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notes515fall10chap9 - STAT 515 - Chapter 9: Two-Sample...

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STAT 515 -- Chapter 9: Two-Sample Problems Paired Differences (Section 9.3) Examples of Paired Differences studies: • Similar subjects are paired off and one of two treatments is given to each subject in the pair. or • We could have two observations on the same subject. The key: With paired data, the pairings cannot be switched around without affecting the analysis. We typically wish to perform inference about the mean of the differences, denoted D . Example 1: Six students are given two tests, one after being fed, and one on an empty stomach. Is there evidence that students perform better on a full stomach? (Assume normality of data, and use = .05.) Student Scores | 1 2 3 4 5 6 X 1 (with food) | 74 71 82 77 72 81 X 2 (without food) | 68 71 86 70 67 80
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Calculate differences: D = X 1 X 2 D: Example 2: Find a 98% CI for the mean difference in arm strength for right-handed people (measured by the number of seconds a certain weight can be held extended). Person | 1 2 3 4 5 6 7 X 1 (Right) | 26 35 17 47 22 16 32 X 2 (Left) | 20 31 10 38 23 16 29 D:
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Interpretation: With 98% confidence, the mean right- arm strength is between 0.336 seconds less and 8.336 seconds greater than the mean left-arm strength. (We are 98% confident the mean difference is between -0.336 and 8.336 seconds.) Note: With paired data, the two-sample problem really reduces to a one-sample problem on the sample of differences .
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Two Independent Samples (Section 9.2) Sometimes there’s no natural pairing between samples. Example 1:
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notes515fall10chap9 - STAT 515 - Chapter 9: Two-Sample...

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