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The Latin Square design
The Latin square design is used where the researcher desires to
control the variation in an experiment that is related to rows and
columns in the field.
Field marks:
- Treatments are assigned at random within rows and columns, with each treatment once per row and once per column.
- There are equal numbers of rows, columns, and treatments.
- Useful where the experimenter desires to control variation in two different directions
Sample layout:
Different colors represent different treatments. There are
4 treatments (A-D) assigned to 4 rows (I-IV) and 4
columns (1-4).
Row I A B C D
Row II C D A B
Row III D C B A
Row IV B A D C
Column 1 2 3 4
ANOVA table format:
Source of
variation |
Degrees of
freedoma |
Sums of
squares (SSQ) |
Mean
square (MS) |
F |
| Rows (R) |
r-1 |
SSQR |
SSQR/(r-1) |
MSR/MSE |
| Columns (C) |
r-1 |
SSQC |
SSQC/(r-1) |
MSC/MSE |
| Treatments (Tr) |
r-1 |
SSQTr |
SSQTr/(r-1) |
MSTr/MSE |
| Error (E) |
(r-1)(r-2) |
SSQE |
SSQE/((r-1)(r-2)) |
|
| Total (Tot) |
r2-1 |
SSQTot |
|
|
| awhere r=number of treatments, rows, and columns. |
Sample ANOVA table:
Source of
variation |
Degrees of
freedom |
Sums of
squares (SSQ) |
Mean
square (MS) |
F |
| Rows |
3 |
40.77 |
13.59 |
5.91a |
| Columns |
3 |
125.39 |
41.80 |
18.16a |
| Treatments |
3 |
160.57 |
53.52 |
23.26a |
| Error |
6 |
13.81 |
2.30 |
|
| Total |
15 |
340.54 |
|
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| aF test with 3,6 degrees of freedom at P=0.05 is 4.76 |
Sample SAS GLM statements:
PROC GLM;
CLASS ROWS COLUMNS TREATS;
MODEL WHATEVER = ROWS COLUMNS TREATS;
RUN;
Compare with:
Washington State University
Tree Fruit Research and Extension Center
1100 N. Western Ave.
Wenatchee WA 98801
phone: 509-663-8181
fax: 509-662-8714
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Wednesday, August 16, 2000
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