Chapter 8 - Math3200 Intermediate Probability and Statistics Prof Nan Lin Department of Mathematics Washington University Outline Independent samples

# Chapter 8 - Math3200 Intermediate Probability and...

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Math3200 Intermediate Probability and Statistics Prof. Nan Lin Department of Mathematics Washington University

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Outline Independent samples design vs paired design Comparing means of two populations Graphical methods Two-sample z-test and z-interval Two-sample t-test and t-interval Equal variance Unequal variances Paired t-test Sample size calculation Nan Lin, Washington University 2
Simple comparative experiments Two groups: treatment vs control (placebo) Sample 1: ? 1 , … , ? 𝑛 1 Sample 2: ? 1 , … , ? 𝑛 2 Design Two independent samples Randomized trial Smokers to non-smokers Paired: observations in the same pair are correlated Before-after data Twin data Matched case-control Nan Lin, Washington University 3

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Two independent samples design Example: “A Low Carbohydrate as Compared with a Low Fat Diet in Severe Obesity”, New England Journal of Medicine , 348: 21, (2003) Scientific Question Is Weight Change Associated with Diet Type? Design 132 severely obese subjects randomized to one of two diet groups, low-fat vs low-carb Subjects followed for six month period At the End of Study Period, “Subjects on the low - carbohydrate diet lost more weight than those on a low fat diet (95% confidence interval for the difference in weight loss between groups, -1.6 to - 6.2 kg; p< .01)” Nan Lin, Washington University 4
Paired design Example: Before vs. After Ten non-pregnant, pre-menopausal women 16-49 years old who were beginning a regimen of oral contraceptive (OC) use had their blood pressures measured prior to starting OC use, and three-months after consistent OC use. The goal of this small study was to see what, if any, changes in average blood pressure were associated with OC use in such women . The data on the following slides shows the resulting pre- and post-OC use systolic BP measurements for the 10 women in the study. From Rosner B Fundamentals of Biostatistics, 6th ed. (2005) Duxbury Press. Nan Lin, Washington University 5

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Example: Blood Pressure and Oral Contraceptive Use BP Before OC BP After OC After-Before 1. 115 128 13 2. 112 115 3 3. 107 106 -1 4. 119 128 9 5. 115 122 7 6. 138 145 7 7. 126 132 6 8. 105 109 4 9. 104 102 -2 10. 115 117 2 6 . 115 before x 4 . 120 after x 8 . 4 diff x Nan Lin, Washington University 6 This reduces to a one-sample problem.
Graphical method Two-independent samples Side-by-side boxplot Paired design Boxplot of the differences Nan Lin, Washington University 7

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Example: diet type study Nan Lin, Washington University 8
Large sample inference for two independent samples Data from two independent samples design Sample 1: ?

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