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# chapter7 - Comparing 2 Groups Most Research is Interested...

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Comparing 2 Groups Most Research is Interested in Comparing 2 (or more) Groups (Populations, Treatments, Conditions) Longitudinal: Same subjects at different times Cross-sectional: Different groups of subjects Independent samples: No connection between the subjects in the 2 groups Dependent samples: Subjects in the 2 groups are “paired” in some manner.

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Explanatory Variables/Responses Subjects (or measurements) in a study are first classified by which group they are in. The variable defining the group is the explanatory or independent variable . The measurement being made on the subject is the response or dependent variable . Research questions are typically of the form: Does the independent variable cause (or is associated with) the dependent variable? I.V. D.V. ?????
Qualitative Responses For quantitative outcomes, we wish to compare 2 population proportions. – Parameter: π 2 - π 1 Estimator: Standard error: Sampling distribution : Approximately normal 1 ^ 2 ^ π π - 2 2 2 1 1 1 ) 1 ( ) 1 ( 1 ^ 2 ^ n n π π π π σ π π - + - = - - + - = - - - 2 2 2 1 1 1 1 2 1 ^ 2 ^ ) 1 ( ) 1 ( , ~ 1 ^ 2 ^ n n N π π π π σ π π π π π π

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Large-Sample CI for π 2 - π 1 Independent, Large samples (see sample size criteria from Chapter 6 for π ) Estimated standard error of the difference in sample proportions: • (1- α )100% CI for π 2 - π 1 : 2 2 ^ 2 ^ 1 1 ^ 1 ^ ^ ) 1 ( ) 1 ( 1 ^ 2 ^ n n π π π π σ π π - + - = - 2 2 ^ 2 ^ 1 1 ^ 1 ^ 2 / 1 ^ 2 ^ ^ 2 / 1 ^ 2 ^ ) 1 ( ) 1 ( 1 ^ 2 ^ n n z z π π π π π π σ π π α π π α - + - ± - ± - -
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) and of activities perhaps influenced by it? “Have you engaged in unplanned sexual activities because of drinking alcohol?” 1993: 19.2% yes of n = 12,708 2001: 21.3% yes of n = 8783 What is 95% CI for change saying “yes”?

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Estimated change in proportion saying “yes” is 0.213 – 0.192 = 0.021. 95% CI for change in population proportion is 0.021 ± 1.96(0.0056) = 0.021 ± 0.011, or roughly (0.01, 0.03) We can be 95% confident that the population proportion saying “yes” was between about 0.01 larger and 0.03 larger in 2001 than in 1993.
Comments about CIs for difference between two population proportions If 95% CI for is (0.01, 0.03), then 95% CI for is (-0.03, -0.01). It is arbitrary what we call Group 1 and Group 2 and what the order is for comparing the proportions. When 0 is not in the CI, we can conclude that one population proportion is higher than the other.

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chapter7 - Comparing 2 Groups Most Research is Interested...

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