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# part14 - Public Health 6450 Fall 2011 Lynn Eberly and Andy...

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Public Health 6450 Fall 2011 Lynn Eberly and Andy Mugglin Division of Biostatistics School of Public Health University of Minnesota [email protected] Part 14

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Review CIs for the Difference of Two Proportions from the Binomial Setting Hypothesis Tests for the Difference of Two Proportions Arising from the Binomial Setting Turning Point Evaluation Evaluation of Turning Point Technology Eberly and Mugglin PubH 6450 Fall 2011 Part 14 2 / 25
Review CIs for the Difference of Two Proportions from the Binomial Setting Hypothesis Tests for the Difference of Two Proportions Arising from the Binomial Setting Where are we going? Previously: One-sample hypothesis testing and CIs for H 0 : p = p 0 (Chapter 8.1) Current topic: Two-sample hypothesis testing and CIs for H 0 : p 1 - p 2 = p 0 (Chapter 8.2) Next topic: Other approaches for comparing proportions that arise from the Binomial setting (not in M,M&C) Eberly and Mugglin PubH 6450 Fall 2011 Part 14 3 / 25

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Review CIs for the Difference of Two Proportions from the Binomial Setting Hypothesis Tests for the Difference of Two Proportions Arising from the Binomial Setting CLT-based CI and test for a Binomial proportion For a binomial variable X , when n ˆ p 15 and n (1 - ˆ p ) 15, a 100 C % confidence interval for the proportion of successes p is ˆ p ± z * ˆ p (1 - ˆ p ) n . For testing a proportion, when np 0 10 and n (1 - p 0 ) 10, with H 0 : p = p 0 , we use the z -statistic based on ˆ p = X / n : z = ( ˆ p - p 0 ) p 0 (1 - p 0 ) n . Eberly and Mugglin PubH 6450 Fall 2011 Part 14 4 / 25
Review CIs for the Difference of Two Proportions from the Binomial Setting Hypothesis Tests for the Difference of Two Proportions Arising from the Binomial Setting CLT-based CIs Plus Four CIs Structure of CIs for two-sample problems Our two-sample CI and test statistic formulas also have the same common structure as the one-sample formulas: estimate ± (quantile)(std.error) test statistic = estimate - null value std.error except here estimate is a difference between two groups and std.error is the standard error of that difference, just as we saw in Part 12 for testing the difference of population means. Next we’ll consider these same structures for the difference of proportions. Eberly and Mugglin PubH 6450 Fall 2011 Part 14 5 / 25

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Review CIs for the Difference of Two Proportions from the Binomial Setting Hypothesis Tests for the Difference of Two Proportions Arising from the Binomial Setting CLT-based CIs Plus Four CIs Assumptions in two-sample proportion problems The goal of inference here is to compare a proportion across two groups. We assume: The first group is drawn as a simple random sample of size n 1 from one population. Their number of successes X 1 ∼ B ( n 1 , p 1 ), so ˆ p 1 = X 1 / n 1 . The second group is drawn as a simple random sample of size n 2 from another population. Their number of successes X 2 ∼ B ( n 2 , p 2 ), so ˆ p 2 = X 2 / n 2 .
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part14 - Public Health 6450 Fall 2011 Lynn Eberly and Andy...

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