Variations of One Factor ANOVA Designs - Agricultural Statistical Data Analysis Using Stata - page 77

unit was 120 ft 2 and the yield per plot is listed in the yield variable. I
often extrapolate such data into the units that will be most useful in
either publications or for grower meetings. Using 50-lb bags/acre is a
common method for presenting onion data. Depending on the situa-
tion and crop, you may wish to calculate boxes/acre, lbs/acre, or some
other common unit. It makes it easier when calculating and present-
ing results in tables and graphs. Whether the analysis is conducted
on the raw results (lbs/plot) or the extrapolated results, this will not
change the outcome.
There are several pieces of information presented in the ANOVA
table. The number of observations (60) reflects the total number of
experimental units, 20 varieties with three replications each. The
R-square (R 2 ) is the same value discussed previously with the one-
way ANOVA and, in this case, it is the Model sum of squares divided
by the Total sum of squares. This is often referred to as the coefficient
of determination with the following formula:

SS
SS

2 Residual

R =−

Total

he R 2 will increase in value as more independent variables are
added, but may not truly reflect an increase in its predictive ability. To
compensate for the phenomenon, an adjustment to the R 2 value has
been proposed with the formula

MS
MS

2 Residual

R =−

a

Total

This value will always be lower than the R 2 and compensates for
the number of independent factors in the model, thus, with models
with several independent factors, this may better reflect the actual
predictive nature of the model.
The Root MSE is the square root of the mean square error or
the residual mean square. In this case, it is 10294 921. , which is
101.464. The remainder of the table is much as it was described in
the one-way ANOVA described previously. There are, however, more
rows listed in the RCBD. The Model is an estimate of the combined
entry and rep sources in the experiment. The entry in this case are the
varieties, the rep are the blocks with one replication of each variety