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TAMU STAT 303 - Chapter3

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IntroductionTerminologyTypes of Statistical StudiesObservational StudyDesign of ExperimentsPrinciples of Design of ExperimentRandomized ExperimentHow to do RandomizationTypes of Experimental DesignsElements of Good ExperimentSampling Design: Sampling a Single PopulationPrinciples for SamplingSampling TechniquesSampling ProblemsSampling Design: Sampling More Than One PopulationExamplesImportant ConsiderationsStatistical InferenceGeneral Idea of Statistical InferenceExamplesCensus vs. SampleExample: The Steering Committee of the Physicians' Health Study Research Group (1988)Notation for Parameters of a PopulationNotation for Statistics of a SampleInference OverviewSampling VariabilitySampling DistributionBias and VarianceChapter 3 - Producing DataAnh DaoJuly 10th, 2009Chapter 3 - Producing DataIntroductionTerminologyExperimental unit refers to the individuals on which the experiment isperformed and measurements are recorded. When the individuals arehuman beings they are called subjects.Treatment refers to the experimental condition applied to the units.Factors refer to explanatory variables in an experiment.Level refers to a specific treatment value formed by combining value ofeach of the factors.Chapter 3 - Producing DataIntroductionTypes of Statistical StudiesIn experimental study we record information about units after applyingtreatments to units.Examples: Clinical trials, different kinds of experiments.In observational study we record information about units (or response)without imposing any treatment (passive participation of researcher).Examples: Opinion polls, market studies and surveys.Chapter 3 - Producing DataIntroductionObservational StudyWe are forced to select samples from different pre-existing populationsChapter 3 - Producing DataIntroductionObservational StudyAdvantage: The data is much easier to obtain.DisadvantagesWe cannot say the explanatory variable caused theresponse.There may be lurking or confounding variables.Observational studies should be more to describe the past,not predict the future.Chapter 3 - Producing DataIntroductionObservational StudyThere are 3 basic types for observational studies.Sample survey provides sample observed a point in timeProspective study follows a sample forward in time: cohort studiesRetrospective study follows a sample backward in time: case-controlstudiesCase-Control Study: A study in which cases having a particular condition arecompared to controls who do not. The purpose is to find out whether or notone or more explanatory variables are related to a certain disease.Although you cannot usually determine cause and effect, these studiesare more efficient and they can reduce the potential confoundingvariables.Chapter 3 - Producing DataIntroductionObservational StudyExample 1: Sample SurveySuppose we are interested in comparing GRE scores for students in fivedifferent majors.We cannot do a randomized experiment because we cannot randomlyassign individuals to a specific major. The individuals decide that forthemselves.Thus, we observe students from 5 different pre-existing populations: thefive majors.We obtain a random sample of size 15 from each of the five majors.We calculate statistics and compare the 5 groups.Can we say being in a specific major causes someone to get a higherGRE score?What are some possible confounding variables?How might we reduce the effect of these confounding variables?Chapter 3 - Producing DataIntroductionObservational StudyExample 2: Cohort StudySuppose we are interested finding out which age group talks the most on thetelephone: 0-10 years, 10-20 years, 20-30 years, or 30-40 yearsWe cannot do a randomized experiment because we cannot randomlyassign individuals to an age group.Thus, we observe (through polling or wire tapping) individuals from 4different pre-existing populations: the four age groups.We obtain a random sample of size 25 from each of the four age groups.We calculate statistics and compare the 4 groups.Can we say being in a specific age group causes someone to talk moreon the telephone?What are some possible confounding variables?How might we control these confounding variables?Chapter 3 - Producing DataDesign of ExperimentsDesign of Experiment refers to the process of planning, designing andanalyzing the experiment so that valid and objective conclusions can bedrawn efficiently.Chapter 3 - Producing DataDesign of ExperimentsPrinciples of Design of ExperimentRandomization refers to the random allotment of units to treatmentsthrough some random mechanism, like random numbers. The mainpurpose of randomization is to treat all the experimental units identicallyin every possible way except for the actual treatments being compared.Replication refers to the repetition of each treatment on manyexperimental units. The number of experimental units in each treatmentgroup refers to number of replications.Blocking is arrangement of experimental units into groups (blocks) thatare homogeneous (similar to one another).Chapter 3 - Producing DataDesign of ExperimentsRandomized ExperimentThe key to a randomized experiment: The treatment (explanatory variable) israndomly assigned to the experimental units or subjects.Chapter 3 - Producing DataDesign of ExperimentsRandomized ExperimentExampleSuppose that before we want to test the effect of aspirin on the physicians,we wish to do a study on the effect of aspirin on mice, comparing heart rates.We obtain a random sample of 100 mice.We randomly assign 50 mice to receive a placebo.We randomly assign 50 mice to receive aspirin.After 20 days of administering the placebo and aspirin, we measure theheart rates and obtain summary statistics for comparison.Chapter 3 - Producing DataDesign of ExperimentsRandomized ExperimentThe single greatest advantage of a randomized experiment is that wecan infer causation.Through randomization to groups, we have controlled all other factorsand eliminated the possibility of a confounding variable.Unfortunately or perhaps fortunately, we cannot always use arandomized experimentOften impossible or unethical, particularly with humansChapter 3 - Producing DataDesign of ExperimentsHow to do RandomizationRandom Number Table is a list of digits 0,1,. . . ,9 which are all equallyprobable and the probability of any given digit is unaffected by the digitsthat precede it (or digits are independent).Example Ebook: Chapter 3.1 (5/8), Example 3.10.Chapter 3 - Producing DataDesign of ExperimentsTypes of Experimental DesignsDepending on the method of


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