Two Sample Tests - Agricultural Statistical Data Analysis Using Stata - page 70

Fisher (English statistician, 1890-1962) who first proposed this type
of testing. There is a relationship between this analysis and the t-test
where only two treatments are involved. If the t-test value is squared,
it will equal the F value from an ANOVA. In this type of analysis
(in its simplest form), variances are calculated for experimental units
treated in the same fashion, often called the within group variance and
for treatments treated differently called the between group variance . If
the treatments are different, then the between group variance will be
larger than the within group variance. This usually is represented as
a ratio of the between group variance over the within group variance
and is called F . A probability is then calculated to indicate what is
the chance of this difference occurring by chance alone. By custom,
probabilities of 0.01, 0.05, or 0.10 are often used to declare treatment
effects having a statistical difference.
This simple experimental design is called a completely randomized
design (CRD). With this design, treatments are assigned randomly
to experimental units. This type of experimental design is used where
there is a great deal of uniformity between the experimental units other
than treatment effects or there is very little difference between experi-
mental units because of environment or location. Examples where this
type of design might be used include a growth chamber where condi-
tions other than the treatments would be very uniform. Greenhouse
experiments also may be arranged in this fashion, although there are
often sufficient differences between locations in a greenhouse to war-
rant the use of a different experimental design. Finally, in animal
experiments where the animals (experimental units) are considered
reasonably uniform before treatment application can be tested with
a completely randomized design. Animal uniformity might include
selecting animals with similar weights or ages and, in addition, no
attempt is made to segregate the animals.
There are several ANOVA commands within Stata that can be used
to analyze this type of design. They include oneway , loneway , and
anova . Each arrives at the same solution, while each offers slightly
different information. At this time, we will concentrate on oneway
and loneway because they restrict the model to just one indepen-
dent variable. The oneway command can be entered as follows:
oneway response_var factor_var [ if ] [ in ] [ weight ] [, options ]