Two Sample Tests - Agricultural Statistical Data Analysis Using Stata - page 72

In the CRD under Source is listed Between groups, which rep-
resents the treatments or, in this case, the watermelon varieties. The
Within groups represents the experimental error or differences that
occur due to such things as minor errors in measurement or the natu-
ral differences that occur between individuals.
The next column, SS, is the abbreviation for sum of squares , which
is followed by the df column. The df stands for degrees of freedom and
represents one less than the number of items in this source of varia-
tion. In this case (Between groups), there were nine cultivars, thus,
the number listed is (9 - 1) or 8. The Within groups degrees of free-
dom is 90, which is the total of all the degrees of freedom for each
cultivar. The total number of experimental units in this study was 99,
so the total degrees of freedom is 98.
The next column, MS, is the mean square column and this is calcu-
lated by dividing the sum of squares by the degrees of freedom. The
mean squares listed are variances, from which is calculated the F value.
The F value is the Between groups variance or mean square divided by
the Within groups mean square. The Prop > F is the probability of the F
value occurring by chance alone. In this case, a value of 0.0000 indicates
that there is a real difference based on a 0.01 or even a 0.001 threshold.
The last line in the table calculates Bartlett's test for equal vari-
ances. One of the underlying assumptions with ANOVA is that the
variances between the treatments (cultivars) be the same, and, in this
case, they are not. For the time being, we will ignore this and come
back to it in a later chapter.
As mentioned earlier, there is more than one command that can
calculate an ANOVA. The loneway command can do the same
calculation. The loneway command is primarily used for large
one-way ANOVAs. he loneway command can be used to calcu-
late ANOVAs with levels (treatments) greater than 376, while the
oneway can only calculate experiments up to 376 levels.
Below is the output from the loneway command of the same
virus screening data. Note the ANOVA table is the same, but there
are again more data present. First there is the addition of an R-squared
value. This is a value from 0-1 that reflects how well the treatments
predict the outcome and, in this case, is calculated as the between
treatment sum of squares divided by the total sum of squares. The
closer this value is to 1, the better the model fits.