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Sampling Neuman and Robson Ch. 7Qualitative and Quantitative Sampling

IntroductionQualitative vs. Quantitative Sampling

Non-Random SamplingNon-probabilityNot representative of population

Random samplingProbabilityRepresentative of population

The sampling distributionUsed in probability sample to allow us to generalize from sample to population

Non-Probability SamplesHaphazard, convenience or accidentalChoose any convenient casesHighly distortedQuotaEstablish categories of casesChoose fixed number in each categoryPurposive (judgmental)Use expert judgment to pick casesUsed for exploratory or field research

Non-Probability (cont.)SnowballNetwork or chain referralUse of sociograms to represent

Other typesDeviant caseChoose cases for difference from dominant patternSequentialSelect cases until all possible information obtained

Probability SamplingUsed for quantitative research

Representative of population

Can generalize from sample to population through use of sampling distribution

Logic Behind Probability SamplingProblem: The populations we wish to study are almost always so large that we are unable to gather information from every case.

Logic (cont.)

Solution: We choose a sample -- a carefully chosen subset of the population and use information gathered from the cases in the sample to generalize to the population.

TerminologyStatistics are mathematical characteristics of samples.Parameters are mathematical characteristics of populations.Statistics are used to estimate parameters.PARAMETERSTATISTIC

Probability Samples:Must be representative of the population.Representative: The sample has the same characteristics as the population.

How can we ensure samples are representative?Samples drawn according to the rule of EPSEM (every case in the population has the same chance of being selected for the sample) are likely to be representative.

The Sampling DistributionWe can use the sampling distribution to calculate our population parameter based on our sample statistic.The single most important concept in inferential statistics.Definition: The distribution of a statistic for all possible samples of a given size (N). The sampling distribution is a theoretical concept.

The Sampling DistributionEvery application of inferential statistics involves 3 different distributions.

Information from the sample is linked to the population via the sampling distribution.PopulationSampling DistributionSample

The Sampling Distribution: Properties1. Normal in shape.

2. Has a mean equal to the population mean.x=

3. Has a standard deviation (standard error) equal to the population standard deviation divided by the square root of N. x= /N

First TheoremTells us the shape of the sampling distribution and defines its mean and standard deviation. If we begin with a trait that is normally distributed across a population (IQ, height) and take an infinite number of equally sized random samples from that population, the sampling distribution of sample means will be normal.

Central Limit TheoremFor any trait or variable, even those that are not normally distributed in the population, as sample size grows larger, the sampling distribution of sample means will become normal in shape.

Note: The Census is a sample of the entire population

Simple Random Sampling (SRS)

Sampling frame and elements

Selection techniquesTable of random numbers

Other types of samples are variants of the simple random sample

Other Probability SamplesSystematic Random Sampling

Stratified Random Sampling

Cluster Sampling

Random Route Sampling

Other Strategies and Issues Related to Random SamplingRandom Digit Dialing (RDD)

Hidden Populations

Sampling Error and Bias

Sample Size