Agriculture Reference
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the design. Often this design is used where two different gradients
may occur in a field, perhaps soil fertility in one direction and soil
moisture in another. The limitation that the number of treatments
equals the number of columns and rows limits the usefulness of such
designs because as the number of treatments increases, the number
of experimental units can quickly increase to an unwieldy number.
Often with a small number of treatments, four or less, two identical
LSs are used to increase the precision of the experiment. Generally
LSs with more than eight treatments are not conducted because of the
unwieldy nature and size of such experiments.
Load the data file Latin square 1.dta into Stata and enter the fol-
lowing command:
anova
pyr trt row column
This dataset represents an experiment where the variable trt rep-
resents four different rates of sulfur fertilizer (0, 20, 40, 60 lbs/
acre) applied to onions as part of a complete fertilizer program.
The row and column variables represent the plot position in the
experiment. The pyr variable represents the pyruvate value meas-
ured from 10 bulbs from each experimental unit. The pyruvate test
is a relative measure of onion pungency. This results in the follow-
ing output:
Number of obs = 16 R-squared = 0.9446
Root MSE = .260192 Adj R-squared = 0.8615
Source | Partial SS df MS F Prob > F
-------+----------------------------------------------------
Model | 6.92497434 9 .769441593 11.37 0.0039
|
trt | 2.96342539 3 .987808464 14.59 0.0037
row | .38727494 3 .129091647 1.91 0.2296
column | 3.574274 3 1.19142467 17.60 0.0022
|
Residual | .406200239 6 .06770004
---------+----------------------------------------------------
Total | 7.33117457 15 .488744972
Unlike the previous analysis, there are now two additional sources
of variation; in addition to the treatment effect (trt), there are row and
column effects. In the previous experiment, the rep variable represents
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