Midterm
1. Consider a RCBD comparing a control to new treatments A, B, C, and D. Under the
usual ANOVA null hypothesis
H
o
:
μ
1
=
. . .
=
μ
a
, suppose the experimenter wants to
be able to detect when each treatment mean is
k
units greater than the control mean
at
α
=
.
01.
(a) Find the noncentrality parameter
λ
for the researcher’s alternative as a function
of
k
.
(b) Conduct an analysis of the pilot study below.
(c) Write a SAS program to compute power for various choices of
k
and
b
. Use an
estimate of
σ
from the pilot study. Construct a contour plot with
k
and
b
as the
coordinate axes.
(d) How many blocks would we need to detect
k
=
.
1,
k
=
.
2,
k
=
.
3 with 80%
power?
Block
Treatment
1
2
3
Control
9.60
9.61
9.52
A
9.75
9.64
9.79
B
9.87
9.83
9.60
C
9.72
9.82
9.69
D
9.56
9.90
9.87
2. Consider the following SAS output from analysis of a twoway model.
(a) Compute variance components assuming both factors are random.
(b) Construct tests for A, B and AB for both the unrestricted and restricted mixed
effects models. Assume A is fixed and B is random for this exercise.
Source
DF
Type III SS
Mean Square
F Value
Pr>F
A
2
5467.85
2733.93
30.03
.000
B
4
2451.90
612.97
6.73
.003
A*B
8
1857.29
232.16
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 Spring '08
 JohnM.Grego
 RCBD, residual treatment eﬀect

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