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Week 6 and 7

Week 6 and 7 - STAT 218 Week#6 7(Monday Chapter 9 Chapter 8...

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Unformatted text preview: STAT 218 Week #6, 7(Monday) Chapter 9 / Chapter 8 Questions from Previous Lecture / HW (10 minutes) ANNOUNCEMENT: Test next Week – Chapters 6-9, one page of notes, tables in book, CHAPTER 9 - PAIRED DATA Paired Design / Paired Data • Often possible to study your population in “pairs” • The Concept – the subject (or experimental unit) becomes his/her own control • Used with two treatments • The subject receives BOTH treatments Examples • Test a sunscreen – use left and right side of body for each treatment • Sunglass protection – put a different lens in the two eye lens • Hand Lotion – Different lotion on left and right hands • Evaluate 6 minute walking distance before and after a treatment • Evaluate growth factors in twins Important • Subjects are selected at random from your population, as they are in all experiments • The application of the treatment to the left or right side is done via a randomization process (and/or the data is representative of the population) • The observations from subject to subject are independent • But the observation of the two treatments on the same subject are NOT independent Illustration • Compare A natural herbal oil to a chemically developed oil for sunscreen protection • 10 subjects • Measure redness of sunburn on both sides of a back after 2 hours in the sun • 10 backs • Left/Right randomization (subject, application person unblinded, observer) • Measurement of data and differences • Analysis is done as a “one sample” problem 1 Statistical View • The Concept – the subject becomes his/her own control • The data is looked at as differences between the two Again, the key point: The data we analyze is not the original data but the difference in response of the two treatments • Hypothesis tests and confidence intervals are done based upon comparing two treatments • But the analysis is identical to the one sample methods of Chapter 6. o CI = Estimate +/- (t/Z) * SE o Hypothesis test: Ho: u 1-u 2 = 0 or µ d = 0 vs Ha: u 1-u 2 ≠ 0 or µ d ≠ 0 o The sample mean and SE are calculated the same as Chapter 6 Example Data Set: Chronic Lung Hypertension • Patients with inability to breath normally are given a new product and a placebo, on two different days. • The order they receive these products is randomized via a coin flip. • The endpoint is the distance walked (meters) in 6 minutes. • The research is interested is evaluating whether his new product is effective • Assume the subjects were obtained randomly and the data (the difference) follows a normal distribution. Assume this is the data Subject NEW DRUG Walk Distance (feet) PLACEBO Walk Distance (ft) DIFFERENCE New-Plac (feet) Sam 400 375 25 Fred 250 220 30 Joe 404 419-15 Mary 500 450 50 Clyde 350 330 20 Bob 430 435-5 Sally 460 420 40 Dude 190 175 15 ESTIMATION Confidence Interval • What is the 95% CI for the difference in walking distance?...
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Week 6 and 7 - STAT 218 Week#6 7(Monday Chapter 9 Chapter 8...

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