8 SECTION 1 DEFINITIONS AND CONCEPTS Terminology: Population = The group of people we are sampling and studying Sampling Design = The strategy followed in selecting a sample from a population Sampling Unit = Unit designated for listing and selection in a sample survey (e.g., persons, dwellings, households, area units, pharmacies) Sampling Frame = List of sampling units from which a sample is drawn Reporting Unit = 1) Unit about which data are collected (e.g., women aged 15-49 years in a family planning survey) 2) Sometimes called “observational unit” 3) May differ from "respondent" (e.g., interview individuals and analysis relates to provider visit)9 List Sample = 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 (e.g., sample of clinic patients from a list of clinic patients) Variable = Some measurement taken on members of the sample (e.g., number of children ever born to a woman aged 15-49 years); might call this the y-variable or x-variable Probability = Long-range relative frequency that an event will take place (e.g., that a particular household would be selected into a sample, if the sampling procedure were repeated); measured likelihood of occurrence; number between 0 and 1 Random Variable = A special kind of variable taking on (for survey samples) a countably finite number of possible values, each with some probability of occurrence; sum of these probabilities equals 110 Unit's Selection Probability = Likelihood over repeated applications of the sampling design that the unit would be chosen for the sample (e.g., for each woman aged 15-49 years in the family planning survey) Yi ; Xi = Variable associated with the i-th member of a population Probability Sampling = 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 Equal-Probability Sampling = 1) Probability sampling in which everyone in the population has the same selection probability 2) AKA "self-weighted" sampling; "epsem" sampling11 Nonprobability Sampling = 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) Difficult to determine if sample is "representative" (i.e., includes members from all relevant segments of the population) Parameter = Some characteristic of the population to be estimated from sample data (e.g., proportion deceased among children ever born to women of childbearing age; for now we use the symbol, R, to denote this kind of parameter) Estimator = Mathematical formula used to estimate the parameter using sample data (e.g., R to denote estimator for R); a random variable12 Estimate = Number resulting from applying the estimator to the sample data (e.g., 0.27 as the estimate of R, the proportion of deceased children among those ever-born to women aged 15-49 years in the survey population) Unbiased Estimator = 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 (e.g., sample mean from a simple random sample is an unbiased estimator of the population mean) Biased Estimator = 1) An estimate produced in such a way that, averaged over all possible samples, tends to differ somewhat from the parameter it is intended to reflect 2) Some sources of bias: sample design, inappropriate estimator, badly designed questionnaire, poorly trained staff, nonresponse, frame problems 3) Samples are not biased per se13 Sampling Error = 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 Variance of an Estimator = 1) Expected value (in essence average) of the squared sampling error over all possible samples that could be selected from the population; e.g., 2ˆ ˆV(R) E(R R)= − 2) If the estimator is biased, then {}2ˆ ˆ ˆV (R ) E (R E (R )= − 3) Variance is one of several statistical measures of the quality of estimates; Some Others: - Standard Error: ˆ ˆSE(R) V(R)= - Coefficient of Variation: ˆ ˆ ˆCV(R) SE(R)/E(R)=14 4) Indeterminable; must be estimated from the chosen sample Other Variances and Measures of Dispersion 5) Dispersion measures often confused with the above Population Element Variance: A descriptive measure of the dispersion of a variable among members of a population. SY YNiiN2211=−−=( ) Note: Element variances may apply to other collections of units as well (e.g., samples, strata, etc.) Population Element Standard Deviation: