# Chapter_10_2 - Chapter 10: Comparing Two Groups Bivariate...

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Chapter 10: Comparing Two Groups Read: Chapters 10 and 11 Bivariate Analyses Methods for comparing two groups are special cases of bivariate statistical methods: there are two variables z The outcome variable on which comparisons are made is the response variable z The binary variable that specifies the groups is the explanatory variable { Statistical methods analyze how the outcome on the response variable depends on or is explained by the value of the explanatory variable Independent Samples Most comparisons of groups use independent samples from the groups: { The observations in one sample are independent of those in the other sample z Example: Randomized experiments that randomly allocate subjects to two treatments z Example: An observational study that separates subjects into groups according to their value for an explanatory variable Dependent Samples { Dependent samples result when the data are matched pairs –each subject in one sample is matched with a subject in the other sample z Example: set of married couples, the men being in one sample and the women in the other. z Example: Each subject is observed at two times, so the two samples have the same subject Comparing Proportions: Wrap-up Comparing Means { We can compare two groups on a quantitative response variable by comparing their means

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Example: Teenagers Hooked on Nicotine { A 30-month study: z Evaluated the degree of addiction that teenagers form to nicotine z 332 students who had used nicotine were evaluated z The response variable was constructed using a questionnaire called the Hooked on Nicotine Checklist (HONC) { The HONC score is the total number of questions to which a student answered “yes” during the study { The higher the score, the more hooked on nicotine a student is judged to be Example: Teenagers Hooked on Nicotine { How can we compare the sample HONC scores for females and males? { We estimate ( μ 1 2 ) by 2.8 – 1.6 = 1.2 { On average, females answered “yes” to about one more question on the HONC scale than males did Example: Teenagers Hooked on Nicotine x 1 x 2 Standard Error for Comparing Two Means { To make an inference about the difference between population means, 1 –μ 2 ), we need to learn about the variability of the sampling distribution of: { The difference, , is obtained from sample data. It will vary from sample to sample. { This variation is the standard error of the sampling distribution of : 2 2 2 1 2 1 n s n s se + = ) ( 2 1 x x ) ( 2 1 x x ) ( 2 1 x x Confidence Interval for the Difference Between Two Population Means A confidence interval for μ 1 2 is: z t .025 is the critical value for a 95% confidence level from the t distribution z The degrees of freedom are calculated using software. If you are not using software, you can take df to be the smaller of (n 1 -1) and (n 2 -1) as a “safe” estimate x 1 x 2 () ± t .025 s
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## This note was uploaded on 01/09/2010 for the course ILRST 2100 at Cornell University (Engineering School).

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Chapter_10_2 - Chapter 10: Comparing Two Groups Bivariate...

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