Chapter 10--Hypothesis Testing--Categorical Data

The data can be summarized in a 2 2 table as type of

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Unformatted text preview: Method Fisher’s-Exact Test Fisher’s-Exact Test Cont’d... Let p1 be the probability that the man was on a high-salt diet given that his cause was non-CVD and p2 be the be the probability that the man was on a high-salt 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 Non-CVD 2 23 25 CVD 5 30 35 Total 7 53 60 Chapter 10: Hypothesis Testing: Categorical Data Stat 491: Biostatistics Introduction Two-Sample Test for Binomial Proportions McNemar’s Test Estimation of Sample Size and Power R × C Contingency Tables Chi-Square Goodness-of-Fit Test The Kappa Statistic Normal-Theory Method Fisher’s-Exact Test Fisher’s-Exact 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 Two-Sample Test for Binomial Proportions McNemar’s Test Estimation of Sample Size and Power R × C Contingency Tables Chi-Square Goodness-of-Fit Test The Kappa Statistic Normal-Theory Method Fisher’s-Exact Test Fisher’s-Exact 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 Non-CVD 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.

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