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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 cellphone, control) Or, could express experimental group as “cellphone 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 “crosssectional 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 cellphone 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 redo 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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 Fall '10
 ALAN
 Standard Deviation, Statistical hypothesis testing, Dependent Samples

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