Sample size calculation
Let us calculate the sample size needed to achieve Option 4. As the 60-day period is
the primary period of interest we shall use the residual mean square 1653 g2 from the
analysis of covariance for the 60-day period for the first two batches as the estimate of the
residual variance that might occur in the complete experiment. Let the total number of animals
to be used per diet be n. From the formula for the t-test shown earlier, namely n=2s2t2/( )2, we estimate: n = (2 x 1653 x t2) / (219.9-188.4)2
where means 219.9 (diet A+B) and 188.4 (diet C) shown in the output are substituted
for
and respectively.
Analysis of variance (adjusted for covariate)
Source
|
d.f.
|
s.s.
|
m.s.
|
v.r.
|
F pr.
|
Batch stratum
|
Covariate
|
1
|
32310
|
32310
|
|
|
Batch.*Units* stratum
|
Diet60
|
2
|
4313
|
2157
|
1.30
|
0.305
|
Covariate
|
1
|
85893
|
85893
|
51.95
|
<.001
|
Residual
|
13
|
21492
|
1653
|
4.64
|
|
Total
|
17
|
154607
|
|
|
|
|
|
|
|
|
|
Grand mean
|
198.0
|
|
|
|
|
Diet60
|
C
|
A+B
|
B
|
|
|
|
188.4
|
219.9
|
185.7
|
|
|
rep.
|
6
|
|
|
|
|
d.f.
|
13
|
|
|
|
|
s.e.d.
|
23.92
|
|
|
|
|
|