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1
Methods for Proportions and Nominal Variables
BME 423 Lecture Notes
 Oct. 8, 2008
V.
Association Between Nominal Variables
A. Relative Risk
B. Odds Ratio
Types of Error in Inferences and
Power of a Statistical Test
I. The Idea
II.
Two Types of Errors
z Test
()
1
ˆˆ 11
2
ˆˆ
11
1
asp
pla
asp
pla
asp
pla
pp
n
n
z
n
n
−−
+
=
−+
12
ˆ
mm
p
nn
+
=
+
==
zt
α
ν
>→
∞
Reject H0
P
<
1
n
2
n
1
m
2
m
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Test
j
ij
i
C
ER
n
=
( )
2
2
11
c
r
n
n
ij
ij
ij
ij
OE
E
χ
==
−
=
∑∑
( )( )
rc
vn
n
=
−−
22
()
α
χν
>
Reject H0
P
<
2
(use Yates correction
only if 2x2)
Quantifying the Size
of a Treatment Effect –
Association Between Nominal Variables
Clinical Trials
Patients are randomized to treatment groups and then
the outcome is observed.
e.g., thrombosis development w/ aspirin vs placebo
Prospectively Designed: hypothesis, # of subjects,
exclusion criteria, statistical tests, etc.
Clinical Trials vs Epidemiological Studies
3
Quantifying the Size of a Treatment Effect –
Association Between Nominal Variables
Epidemiological Studies
Subjects not
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This note was uploaded on 12/02/2008 for the course BME 423 taught by Professor D'argenio during the Fall '06 term at USC.
 Fall '06
 D'Argenio
 Biomedical Engineering

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