203ch19_slides.pdf - STAT 203 Chapter 19 Two-Sample...

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STAT 203 Chapter 19 Two-Sample Inference: Comparing Means between Two Groups Objective: to compare the means of two populations We draw a random sample from each of the two populations ( y is some quantitative variable of interest): y 11 , y 12 , · · · , y 1 n 1 (sample size n 1 ) from a population with mean μ 1 and standard deviation σ 1 y 21 , y 22 , · · · , y 2 n 2 (sample size n 2 ) from a population with mean μ 2 and standard deviation σ 2 Eugenia Yu, UBC Department of Statistics. Not to be copied, used, or revised without explicit written permission from the copyright owner. 1
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STAT 203 Examples where two-sample inference is needed: 1. You want to compare the mean IQ between males and females. To test for a difference, you randomly select a sample of females and another sample of males. Two sets of IQ scores (one per gender group) are obtained. 2. You want to compare the mean reduction in blood pressure between two treatments (existing drug versus new drug) in treating hypertension. To test for a difference between the two treatments, you may conduct an experiment with the two treatment groups and measure the reduction in blood pressure in each patient receiving either type of drug. Eugenia Yu, UBC Department of Statistics. Not to be copied, used, or revised without explicit written permission from the copyright owner. 2
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STAT 203 In order to compare two population means, μ 1 and μ 2 , we will consider the difference between the two means: μ 1 - μ 2 . To estimate μ 1 - μ 2 , we use y 1 - y 2 where y 1 and y 2 are sample means from the two samples. Due to sampling variability, y 1 varies from sample to sample. Similarly for y 2 . Hence, the observed difference between the two sample means y 1 - y 2 will also vary. In the long run, over all possible random samples (of sizes n 1 and n 2 ) that can be drawn from population 1 and population 2 respectively, the differences ( y 1 - y 2 ) s will follow a distribution that has: mean: μ 1 - μ 2 standard deviation: SD ( y 1 - y 2 ) = σ 2 1 n 1 + σ 2 2 n 2 Eugenia Yu, UBC Department of Statistics. Not to be copied, used, or revised without explicit written permission from the copyright owner. 3
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