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4: CHAPTER PRODUCING DATA 4.1 Introduction How to verify the following statements? 1. 2. Pet owners are less likely to die of coronary heart disease. Regular large doses of vitamin C reduce the chance of getting a common cold. Response variable a variable whose changes we wish to study; an outcome or result. Explanatory variable- a variable that explains or causes changes in the response variable. Example: We want to know whether people who exercise regularly are less likely to catch colds. Explanatory variable =status (exercise, no exercise), Response variable = number of colds in a specified period. Study Designs Observational studies Experiments 1 Observational study observes individuals and measures variables of interest but does not attempt influence the responses Experiment deliberately imposes some action on individuals in order to observe their responses. Example: Pet ownership and CHD survival Each of 92 patients with coronary heart disease (CHD) was classified as having a pet or not and by whether they survived for 1 year. Patient Alive Dead No 28 11 Pet Ownership Yes 50 3 Survival rate among patients with pets is 50/53 or 94%, whereas survival rate among patients without pets is 28/39 or 72%. Is higher survival rate among patients with pets due to the pet ownership? Group 1 (pet) Group 2 (no pet) Survival rate Survival rate Comparison Explanatory variable: Pet ownership (pet, no pet), Response variable: Survival (yes, no) 2 Pet ownership Personality Lifestyle Diet Other Survival A lurking variable is a variable that has an important effect on the relationship among the variables in a study but is not included among the variables studied. Two variables are confounded when their effects on a response variable cannot be distinguished from each other. The confounded variables may be either explanatory variables or lurking variables. Example: Smoking during Pregnancy and Child's IQ Study: Smoking May Lower Kids' IQs Rochester, N.Y. Women who light up while pregnant could be dooming their babies to lower IQ's, according to a study released Thursday. Children age 4 whose mothers smoked 10 or more cigarettes a day during pregnancy scored about 9 points lower on the intelligence tests than the offspring of nonsmokers, researchers at Cornell University reported in this month's Pediatrics journal. Explanatory variable: Mother's smoking status during pregnancy (yes or no), Response variable: Child's IQ at 4 year of age. 3 Is that an observational study or an experiment? Smoking status of mother Nutrition Lifestyle Diet Other Child's IQ How to redesign the study to prove that maternal smoking caused the lower IQ in their children? 4.2 How to Get a Good Sample Census a survey in which the entire population is measured (time consuming and expensive) Population = the entire collection of individuals or objects about which information is desired Sample = the collection of individuals or objects we will actually measure Generalization Sample Population 4 Sampling frame- the list of subjects in the population from which the sample is taken. Inferences - statements about the population based on the sample data Valid inferences about population can be reached if sample is representative of the population. Larger random samples give more accurate results than smaller samples. No inferences with absolute certainty (partial information about the population, unrepresentative samples) Study is biased if it systematically favors certain outcomes. Biased Sampling Methods Voluntary response sample chooses itself by responding to a general appeal (call-in opinion polls, people with strong opinions are most likely to respond). Nonresponse responded). (small fraction of the population Undercoverage (homeless, prison inmates, students in dormitories, people without phones may be missed) Convenience sampling (interviews at shopping malls). 5 Telephone sampling: (a) using telephone directory introduces strong biasexcludes those who move often, those with unlisted home numbers and those without a phone. (b) random digit dialing (RDD) callbacks because people who are easy to reach with one call differ from those who are hard to reach, bias not large. Example: Women about Their Husbands Survey Finds Most Women Unhappy in Their Choice of Husbands A popular women's magazine, in a survey of its subscribers, found that over 90% of them are unhappy in their choice of whom they married. Copies of the survey were mailed to the magazine's 100,000 subscribers. Surveys were returned by 5,000 Of readers. those responding, 4520, or slightly over 90%, answered no to the question: "If you had it to do over again, would you marry the same man? Comments: 6 Unbiased Sampling Methods Simple Random Samples A simple random sample (SRS) of size n consists of n individuals from the population chosen in such a way that every set of n individuals has the same chance to be chosen. Methods to produce SRS: (a) Place names in a hat (the population) and draw out a handful (sample). (b) Table of random digits (Table E): Long string of the digits 0, 1, 2, ..., 9 such that each entry is equally likely to be any of the 10 digits and the entries are independent of each other. Example: Choosing an SRS of 20 from the class. 1. 2. Assign a numerical label to every student in the class (population): 01, 02, ..., 99. Use Table E to select labels at random. 01 . ... ... . 02 Read 2 digit numbers from Table E SRS 7 Stratified Random Sample To choose a stratified random sample, divide the population into strata, groups of individuals that are similar in some way that is important to the response. Then choose a separate SRS from each stratum. Population (consists of 5 strata) A stratified sample allows us to gather separate information about each stratum In an SRS from the whole population, the clouds may be underrepresented 4.3 Designing a Good Experiment Experimental units = individuals on which the experiment is done (they are called subjects when human beings). Treatment = condition applied to the units. Factor = explanatory variable in the experiment. 8 Treatment Factor .... .... Response Experimental Units Randomized Comparative Experiments Randomization using a random mechanism to divide experimental units into groups (Table B) Randomized comparative experiment to compare the response among several groups when experimental units were randomly assigned to the groups. Placebo effect = favorable response to a dummy treatment. Example: Testing a Pain Reliever Experimental units = 100 subjects (subjected to pain), Treatment = Injection of a pain reliever, Factor = Dosage of the drug (pain reliever), Response = Time until relief. 