Statistics Review - Mathematics and Statistics for the Environment - page 152

With the partitioning the analysis has become:

Source of Variation Degrees of Freedom Sum of Squares Mean Square F

Blocks 2 11.6296 5.8148 —

Species 2 109.8518 54.9259 2.992 a

2B vs. (A + C) 1 109.7963 109.7963 5.981 b

A vs. C 1 0.0555 0.0555 —

Nitrogen 2 1725.6296 862.8148 47.003 c

2N 0 vs. (N 1 + N 2 ) 1 1711.4074 1711.4074 93.232 c

N 1 vs. N 2 1 14.2222 14.2222 —

4 134.8149 33.7037 1.836 a

Species × nitrogen interaction

Error 16 293.7037 18.3565 —

Total 26 2275.6296 —

a Not significant.
b Significant at the 0.05 level.
c Significant at the 0.01 level.

We conclude that species B is poorer than A or C and that there is no difference in growth between
A and C. We also conclude that nitrogen adversely affected growth and that 100 lb was about as bad
as 200 lb. The nitrogen effect was about the same for all species (i.e., no interaction).
It is worth repeating that the comparisons to be made in an analysis should, whenever possible,
be planned and specified prior to an examination of the data. A good procedure is to outline the
analysis, putting in all the times that are to appear in the first two columns (source of variation and
degrees of freedom) of the table.
The factorial experiment, it will be noted, is not an experimental design. It is, instead, a way
of selecting treatments; given two or more factors each at two or more levels, the treatments are
all possible combinations of the levels of each factor. If we have three factors with the first at four
levels, the second at two levels, and the third at three levels, we will have 4 × 2 × 3 = 24 facto-
rial combinations or treatments. Factorial experiments may be conducted in any of the standard
designs. The randomized block and split plot design are the most common for factorial experi-
ments in forest research.

7.16.6 s plit -p lot d esign
When two or more types of treatment are applied in factorial combinations, it may be that one type
can be applied on relatively small plots while the other type is best applied to larger plots. Rather
than make all plots of the size needed for the second type, a split-plot design can be employed.
In this design, the major (large-plot) treatments are applied to a number of plots with replication
accomplished through any of the common designs (such as complete randomization, randomized
blocks, Latin square). Each major plot is then split into a number of subplots, equal to the number
of minor (small-plot) treatments. Minor treatments are assigned at random to subplots within each
major plot.
As an example, a test was to be made of direct seeding of loblolly pine at six different dates
on burned and unburned seedbeds. To get typical burn effects, major plots 6 acres in size were
selected. There were to be four replications of major treatments in randomized blocks. Each major
plot was divided into six 1-acre subplots for seeding at six dates. The field layout was somewhat as
follows (blocks denoted by Roman numerals, burning treatment by capital letters, day of seeding
by small letters):