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Chapter 10--Hypothesis Testing--Categorical Data

# in general assume the table is rearranged in such a

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Unformatted text preview: P (X ≤ 2) = P (X = 0) + P (X = 1) + P (X = 2). 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... In general, assume the table is rearranged in such a way that n1 ≤ n2 and M1 ≤ M2 . Then your p1 corresponds to the population with the smaller sample. Let k = min(M1 , n1 ). For the lower-sided alternative Ha : p1 < p2 , p −value = P (X ≤ a) = P (X = 0)+P (X = 1)+· · ·+P (X = a) This can be computed in R using phyper(a,n1,n2,M1). For upper-sided alternative Ha : p1 > p2 p −value = P (X ≥ a) = P (X = a)+P (X = a+1)+· · ·+P (X = k ) For the two-sided alternative Ha : p1 = p2 p −value = 2 × min[P (X ≤ a), P (X ≥ a), 0.5]. Evaluate the statistical signiﬁcance of the CVD data. 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: Random Column Totals The test ﬁnds p-value for one subset of the sample space (subset deﬁned by the value assumed by M1 ). The subsets deﬁned by the values of M1 partition the sample space into mutually exclusive subsets. Then we can see that PH0 (X ≥ a) = PH0 (X ≥ a|M1 = m)P (M = m) m ≤ α. Fisher’s exact test is valid for random column margins. The power of the exact test is usually lower than that of a more appropriate power test. 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 McNemar’s Test: Introduction This is a test for two-samples binomial proport...
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