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Unformatted text preview: Method
Fisher’sExact Test Fisher’sExact Test Cont’d...
Let p1 be the probability that the man was on a highsalt diet
given that his cause was nonCVD and p2 be the be the
probability that the man was on a highsalt diet given that his
cause of death was CVD. We are interested in testing
H0 : p 1 ≥ p 2 and Ha : p1 < p2 . The data can be summarized in a 2 × 2 table as:
Type of Diet
Cause of Death High Salt Low Salt Total
NonCVD
2
23
25
CVD
5
30
35
Total
7
53
60
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 NormalTheory Method
Fisher’sExact Test Fisher’sExact Test: Hypergeometric Distribution
What is the probability of getting a data as extreme as or
more extreme than the observed data if H0 was true? This
would be our p value.
This probability can be computed under the assumption that
the column totals (column margins) are ﬁxed.
The Urn (Hypergeometic) model. Suppose an urn contains
n1 blue balls and n2 red balls, and M1 balls are drawn
randomly. What is the probability that exactly a of the balls
are blue?
Let X be the number of blue balls drawn.
n1
n2
a × M1 −a
P (X = a) =
for a = 0, 1, 2, . . . , min(M1 , n1 )
n1 +n2
M1
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 NormalTheory Method
Fisher’sExact Test Fisher’sExact Test Cont’d...
Returning to the CVD example, assume the column totals are
ﬁxed.
The urn model can be applied to compute the probability of
getting a data as extreme as or more extreme than the
observed data if p1 = p2 as follows:
Type of Diet
Cause of Death High Salt Low Salt
Total
NonCVD
a=2
23
n1 = 25
CVD
5
30
n2 = 35
Total
M1 = 7
53
60
Then
p −value =...
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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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