Two and More Factors ANOVA - Agricultural Statistical Data Analysis Using Stata - page 101

6
t wo anD m ore
f actorS anova
Up until this point, all of the experiments (utilizing ANOVA [analysis
of variance]) we have examined have dealt with a single experimental
factor whether varieties, fertility levels, etc. It is possible to conduct
experiments in which more than one experimental factor at a time
is considered. In fact, in most biological systems, there are several
factors in play at any one time. Conducting experiments with more
than one factor is more likely to mimic real environmental conditions
and allows the researcher to see how these factors interact with one
another. In addition, time and resources may be conserved because
more than one factor is considered in a single experiment.
The number of factors that can be considered in an experiment is
theoretically unlimited. In fact, the analysis of experiments with up to
five factors has been worked out with considerations of various combina-
tions of random and fixed effect models. Caution, however, should be
exercised when considering experiments with greater than three factors.
It has been shown that a random set of numbers coded with a high num-
ber of factors will have a high likelihood of showing some significance.
Factorial experiments can be implemented in any number of exper-
imental designs, such as RCBD (randomized complete block design),
split-plot design, split-block design, etc. In addition, factorial experi-
ments can include more than two factors; however, the number of fac-
tors is usually limited because of resource limitations and the potential
increase in type I errors. Figure 6.1 shows several possible interaction
effects that might occur in an experiment. Statistical analysis of facto-
rial experiments can help identify these interactions and help deter-
mine why they occur.
Load the dataset SeedstemFactor.dta. This experiment is an exam-
ple of a factorial experiment arranged as an RCBD involving onion
varieties and sowing dates as the treatment factors. The dataset is of
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