ELEM STATISTICS [C3T1G1]
ELEM STATISTICS [C3T1G1] MATH 220
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This 11 page Class Notes was uploaded by Eunice Schoen on Saturday September 26, 2015. The Class Notes belongs to MATH 220 at James Madison University taught by Rickie Domangue in Fall. Since its upload, it has received 35 views. For similar materials see /class/214024/math-220-james-madison-university in Mathematics (M) at James Madison University.
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Chapter 4 Gathering Data 41 Should We Experiment or Should We Merely Observe A Types of Studies Experimental or Observa tional 0 Experiment page 148 A researcher conducts an experiment by as signing subjects to certain experimental condi tions and then observing outcomes on the re sponse variable The experimental conditions which correspond to assigned values of the ex planatory variable are called treatments Examples Observational Study page 149 In an observational study the researcher ob serves values of the response variable and ex planatory variables for the sampled subjects with 1 out anything being done to the subjects subject as imposing a treatment Examples B Advantages of Experiments over Observational Studies 0 Lurking variables possible in observational stud ies Lurking variables less likely in experiments can balance groups with random selection so there is no association between lurking variable and ex planatory variable treatment variable Establishing cause and effect is central to sci ence page 151 Observational studies cannot give de nitive answers about cause and effect be cause of lurking variables Remember Associa tion does not imply causation Can study the effect of an explanatory varible on a response variable more accurately with an ex periments because researcher has control of which treatments subjects receive C What Type of Study is Possible o If experiments preferred why conduct observa tional studies 7 Possible ethical issues with experimentation 3 7 Sometimes dif cult to get subjects in experi ments to comply with treatment regimen Experiments may take very long time to com plete Many questions of interest do not involve try ing to assess causality Examples Surveys D Using Data Already Available 0 Available from Anecdotal evidence Evidence data based on informal observations Not usually reliable for drawing conclusions about populations 0 Available from results of well designed research studies Use search engines to nd on Internet E The Census and Other Sample Surveys 0 A sample survey selects a sample of people from a population and interviews them to collect data page 152 Survey is type of observational study Examples 0 A census is a survey that attempts to count the number of people in the population and to measure certain characteristics about them page 153 4 42 What are Good Ways and Poor Ways to Sample A Steps in Carrying out a Sample Survey 0 De ne population targeted by the study 0 Compile list of subjects Sampling frame in the population from which the sample is to be taken Not always easy 0 Specify sampling design method for selecting subjects from sampling frame B Methods of selecting subjects 0 Nonrandom sampling See Section G 0 Random Sampling 7 More likely to obtain repesentative sample 7 Enable researcher to measure likelihood of sam ple characteristic falling close to correspond ing population characteristic C Simple Random Sampling One type of random sam pling o A simple random sample of n subjects from a population is one in which each possible sample of that size has the same chance of being selected 0 How to Select a Simple Random Sample 7 Pull names from a hat 7 Using random numbers to select a simple ran dom sample See page 158 5 D Methods of Collecting Data from Selected lndividu als in Sample Surveys Methods 0 Personal Interview 0 Telephone interview random digit dialing often used don t need sampling frame 0 Self administered questionnaire E How Accurate are Results from Surveys with Ran dom Sampling 0 margin of error 0 i X 100 rough approximation for margin of error F Be Wary of Sources of Potential Bias in Sample Sur veys o Bias in Sample Surveys Results from sample not representative of the population 0 Types of Bias in Sample Surveys page 163 7 Sampling bias occurs from using nonran dom samples see section G or having un dercoverage Examples Nonresponse bias occurs when some sam pled subjects cannot be reached or refuse to participate or fail to answer some questions Examples 7 Response bias occurs when the subject gives an incorrect response person lying or the question wording or the way the interviewer asks the question is confusing or misleading Examples G Sampling Bias from Convenience Sampling 0 Convenience Sampling Subjects enter survey because they