Agriculture Reference
In-Depth Information
Table 5.5
Source of variation and degrees of freedom for CRD, RCBD, and split-plot designs
with subsampling
DEGREES OF FREEDOM (DF)
SOURCE OF VARIATION
CRD
RCBD
SPLIT-PLOT DESIGN
Replication (r)
r
- 1
r
- 1
r
- 1
Main-plot treatment (a)
a
- 1
a
- 1
a
- 1
Error
a
(
r
- 1)
(
r
- 1)(
t
- 1)
(
r
- 1)(
t
- 1)
Subplot treatment (b)
b
- 1
a × b
(
a
- 1)(
b
- 1)
Error
a
(
r
- 1)(
b
- 1)
Sampling error (s)
rt
(
s
- 1)
rt
(
s
- 1)
abr
(
s
- 1)
Note:
Arrows indicate the ratio of mean squares for calculating F values.
Several criteria should be considered with subsampling. It should
be easy to obtain, have good precision, and be low cost. Subsampling
information from previous experiments also can help determine sam-
ple size for future experiments.
One approach evaluates the variance of a treatment mean and the
CV to determine an appropriate subsample size. Deciding on a sam-
ple size should have a low sampling variance and meet the degree
of precision desired. Computing the variance of a treatment mean
can be accomplished by calculating the experimental error variance
as follows:
2
2
σσ
−
2
es
+
s
σ
=
e
n
2
is the mean square for
rep#trt
and
σ
s
2
is the residual
mean square. he
n
is the number of subsamples. To do this from the
above ANOVA, enter the following:
where the
σ
es
display (
.065124501
-
.016989407
)/
2
which results in 0.02406755. The experimental error variance is then used
to calculate the variance of a treatment mean represented by the formula
2
2
σσ
+
n
rn
2
s
e
σ
=
where the variables are defined above and
r
is the number of replica-
tions. Enter the following and see the results:
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