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Unformatted text preview: 1 Chapter 4: Gathering Data Read Chapter 4 Simpson s Paradox Simpsons Paradox: When the direction of an association between two variables changes after we include a third variable and analyze the data at separate levels of that variable Simpsons Paradox Example Probability of Death of Smoker = 139/582=24% Probability of Death of Nonsmoker = 230/732=31% Is Smoking Actually Beneficial to Your Health? This cant be true that smoking improves your chances of living! Whats going on! Simpsons Paradox Example Break out Data by Age Berkeley 73 Admissions Data: Simpsons Paradox Lets settle the law suit regarding under-admission of females to UCB graduate school Males Females Major #App %Admit #App %Admit A 825 62 108 82 B 560 63 25 68 C 325 37 593 34 D 417 33 375 35 E 191 28 393 34 F 373 06 341 07 Listed 44% 30% All 8442 44% 4321 35% Women applied to majors with low admission rates (C-F) and men applied to majors with higher admission rates. Perils of Aggregation You win a $1,000,000,000, 000 if you select a red ball! Which urn would you select? Blue or White? Game 1: Blue Urn: 5 Red 6 Green White Urn: 3 Red 4 Green P(Red in Blue urn)= 5/11=.455 P(Red in White urn)=3/7=.429 Blue better! Game 2: Blue Urn: 6 Red 3 Green White Urn: 9 Red 5 Green P(Red in Blue urn)= 6/9=.667 P(Red in White urn)=9/14=.643 Blue better! Combined Game: Blue Urn: 11 Red 9 Green White Urn: 12 Red 9 Green P(Red in Blue urn)= 11/20=.55 P(Red in White urn)=12/21=.571 White better! 2 1. Population versus Sample 2. Types of Studies: Experimental and Observational 3. Comparing Experimental and Observational Studies Learning Objectives: Population Population: all the subjects of interest We use statistics to learn about the population, the entire group of interest Sample: subset of the population Data is collected for the sample because we cannot typically measure all subjects in the population Population and Sample Sample Type of Study: Observational Study In an observational study, the researcher observes values of the response variable and explanatory variables for the sampled subjects, without anything being done to the subjects (such as imposing a treatment) Observational Study Sample Survey A sample survey selects a sample of people from a population and interviews them to collect data. A sample survey is a type of observational study. A census is a survey that attempts to count the number of people in the population and to measure certain characteristics about them Type of Study: Experiment A researcher conducts an experiment by assigning subjects to certain experimental conditions and then observing outcomes on the response variable The experimental conditions, which correspond to assigned values of the explanatory variable, are called treatments Example 1: Headline: Student Drug Testing Not Effective in Reducing Drug Use Facts about the study: 76,000 students nationwide Schools selected for the study included schools...
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This note was uploaded on 01/09/2010 for the course ILRST 2100 at Cornell University (Engineering School).