Variations of One Factor ANOVA Designs - Agricultural Statistical Data Analysis Using Stata - page 93

Table 5.4 Source of variation and degrees of freedom for a group balanced block design experiment

SOURCE OF VARIATION DEGREES OF FREEDOM (DF) RESULTS OF DF

Replication (rep) r - 1 3 - 1 = 2

Group (maturity) g - 1 3 - 1 = 2

Replication × Group (rep#maturity) (r - 1)( g - 1) (3 - 1)(3 - 1) = 4

t
g − 1

45
3

−= 114

Treatment with Group 1

t
g − 1

45
3

−= 114

Treatment with Group 2

t
g − 1

45
3

−= 114

Treatment with Group 3

t
g

45
3

( ) ( )

gr − 1 − 1 33 1 − − 1

Error (Residual)

arranged, treatments within a group can be compared to each other
with a greater degree of precision than treatments in different groups.
Table 5.4 shows the degrees of freedom for an experiment with 45
varieties arranged into 3 groups of 15 varieties.
Load the dataset GroupBalBlock.dta into Stata. This dataset is
from a variety trial of 45 rice varieties that consisted of 15 varieties in
each of 3 different maturity groups (Gomez and Gomez, 1984, p. 77).
The groups have maturities of less than 105 days, 105-115 days, and
those that mature in over 115 days. After loading the dataset, enter
the following command:

anova yield rep maturity / maturity # rep var | maturity

This results in the following output:

Number of obs = 135 R-squared = 0.7485
Root MSE = .296459 Adj R-squared = 0.5988

Source | Partial SS df MS F Prob > F
-----------+--------------------------------------------------
Model | 21.9712995 50 .43942599 5.00 0.0000
|
rep | 5.52888354 2 2.76444177 17.48 0.0105
maturity | 3.35749913 2 1.67874957 10.61 0.0251
maturity#rep | .632773299 4 .158193325
------------+--------------------------------------------------