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- 1. 1Sampling
- 2. OUTLINE Introduction The Logic of Probability Sampling Conscious and Unconscious Sampling Bias Probability Theory and Sampling Distribution Probability Sampling Illustration: Two National Crime Surveys Nonprobability Sampling
- 3. 3•Sampling - The process of selectingobservations•Often not possible to collect information fromall persons or other units you wish to study•Often not necessary to collect data fromeveryone out there•Allows researcher to make a small subset ofobservations and then generalize to the rest ofthe population
- 4. 4•Enables us to generalize findings fromobserving cases to a larger unobservedpopulation•Representative - Each member of thepopulation has a known and equal chance ofbeing selected into the sample•Since we are not completely homogeneous,our sample must reflect – and berepresentative of – the variations that existamong us
- 5. 5•What is the proportion of FAU students whohave been to an FAU football game?•Be conscious of bias – When sample is notfully representative of the larger populationfrom which it was selected•Equal Probability of Selection Method(EPSEM) •A sample is representative if its aggregate characteristics closely match the population’s aggregate characteristics; basis of probability sampling
- 6. 6•Sample Element: Who or what are westudying (student)•Population: Whole group (college freshmen)•Population Parameter: The value for a givenvariable in a population•Sample Statistic: The summary description ofa given variable in the sample; we use samplestatistics to make estimates or inferences ofpopulation parameters
- 7. 7•Purpose of sampling: To select a set ofelements from a population in such a way thatdescriptions of those elements (samplestatistics) accurately portray the parametersof the total population from which theelements are selected •The key to this process is random selection•Sampling Distribution: The range of samplestatistics we will obtain if we select manysamples
- 8. 8•Sampling Frame: list of elements in ourpopulation•By increasing the number of samples selectedand interviewed increased the range ofestimates provided by the sampling operation
- 9. 9•If many independent random samples areselected from a population, then the samplestatistics provided by those samples will bedistributed around population parameter in aknown way•Probability theory gives us a formula forestimating how closely the sample statisticsare clustered around the true value •Standard Error: A measure of sampling error •Tells us how sample statistics will be dispersed or clustered around a population parameter
- 10. 10•Two key components of sampling error•We express the accuracy of our samplestatistics in terms of a level of confidence thatthe statistics fall within a specified intervalfrom the parameter•The logic of confidence levels and confidenceintervals also provides the basis fordetermining the appropriate sample size for astudy
- 11. 11•Random selection permits the researcher tolink findings from a sample to the body ofprobability theory so as to estimate theaccuracy of those findings•All statements of accuracy in sampling mustspecify both a confidence level and aconfidence interval•The researcher must report that he or she isx percent confident that the populationparameter is between two specific values
- 12. 12•Different types of probability samplingdesigns can be used alone or in combinationfor different research purposes•Key feature of all probability samplingdesigns: the relationship between populationsand sampling frames •Sampling frame: The quasi-list of elements from which a probability sample is selected
- 13. 13•Each element in a sampling frame is assigneda number, choices are then made throughrandom number generation as to whichelements will be included in your sample •Forms the basis of probability theory and the statistical tools we use to estimate population parameters, standard error, and confidence intervals
- 14. 14•Systematic Sampling – Elements in the totallist are chosen (systematically) for inclusion inthe sample •List of 10,000 elements, we want a sample of 1,000, select every tenth element •Choose first element randomly •Danger: “Periodicity" A periodic arrangement of elements in the list can make systematic sampling unwise
- 15. 15•Stratified sampling: Ensures that appropriatenumbers are drawn from homogeneoussubsets of that population •Method for obtaining a greater degree of representativeness—decreasing the probable sampling error•Disproportionate stratified sampling: Way ofobtaining sufficient # of rare cases byselecting a disproportionate # •To purposively produce samples that are not representative of a population on some variable
- 16. 16•Compile a stratified group (cluster), sampleit, then subsample that set...•May be used when it is either impossible orimpractical to compile an exhaustive list ofthe elements that compose the targetpopulation, (Ex.: All law enforcement officersin the US)•Involves the repetition of two basic steps: •Listing •Sampling
- 17. 17•Seeks to represent the nationwide population ofpersons 12+ living in households (≈ 42K units,74K occupants in 2004)•First defined are primary sampling units (PSUs) •Largest are automatically included, smaller ones are stratified by size, population density, reported crimes, and other variables into about 150 strata•Census enumeration districts are selected (CED) •Clusters of 4 housing units from each CED are selected
- 18. 18•First stage – 289 Parliamentary constituencies,stratified by geographic area and populationdensity•Two sample points were selected, which weredivided into four segments with equal #’s ofdelivery addresses •One of these four segments was selected at random, then disproportionate sampling was conducted to obtain a greater number of inner-city respondents •Household residents aged 16+ were listed, and one was randomly selected by interviewers (n=37,213 in 2004)
- 19. 19•Purposive sampling: Selecting a sample on thebasis of your judgment and the purpose of thestudy•Quota sampling: Units are selected so that totalsample has the same distribution ofcharacteristics as are assumed to exist in thepopulation being studied•Reliance on available subjects•Snowball sampling - You interview someindividuals, and then ask them to identify otherswho will participate in the study, who ask others…etc., etc.

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