are convenient not because of ran dom selection data obtained relatively cheaply Examples Researcher selecting subjects at a mall on the street on the JMU quad Sampling bias convenience sample may poorly represent intended population 0 Convenience Sampling Volunteer Sam pling Volunteer Sampling type of convenience sam pling Subjects choose themselves to be part of sample instead of researcher choosing them as in mall surveys etc Example lnternet surveys 7 Sampling bias one segment of population may be more likely to volunteer than other segments 0 Convenience samples sometimes necessary both in observational studies and in experiments H Large Sample Size Does Not Guarantee Unbiased Samples Page 165 Almost always better off with a simple random sam ple of 100 people than with a volunteer sample of thousands of people 43 What are Good Ways and Poor Ways to Ex periment A Terminology Recall In an experiment researcher assigns sub jects to experimental conditions called treatments to see the effects that treatments have on response variable experimental units The people animals objects etc that receive the treatments 8 B The Elements of a Good Experiment 0 Control Comparison Group 7 Example 436 page 173 7 Control Group no vitamin C Placebo Effect 7 Control Group placebo Control Group existing treatment 0 Randomizing in an experiment Randomizatin refers to randomly assigning ex perimental units to treatments Randomization used to 7 Eliminate bias that may result if the researcher assigns subjects to treatments 7 Balance groups on variables that you know affect the response 7 Balance groups on lurking variables that may be unknown to researcher Blinding the study Single Blind Experiment Subjects do not know what treatment they have received Not always possible Double Blind Experiment Neither subjects nor those measuring response know which treatment are given to subjects 0 Replication C Generalizing Results to Broader Population 9 44 What are Other Ways to Conduct Experi mental and Observational Studies A Multifactor Experiments OMlT B Matched Pairs Experimental Design 0 Previous Examples Completely Randomized Ex perimental Design Experimental units assigned completely at ran dom to treatments 0 Matched Pairs Design Assumes two treatments 7 MP Design Type 1 Each subject receives both treatments Re ceives one treatment selected at random and then crossover to other treatment Two val ues on response variable for each subject 7 MP Design Type ll Units are paired so that two units within pair having same or about same value on some p0 tentially confounding variable One unit in pair gets one treatment and other unit in pair gets other treatment Matched Pairs keep potentially lurking vari ables from affecting results lurking variables have same value within each person or across two units Type ll 10 C Blocks in an Exp Generalization of Matched Pairs more than 2 treatments 0 MP Type 1 Block subject that receives both treatments MP Type ll Block pair of units 0 More than two treatments say K treatments Block subject that receives all K treatments Order of treatments is randomized Block set of units number equal to K which have been grouped according to similar values on some extraneous variable K treatments assigned at random to units Within each block 0 Purpose of Blocking similar to matching Keeps potential lurking variables from affecting the results 0 Randomized Block Design A block design with random assignments of treatments to units Within a block D Samples Surveys Other Random Sampling Designs Useful in Practice 0 Cluster Random Sample 7 De nition page 176 Divide the population into a large number of clusters such as city blocks Select a simple random sample of the clusters Use all the subjects in the sampled clusters as the sample This is a cluster ran dom sample Cluster sampling preferable if gtllt a reliable sampling frame is not available gtllt cost of selecting a simple random sample is excessive Disadvantage usually need a larger sample size as compared to simple random sampling 0 Strati ed Random Sample 7 De nition page 177 A strati ed random sam ple divides the population into separate groups called strata and then selects a simple ran dom sample from each stratum The different simple random samples put together make up the strati ed random sample Advantage can include in your sample how ever many subjects you want from each stra tum Disadvantage must have a sampling frame and know the stratum into which each subject belongs 0 In practice complex surveys some combination of simple cluster and strati ed sampling used E Types of Observational Studies 0 Types of Observational Studies Cross sectional surveys Take a cross section of a population at the current time Retrospective Look back in time to obtain some information