9 Random allocation of units to two groups Control Group (dummy treatment) Drug effect Placebo effect Environment Outcome 1 .... Comparison Treatment Group (real drug) Outcome 2 .... Double-blind experiment = neither the subjects themselves nor the personnel who works with them know which treatment each subject received. Example: Aspirin and Heart Attacks. Aspirin every other day 22,071 male physicians Random Assignment Placebo (dummy pill) 10 The rate of heart attacks within 5 years was 9.42 (per 1,000) in the aspirin group and 17.13 (per 1,000) in the placebo group. Can we therefore conclude that the lower risk of heart attack in the group taking aspirin every other day is caused by the drug? Random allocation 22,071 male physicians Group 1 Aspirin Significant difference in heart attack rate due to aspirin Group 2 Placebo Random allocation similar subjects in both groups Response variable: whether or not a subject had a heart attack Explanatory variable: treatment group (aspirin or placebo). Significant difference- difference that cannot be explained by the natural variation in data alone. Conclusion: Statistical causal inferences can be drawn from randomized experiments, but not from observational studies. 11 Matched Pairs Design Example: Effectiveness of a Training Program Response Variable: Productivity (number of items produced by a worker within a specified time period). Training Program Years of experience Education Motivation Age Other Productivity Productivity of workers "before" Productivity of workers "after" Sample 1 Sample 2 Productivity of the same worker "before" and "after" 12 For each worker a pair of two observations: productivity before and productivity after is obtained. The pair design neutralizes other factors affecting productivity such as experience, motivation, age, education, etc. Block Design Example: Comparison of Four Teaching Methods Subjects: 20 students Treatments: Teaching methods A, B, C, and D Response variable: Final test score Teaching Method Prior knowledge IQ Motivation ... Test Score Prior knowledge of the subject determined by a pretest. 13 Pretest scores: Lowest Scores Highest Scores Block 1 Block 2 Block 3 Block 4 Block 5 A B C D COMPARISON 14
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Path: University of Alberta >> STAT >> 151 Fall, 2007
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Path: New Mexico >> CHNE >> 525 Fall, 2008
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Path: Brandeis >> MATH >> 15a Spring, 2008
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Path: Maryland >> ENES >> 102 Spring, 2008
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Path: UCSB >> HIST >> 80 Spring, 2008
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Path: Maryland >> ENES >> 102 Spring, 2008
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Path: Maryland >> ENES >> 102 Spring, 2008
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Path: Maryland >> ENES >> 102 Spring, 2008
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Path: Syracuse >> CSD >> 315/615 Spring, 2008
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Path: Old Dominion >> ECI >> 301 Fall, 2007
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Path: UCSB >> HIST >> 80 Spring, 2008
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Path: CUNY City >> ECONOMICS >> 290 Spring, 2007
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Path: Texas >> BIO >> 325 Spring, 2008
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Path: Syracuse >> CSD >> 315/615 Spring, 2008
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Path: Bucknell >> EDUC >> 243 Winter, 2008
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Path: Bucknell >> EDUC >> 243 Winter, 2008
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Path: Bucknell >> EDUC >> 243 Winter, 2008
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Path: Bucknell >> ANTHRO >> 290 Winter, 2008
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Path: UCSB >> ECE >> 162c Spring, 2008
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Path: LSU Shreveport >> CHEM >> 121 Fall, 2008
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Path: Syracuse >> CSD >> 315/615 Spring, 2008
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Path: LSU Shreveport >> CHEM >> 121 Fall, 2008
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Path: LSU Shreveport >> CHEM >> 121 Fall, 2008
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HW_Set_14_2
Path: LSU Shreveport >> CHEM >> 121 Fall, 2008
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Path: Kutztown >> CRJ >> 221 Spring, 2008
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Path: Syracuse >> CSD >> 315/615 Spring, 2008
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Path: Kutztown >> CRJ >> 221 Spring, 2008
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Path: Kutztown >> CRJ >> 221 Spring, 2008
Description: Dr. Khondaker Juvenile Justice System Journal 8 1. Probation is the suspension of a jail sentence. A juvenile who has been convicted of a crime does not serve jail time. The court orders probation and the juvenile returns to the community for a certa...
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Path: Kutztown >> CRJ >> 221 Spring, 2008
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jjjournal6
Path: Kutztown >> CRJ >> 221 Spring, 2008
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Path: LSU Shreveport >> CHEM >> 121 Fall, 2008
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Path: Kutztown >> ENG >> 010 Fall, 2007
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Path: LSU Shreveport >> CHEM >> 121 Fall, 2008
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Path: Kutztown >> CRJ >> 101 Spring, 2008
Description: Chapter 6 The difference between screening in vs. screening out applicants for police positions. o Screening in process of identifying police applicants who are the best-qualified candidate for the applicant pool o Screening out process identifying...
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Path: Kutztown >> CRJ >> 101 Spring, 2008
Description: Chapter 1 The distinction between civil & criminal law o Civil law is laws concerned with relationships between individuals (contracts, business transactions, family relations) o Criminal law is laws concerned with the relationship between the indivi...
