# Lec15 - Midterm 2 on November 5 Revise everything up to the...

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Midterm 2 on November 5 - Revise everything up to the next lecture (11/29) - Most of the questions will concern lectures from 09/22 -> 11/29

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Comparison of paired samples Unpaired Design We have already discussed how to compare two samples that are independent of each other. Paired Design In a paired design, the observations ( Y 1 , Y 2 ) occur in pairs. Each pair of observations units have more in common with each other than with members of another pair. What are the pairs? How might the effect of mCPP be tested in an unpaired design? Example: meta -chlorophenylpiperazine is thought to affect appetite. Nine moderately obese women were given mCPP for two weeks, nothing for two weeks, then a placebo for two weeks or they were given the placebo first, nothing for two weeks, and then the treatment. The weight loss was recorded for each condition.
d Comparison of paired samples using confidence intervals μ y 95% confidence interval = y ± t .025 SE SE y SE ( y 1 y 2 ) ( y 1 y 2 ) ± t .025 SE ( y 1 y 2 ) 95% confidence interval = 1 2 y 1 y 2 SE d d ± t .025 SE d 95% confidence interval = d The difference between the means equals the mean of the differences. Example: m -chlorophenylpiperazine is thought to affect appetite. Nine moderately obese women were given mCPP for two weeks, nothing for two weeks, then a placebo for two weeks (or vice versa) The weight loss was recorded for each condition. y 1 y 2 = .91 ( .09) = 1.00 = d

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Comparison of paired samples using confidence intervals d μ y 95% confidence interval = y ± t .025 SE SE y SE ( y 1 y 2 ) ( y 1 y 2 ) ± t .025 SE ( y 1 y 2 ) 95% confidence interval = 1 2 y 1 y 2 SE d d ± t .025 SE d 95% confidence interval = d d = y 1 y 2 = 1.00 d = μ 1 2 SE d = s d d = .72 = .24 df = n d 1 = 8
d Comparison of paired samples using confidence intervals μ y 95% confidence interval = y ± t .025 SE SE y SE ( y 1 y 2 ) ( y 1 y 2 ) ± t .025 SE ( y 1 y 2 ) 95% confidence interval = 1 2 y 1 y 2 SE d d ± t .025 SE d 95% confidence interval = d d = y 1 y 2 = 1.00 d = μ 1 2 SE d = s d d = .72 = .24 df = n d 1 = 8 1.00 ± (2.306)(.24) (.45,1.55)

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Paired sample t test Step 1: Set up your hypotheses and significance level H 0 : μ d = 0 H A : d 0 α = .05 For the mCPP data, I predict that we will … A. Fail to reject H 0 B. Reject H 0 C. Too early to say 95% confidence interval: (.45, 1.55)
Paired sample t test t s = d 0 SE d = 1.00 0 .24 = 4.17 Step 3: Figure out your P -value Step 2: Calculate your test statistic .001 < P < .01 Step 4: Conclude Reject H 0 and conclude that mean weight loss is greater on mCPP than on the placebo Step 1: Set up your hypotheses and significance level H 0 : μ d = 0 H A : d 0 α = .05

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Why pair?
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Lec15 - Midterm 2 on November 5 Revise everything up to the...

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