Chapter 10--Hypothesis Testing--Categorical Data

N1 n2 p is weighted average of the proportions in the

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Unformatted text preview: p ˆ n1 n2 and p can be estimated by the pooled sample proportion: p= ˆ n1 p1 + n2 p2 ˆ ˆ . n1 + n2 p is weighted average of the proportions in the two samples. ˆ 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 Normal-Theory Method: Cont’d... Then a reasonable test statistic is |p1 − p2 | − ˆ ˆ z= p (1 − p ) ˆ ˆ 1 2n1 1 n1 + 1 2n2 + 1 n2 . 1 2n1 + 21 2 is continuity correction. n If n1 and n2 are large, more specifically, if n1 p (1 − p ) > 5 and ˆ ˆ n2 p (1 − p ) > 5, then ˆ ˆ We reject H0 if z > z1−α/2 . The p-value is calculated as p −value = 2×P (Z > zcomputed ) = 2×(1 − P (Z < zcomputed )) . 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 Normal-Theory Method: R command In R, we can use the prop.test command prop.test(x, n, p = NULL, alternative = c("two.sided", "less", "greater"), conf.level = 0.95, correct = TRUE) x and n are specified as vectors of size 2 containing the number of successes and sample sizes, respectively, of the two samples. prop.test() also accepts tabulated data. x can be a 2 × 2 table (typically generated by the table() command) and n should be omitted. 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 Examples (1) For breast-cancer example, it was foun...
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