STAT101_Chap7

# STAT101_Chap7 - 7 Comparing Two Groups Goal Use CI and/or...

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Unformatted text preview: 7. Comparing Two Groups Goal: Use CI and/or significance test to compare means (quantitative variable) proportions (categorical variable) Group 1 Group 2 Estimate Population mean Population proportion We conduct inference about the difference between the means or difference between the proportions (order irrelevant). 1 2 2 1 1 2 2 1 ˆ ˆ y y μ μ π π π π-- Types of variables and samples • The outcome variable on which comparisons are made is the response variable . • The variable that defines the groups to be compared is the explanatory variable . Example : Reaction time is response variable Experimental group is explanatory variable (categorical var. with categories cell-phone, control) Or, could express experimental group as “cell-phone use” with categories (yes, no) • Different methods apply for dependent samples -- natural matching between each subject in one sample and a subject in other sample, such as in “longitudinal studies,” which observe subjects repeatedly over time independent samples -- different samples, no matching, as in “cross-sectional studies” Example : We later consider a separate part of the experiment in which the same subjects formed the control group at one time and the cell-phone group at another time. se for difference between two estimates (independent samples) • The sampling distribution of the difference between two estimates is approximately normal (large n 1 and n 2 ) and has estimated Example: Data on “Response times” has 32 using cell phone with mean 585.2, s = 89.6 32 in control group with mean 533.7, s = 65.3 What is se for difference between means of 585.2 – 533.7 = 51.4? 2 2 1 2 ( ) ( ) se se se = + (Note larger than each separate se. Why? ) So, the estimated difference of 51.4 has a margin of error of about 2( ) = 95% CI is about 51.4 ± , or ( , ). (Good idea to re-do analysis without outlier, to check its influence.) 1 1 1 2 2 2 2 2 1 2 / 89.6 / 32 / 65.3/ 32 ( ) ( ) se s n se s n se se se = = = = = = = + = CI comparing two proportions • Recall se for a sample proportion used in a CI is • So, the se for the difference between sample proportions for two independent samples is • A CI for the difference between population proportions is As usual, z depends on confidence level, 1.96 for 95% confidence ˆ ˆ (1 ) / se n π π =- 2 2 1 2 ( ) ( ) se se se = + = 1 1 2 2 2 1 1 2 ˆ ˆ ˆ ˆ (1 ) (1 ) ˆ ˆ ( ) z n n π π π π π π--- ± + Example: College Alcohol Study conducted by Harvard School of Public Health (http://www.hsph.harvard.edu/cas/) Trends over time in percentage of binge drinking (consumption of 5 or more drinks in a row for men and 4 or more for women, at least once in past two weeks) or activities influenced by it?...
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STAT101_Chap7 - 7 Comparing Two Groups Goal Use CI and/or...

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