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# Intermediate Statistical Methods BIOS 662

UNC

GPA 3.83

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This 7 page Class Notes was uploaded by Nat McClure on Sunday October 25, 2015. The Class Notes belongs to BIOS 662 at University of North Carolina - Chapel Hill taught by Michael Hudgens in Fall. Since its upload, it has received 25 views. For similar materials see /class/228851/bios-662-university-of-north-carolina-chapel-hill in Biostatistics at University of North Carolina - Chapel Hill.

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Date Created: 10/25/15

iSECTION 1 DEFINITIONS AND CONCEPTS Terminology Population Sampling Design Sampling Unit Sampling Frame Reporting Unit The group of people we are sampling and studying The strategy followed in selecting a sample from a population Unit designated for listing and selection in a sample survey eg persons dwellings households area units pharmacies List of sampling units from which a sample is drawn 1 Unit about which data are collected eg women aged 1549 years in a family planning survey 2 Sometimes called observational unit 3 May differ om quotrespondentquot eg interview individuals and analysis relates to provider visit List Sample Variable Probability Random Variable 9 Sample in which the only sampling unit is the analysis unit so that the sample can be chosen from a list of the entire population eg sample of clinic patients om a list of clinic patients Some measurement taken on members of the sample eg number of children ever born to a woman aged 1549 years might call this the yvariable or Xvariable Longrange relative frequency that an event will take place eg that a particular household would be selected into a sample if the sampling procedure were repeated measured likelihood of occurrence number between 0 and l A special kind of variable taking on for survey samples a countably nite number of possible values each with some probability of occurrence sum of these probabilities equals 1 Unit39s Selection Probability Probability Sampling EqualProbability Sampling 10 Likelihood over repeated applications of the sampling design that the unit would be chosen for the sample eg for each woman aged 1549 years in the family planning survey Variable associated with the ith member of a population 1 Sampling in which the design calls for using random methods to ultimately decide which population members are chosen 2 Every population member has a known nonzero selection probability 1 Probability sampling in which everyone in the population has the same selection probability 2 AKA quotselfweightedquot sampling quotepsemquot sampling Nonprobability Sampling Parameter Estimator ll 1 Sampling in which subjective judgment usually by interviewers is used to ultimately decide who is chosen in the sample 2 Selection probabilities cannot be determined 3 Dif cult to determine if sample is quotrepresentativequot ie includes members om all relevant segments of the population Some characteristic of the population to be estimated om sample data eg proportion deceased among children ever born to women of childbearing age for now we use the symbol R to denote this kind of parameter Mathematical formula used to estimate the parameter using sample data eg 1A1 to denote estimator for R a random variable Estimate Unbiased Estimator Biased Estimator 12 Number resulting from applying the estimator to the sample data eg 027 as the estimate of R the proportion of deceased children among those everbom to women aged 1549 years in the survey population An estimator which if repeated over all possible samples that might be selected using a sampling design would yield estimate which on average equals the parameter being estimated eg sample mean from a simple random sample is an unbiased estimator of the population mean 1 An estimate produced in such a way that averaged over all possible samples tends to differ somewhat om the parameter it is intended to re ect 2 Some sources of bias sample design inappropriate estimator badly designed questionnaire poorly trained staff nonresponse frame problems 3 Samples are not biased per se Sampling Error Variance of an Estimator 13 A measure of the numerical difference between an estimate and the parameter it is intended to estimate that can be attributed to the fact that a sample rather than a complete enumeration was used to produce the estimate 1 Expected value in essence average of the squared sampling error over all possible samples that could be selected om the population eg v61 Edi R2 2 If the estimator is biased then A A A 2 VR E R ER 3 Variance is one of several statistical measures of the quality of estimates Some Others Standard Error SER Jw Coef cient of Variation cvai SERER 14 4 Indeterminable must be estimated from the chosen sample 5 Dispersion measures often confused with the above Other Variances and Measures of Dispersion Population Element Variance A descriptive measure of the dispersion of a variable among members of a population N 7 Z Yi Y2 i1 N l 52 Note Element variances may apply to other collections of units as well eg samples strata etc Population Element Standard Deviation SW

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