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Chapter 7
The TwoWay Layout
Some Changes to pages 9 – 12:
7.4 Onesided Comparisons of Treatments with Control
Based on Friedman Rank Sums (Nemenyi, Wilcoxon – Wilcox, Miller)
Used after rejecting the null hypothesis of no difference between treatment effects. Compares
each treatment with a control group (call it treatment 1).
Hypotheses of interest are
•
Ho: τ
u
= τ
1
vs.
Ha: τ
u
> τ
1
for all u = 2, 3, …, k
with decision Rule:
Decide τ
u
> τ
1
if (R
u
– R
1
) ≥ r*
α
.
•
Or Ha: τ
u
> τ
1
for all u = 2, 3, …,k
with decision rule
τ
1
< τ
u
if (R
1
– R
u
) ≥ r*
α
.
Example:
Use the hydrobromide data of the example on page 3 (copied below) to test whether
any of the hydrobromides produce
a higher average number of hours of sleep per night that
does the “no hypnotic,” i.e., treatment A.
Patient
A
B
C
D
1
0.6
(1)
1.3
(2)
2.5
(4)
2.1
(3)
2
1.1
(1.5)
1.1
(1.5)
5.7
(3)
5.8
(4)
3
2.5
(1)
6.2
(2)
8
(3)
8.2
(4)
4
2.8
(1)
3.6
(2)
4.4
(4)
4.3
(3)
5
2.9
(1)
4.9
(2)
6.3
(3)
6.4
(4)
6
3.0
(2)
1.4
(1)
3.8
(3)
4.4
(4)
R
j
(7.5)
(10.5)
(20)
(22)
We are interested in testing
Ho: τ
u
= τ
1
vs. Ha: τ
u
> τ
1
,
for all u = 2, 3, 4
simultaneously.
From Table A25, with n = 6, k = 4 and α = 0.0404, we find
Hence we will decide
τ
u
> τ
1
if R
u
– R
1
≥ 10.
Show that,
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 Summer '11
 YESILCAY

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