree-Factor Design
A three-factor design includes an additional factor for analysis and
allows for both pairwise and three-way interactions to be analyzed.
In theory, any number of factors can be analyzed in this fashion;
however, in practical terms, such experiments become difficult to exe-
cute because of the size of the experiment and costs involved.
For example, a three-factor experiment might include variety, fertil-
ity program, and planting date. Load the file Three factor.dta, which is
a dataset of onion yield with four varieties, five fertility levels, and three
planting dates. This 4 × 5 × 3 factorial experiment has 60 treatments
with four replications. It is evident how quickly such experiments can
become quite large and unwieldy. Enter the following command:
anova wtlbs rep fertility sowingdate variety
fertility # sowingdate fertility # variety
sowingdate # variety fertility # sowingdate # variety
This results in the following output: