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PSLS.PPT.Ch20 - PSLS chapter 20 2009 W.H Freeman and...

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    Comparing 2 proportions PSLS chapter 20 © 2009 W.H. Freeman and Company
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Objectives (PSLS chapter 20) Comparing two proportions Comparing 2 independent samples Confidence interval for 2 proportion Large sample method Plus four method Test of statistical significance Treatment and risk reduction
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Comparing 2 independent samples We often need to compare 2 treatments with 2 independent samples. For large enough samples, the sampling distribution of is approximately Normal. ) ˆ ˆ ( 2 1 p p - However, neither p 1 nor p 2 are known.
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Large-sample CI for 2 proportions For 2 independent SRS of sizes n 1 and n 2 with sample proportion of successes p ̂ 1 and p ̂ 2 respectively, an approximate level C confidence interval for p 1 – p 2 is 2 2 2 1 1 1 2 1 ) ˆ 1 ( ˆ ) ˆ 1 ( ˆ * * error of margin the is , ) ˆ ˆ ( n p p n p p z SE z m m m p p diff - + - = = ± - Use this method when the samples, and the number of successes and the number of failures are each at least 10 in each samples. C is the area under the standard Normal curve between -z* and z*.
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Cholesterol and heart attacks How much does the cholesterol lowering drug Gemfibrozil help reduce the risk of heart attack? We compare the incidence of heart attack over a 5 year period for 2 random samples of middle-aged men taking either the drug or a placebo. So the 90% CI is (0.0414-0.0273) ± 1.645*0.0057 = 0.014 ± 0.009 We are 90% confident that the percent middle-age men who suffer a heart attack is 0.5% to 2.3% lower when taking the cholesterol-lowering drug.
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