Qualitative and Quantitative Sampling
Types of Nonprobability SamplingNonprobability samplingTypically used by qualitative researchersRarely determine sample size in advanceLimited knowledge about larger group or populationTypesHaphazardQuotaPurposiveSnowballDeviant CaseSequential
Populations and SamplesA population is any well-defined set of units of analysis. The population is determined largely by the research question; the population should be consistent through all parts of a research project.A sample is a subset of a population.Samples are drawn through a systematic procedure called a sampling method. Sample statistics measure characteristics of the sample to estimate the value of population parameters that describe the characteristics of a population.
Populations and SamplesA population would be the first choice for analysis.Resources and feasibility usually preclude analysis of population data. Most research uses samples.
Haphazard SamplingCheap and quickCan produce ineffective, highly unrepresentative samplesNOT recommendedPerson-on-the-street interviewsClip out survey from a newspaper and mail it in
Quota SamplingFirst you identify relevant categories of peopleThen you figure out how many to sample from each categoryEnsures that some differences are in the sampleStill haphazard sampling within the category, however
Purposive SamplingExpert uses judgment in selecting cases with a specific purpose in mindEspecially informative casesCultural themed magazinesDifficult-to-reach, specialized populationProstitutesParticular types of casesGamson study in the book
Snowball SamplingIdentifying and sampling the cases in a networkI find a prostitute to talk to, then ask her for some more prostitutes I could talk to, and it goes on and on and on
Deviant Case SamplingSeeks cases that differ from the dominant pattern or that differ from the predominant characteristics of other casesSelected because they are unusualHigh school dropouts example
Sequential SamplingResearcher uses purposive sampling until the amount of new information or diversity of cases is filledGather info until the marginal utility of new information levels off
Probability SamplingSaves time and costAccuracySampling element: unit of analysis or case in a populationPopulation is all of the possible elements, specified for unit, geographical location, and temporal boundaries
Probability SamplingSampling frame is specific list that closely approximates all of the elements in a populationCan be extremely difficult because there just arent good lists for some thingsFrames are almost always inaccurate
Parameter v. StatisticParameter: characteristic of an entire populationStatistic: estimates of population parameters based on sample
Literary Digest Poll MishapSampling frame was automobile registrations and telephone directoriesAccurate predictions in 1920, 24, 28, and 32Send postcard and respondents send backIn 1936, sampled 10 million and predicted massive victory for Landon over FDR
Literary Digest Poll MishapVERY, VERY wrongFrame did NOT represent the target population (all voters)Excluded as much as 65% of voters, including most of FDRs supporters during the Depression
Why Random Sampling?Each element has an equal probability of selectionCan statistically calculate the relationship between sample and the populationsampling errorTypes:Simple RandomSystematicStratifiedCluster
Simple Random SampleNumber all of the elements in a sampling frame and use a list of random numbers to select elements (or pull from a hat etc.)Pulling marbles out of a jarRandom chance can make it so were off on the actual population, but over repeated independent samples, the true number will emerge
Simple Random SampleWe will end up with a normal bell curve the more we sampleRandom sampling does NOT mean that every random sample will perfectly represent the populationConfidence intervals are ranges around a specific point used to estimate a parameterI am 95% certain that the population parameter lies between 2,450 and 2,550 red marbles in the jar
Systematic SamplingSimple random sampling with a shortcut for selectionNumber each element in the sampling frameCalculate a sampling intervaltells researcher how to select elements by skip pattern
Systematic SamplingI want to sample 500 names from a list of 1000Sampling interval is 2I select a random starting point and choose every other name to give me 500Big problem when elements in a sample are organized in some kind of cycle or pattern
Stratified SamplingFirst divide the population into subpopulations on basis of supplemental info and then do a random sample from each subpopulationGuarantees representationThis can allow for oversampling as well for specific research purposes
Cluster SamplingUseful when there is no good sampling frame availableAll high school basketball players, for exampleFirst you random sample clusters of information then draw a random sample of elements from within the clusters you selected
Cluster Sampling ExampleWant to sample individuals from ClevelandRandomly select city blocks, then households within blocks, then individuals within householdsLess expensive, but also less preciseError shows up in each sample drawn
How Large Should a Sample Be?It dependsSmaller the population, the bigger your sampling ratio will need to be to be accurate< 1,000 = 30%10,000 = 10%> 150,000 = 1%> 10,000,000 = .025%
How Large Should a Sample Be?For small samples, small increases in sample size produce big gains in accuracyDecision about best sample size depends on:Degree of accuracy requiredDegree of variability in populationNumber of variables measured simultaneously
InferenceThe goal of statistical inference is to make supportable conclusions about the unknown characteristics, or parameters, of a population based on the known characteristics of a sample measured through sample statistics.Any difference between the value of a population parameter and a sample statistic is bias and can be attributed to sampling error.
InferenceOn average, a sample statistic will equal the value of the population parameter.Any single sample statistic, however, may not equal the value of the population parameter.Consider the sampling distribution: When the means from an infinite number of samples drawn from a population are plotted on a frequency distribution, the mean of the distribution of means will equal the population parameter.
InferenceBy calculating the standard error of the estimator (or sample statistic), which indicates the amount of numerical variation in the sample estimate, we can estimate confidence. More variation means less confidence in the estimate.Less variation means more confidence.
InferenceOne way to increase confidence in an estimate is to collect a larger, rather than a smaller, sample.Measures of variability get smaller with larger samples:But the value of a larger sample may be offset by the increased cost; this is yet another tradeoff in research design.To reduce sampling error by half, a sample must quadruple in size.