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Sleuth_03 - CHAPTER 3 A Closer Look at Assumptions 1!is is...

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CHAPTER 3 A Closer Look at Assumptions 1
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! is is an advanced " apter. Please ask questions #
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CASE STUDY 1: CLOUD SEEDING Cloud seeding to increase rainfall (randomized experiment) 52 cumulus clouds At random 26 were seeded and 26 were controls Experimenter and pilot were “blind” to the treatment
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CLOUD SEEDING DATA
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DATA CHARACTERISTICS Data were positively skewed, and the group with the higher center also had the higher spread Log transform of rainfall was used
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CLOUD SEEDING DATA
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ANALYSIS OF LOG DATA One-sided p-value for two-sample t-test was 0.007. Seeded clouds had exp(1.144) = 3.1 times as mu ! rainfall as the unseeded. 95% con " dence interval for this ratio is 1.3 to 7.7. What is our scope of inference?
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CASE STUDY 2: AGENT ORANGE E # ects of agent orange on troops in Vietnam Observational study 646 Vietnam veterans and 97 other veterans Neither sample was randomly selected Similar shape and spread Scope of inference?
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DIOXIN CONCENTRATIONS
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DATA ANALYSIS
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DROP VETERAN 646
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ALSO DROP VETERAN 645
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Meaning of Robustness: A statistical tool is “robust” to departures from a particular assumption if it is valid even when the assumptions are not met Robustness of the Two-Sample t Assumption True, but it’s
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I. Normal distributions II. Equal standard deviations ( $ 1 = $ 2 ) III. Independence Assumptions of the Two-Sample t
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% e Central Limit % eorem asserts that departures from normality are not serious as long as sample sizes are reasonably large Long-tailed distributions (those with outliers) cause more problems than skewed distributions Robustness against departures from Normality
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