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7. Comparing two groups

# 7. Comparing two groups - 7 Comparing Two Groups Goal Use...

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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 - -

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Example: Does cell phone use while driving impair reaction times? Article in Psych. Science (2001, p. 462) describes experiment that randomly assigned 64 Univ. of Utah students to cell phone group or control group (32 each). Driving simulating machine flashed red or green at irregular periods. Instructions: Press brake pedal as soon as possible when detect red light. See http://www.psych.utah.edu/AppliedCognitionLab/ Cell phone group: Carried out conversation about a political issue with someone in separate room. Control group: Listened to radio broadcast
Outcome measure: mean response time for a subject over a large number of trials Purpose of study: Analyze whether (conceptual) population mean response time differs significantly for the two groups, and if so, by how much. Data Cell-phone group: = 585.2 milliseconds, s 1 = 89.6 Control group: = 533.7, s 2 = 65.3. Shape? Outliers? 1 y 2 y

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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 -- a categorical var. with categories: (cell-phone, control) Or, could express experimental group as “cell-phone use” with categories (yes, no)

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Different methods apply for independent samples -- different samples, no matching, as in this example and in “cross-sectional studies” 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 Example : We later consider a separate 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 sample mean 585.2, s = 89.6 32 in control group with sample mean 533.7, s = 65.3 What is se for difference between sample means of 585.2 – 533.7 = 51.4? 2 2 1 2 ( ) ( ) se se se = +

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( Note this is larger than each separate se. Why? ) So, the estimated difference of 51.4 has a margin of error of about 2(19.6) = 39.2 (more precise details later using t distribution) 95% CI for μ 1 μ 2 is about 51.4 ± 39.2, or (12, 91).
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7. Comparing two groups - 7 Comparing Two Groups Goal Use...

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