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Unformatted text preview: ation of Sample Size and Power
R × C Contingency Tables
ChiSquare GoodnessofFit Test
The Kappa Statistic Independent Samples
Suppose it is anticipate that k times as many people as in
group 1 will be enrolled in group 2.
2 n1 = 1
pq 1 +
¯¯
z1−α/2 +
k p2 q2
p1 q1 +
z1−β
k /∆2 where ∆ = p1 − p2 , p = (p1 + kp2 )/(1 + k ), q1 = 1 − p1 ,
¯
q2 = 1 − p2 and q = 1 − p .
¯
¯
Power Achieved
Power = P Z ≤ ∆
p1 q1 /n1 + p2 q2 /n2 − z1−α/2 p q (1/n1 + 1/n2 )
¯¯
p1 q1 /n1 + p2 q2 /n2 where p = (n1 p1 + n2 p2 )/(n1 + n2 ), ∆, q , q1 and q2 are as
¯
¯
deﬁned before.
For one sided test, replace α/2 with α. Chapter 10: Hypothesis Testing: Categorical Data Stat 491: Biostatistics Introduction
TwoSample Test for Binomial Proportions
McNemar’s Test
Estimation of Sample Size and Power
R × C Contingency Tables
ChiSquare GoodnessofFit Test
The Kappa Statistic Examples: Cancer, Nutrition
Suppose we know from Connecticut tumorregistry data that the
incidence rate of breast cancer over a 1year period for initially
diseasefree women ages 4549 is 150 cases per 100,000. We wish
to study whether ingesting large doses of vitamin E in capsule form
will prevent breast cancer. The study is set up with (1) a control
group of 45 to 49yearold women who are mailed placebo pills
and are expected to have the same disease rate as indicated in the
Connecticut tumorregistry data and (2) a study group of
similarage women who are mailed vitamin Epills and are expected
to have a 20% reduction in risk. How large a sample is needed if a
twosided test with a signiﬁcance level of .05 is used and a power
of 80% is desired?
Chapter 10: Hypothesis Testing: Categorical Data Stat 491: Biostatistics Introduction
TwoSample Test for Binomial Proportions
McNemar’s Test
Estimation of Sample Size and Power
R × C Contingency Tables
ChiSquare GoodnessofFit Test
The Kappa Statistic Otolaryngology Suppose a study comparing a medical and a surgical treatment for
children who have an excessive number of episodes of otitis
media(OTM) during the ﬁrst 3 years of life is planned. Success
rate of 50% and 70% are assumed in the medical and surgical
groups, respectively, and the recruitment of 100 patients for each
group is realistically anticipated. Succ...
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This note was uploaded on 02/03/2014 for the course STAT 491 taught by Professor Solomonharrar during the Fall '12 term at Montana.
 Fall '12
 SolomonHarrar
 Statistics, Biostatistics

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