Chap 9 notes

Chap 9 notes - Lecture 17 page 1 Statistics 371-001 Sp 09...

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Statistics 371-001, Sp 09 Lecture #172 263 Mar 09 Chapter 9. Comparison of Paired Samples Ch 7 introduced comparison of independent samples as a way to compare two treatment conditions or two populations. Uses two separate samples to obtain two sets of data. Paired samples – two sets of data are obtained from same population. “within subjects” design “repeated measures” design Uses same observational units (subjects) in the two conditions. Before and after (e.g., weight loss program) Performance under two different conditions (RT, alcohol/antihist) 2. t Test and Confidence Interval Analysis is based on differences , is the test statistic, μ d = 1 2, what were testing. Example (note confusion for example 9.2) Example: Imagination therapy for phobia, latency, onset of anxiety t -test first: Step 1. State the hypothesis Hypothesis is about the population Mutually exclusive and exhaustive. H 0 : μ d = 0, There is no change in the latency of onset of anxiety. H A : μ d ≠ 0, There is a change in the latency of onset of anxiety. H 0 for two independent sample t test was: μ 1 = μ 2 or ( μ 1 - μ 2 ) = 0. Step 2. Set the criteria for a decision α = .01, two=tailed, df = n d – 1 = 7 – 1 = 6, df(6) .005 = 3.707 Lecture 17 page 1

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Step 3: Collect data, compute sample statistics and test statistic Patient Y 1 (sec) Y 2 (sec)   d i  =y 2 - y 1 A 15 24   9 1 1 B 10 23 13 5 25 C 7 11 4 -4 16 F 18 25 7 -1 1 G 5 14 9 1 1 H 9 14 5 -3 9 I 12 21 9 1 1 Mean 10.9 18.9 Σ = 0 Σ = 5 4 Lecture 17 page 2
Note mean difference , 8, is equal to difference of the means (18.910.9). Step 4. Make a decision t s > t crit ; 7.024 > 3.707 The t we obtained falls in the critical region. Reject H 0 and conclude that the imagination technique does affect the onset of anxiety . The t s = 7.024 is greater than t(6) 0.0005 = 5.959; so > 5.959 represents 0.0005 of the area under the curve. Thus, the probability of getting a t s > 7.024 if the therapy had no effect is > 0.001, two tailed. Reporting in the literature : Guided imagery therapy increases the amount of time that patients could tolerate a feared situation before feeling anxiety (by a mean difference of 8.0 seconds, SD = 3). The treatment effect was statistically significant, t(6) = 7.02, p < .01. confidence interval: 8 ± (3.707)(1.139); 8 ± 4.222; (3.777, 12.22229 The probability is .99 that the confidence interval between 3.777 and 12.222 sec contains the mean difference delay before experiencing anxiety after imagination therapy compared with before therapy. Importance of Pairing Lecture 17 page 3

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The paired sample design uses each observational unit (subject) as it’s own control. This typically reduces the variability such that is smaller than either . Reduces influence of
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This note was uploaded on 04/07/2009 for the course STAT 371 taught by Professor Koscik during the Spring '08 term at University of Wisconsin.

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Chap 9 notes - Lecture 17 page 1 Statistics 371-001 Sp 09...

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