Geoscience Reference
In-Depth Information
The analysis of variance is as follows:
Source of Variation
Degrees of Freedom
Sums of Squares
Mean Squares
Rows
4
16.8
4.2
Columns
4
16.0
4.0
Species
4
46.0
11.5
Error
12
73.2
6.1
Total
24
152.0
11 5
61
.
.
F (forspecies) = =
1 885
.
As the computed value of F is less than the tabular value of F at the 0.05 level (with 4/12 degrees of
freedom), the differences among species are considered nonsignificant.
The Latin square design can be used whenever there is a two-way heterogeneity that cannot be
controlled simply by blocking. In greenhouse studies, distance from a window could be treated as a
row effect while distance from the blower or heater might be regarded as a column effect. Though
the plots are often physically arranged in rows or columns, this is not required. When testing the
use of materials in a manufacturing process where different machines and machine operators will
be involved, the variation between machines could be treated as a row effect and the variation due
to operators could be treated as a column effect.
The Latin square should not be used if an interaction between rows and treatments or columns
and treatments is suspected.
7.16.5 F aCtorial e xperiments
In environmental practice, knowledge that interactions between elements of the environment occur
and an understanding of what their influence or impact on the environment is, or can be, is impor-
tant. Consider a comparison of corn yields following three rates or levels of nitrogen fertilization
indicating that the yields depended on how much phosphorus was used along with the nitrogen. The
differences in yield were smaller when no phosphorus was used than when the nitrogen applications
were accompanied by 100 lb/acre of phosphorus. In statistics, this situation is referred to as an inter-
action between nitrogen and phosphorus. Another example is when leaf litter was removed from
the forest floor, the catch of pine seedlings was much greater than when the litter was not removed,
but for red oak the reverse was true—the seedling catch was lower where litter was removed. Thus,
species and litter treatment were interacting.
Interactions are important in the interpretation of study results. In the presence of an interaction
between species and litter treatment it obviously makes no sense to talk about the effects of litter
removal without specifying the species. The nitrogen-phosphorus interaction means that it may be
misleading to recommend a level of nitrogen without mentioning the associated level of phosphorus.
Factorial experiments are aimed at evaluating known or suspected interactions. In these experi-
ments, each factor to be studied is tested at several levels and each level of a factor is tested at all
possible combinations of the levels of the other factors. In a planting test involving three species of
trees and four methods of preplanting site preparation, each method will be applied to each species,
and the total number of treatment combinations will be 12. In a factorial test of the effects of two
nursery treatments on the survival of four species of pine planted by three different methods, there
would be 24 (2 × 4 × 3 = 24) treatment combinations.
The method of analysis can be illustrated by a factorial test of the effects of three levels of nitro-
gen fertilization (0, 100, and 200 lb/acre) on the growth of three species (A, B, and C) of planted
pine. The nine possible treatment combinations were assigned at random to nine plots in each of
 
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