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Introductory Sampling Theory
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Various types of distributions zPopulation zSample zSampling z(Normal)
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Population Distribution zDistribution of the attributes of a population or universe. zMay have any shape. y“Skewed” left or right yFlat or peaked
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Sample Distribution zDistribution of the attributes of a sample drawn from a specified population or universe zShape will approximate the population or universe distribution zThe larger the sample size, the closer the approximation, in all likelihood.
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Sampling Distribution zDistribution of the means (could be other statistics) of all possible samples zTheoretical distribution since all possible samples cannot be drawn zWill always be normal, because of the laws of probability
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Normal Distribution zSymmetrical zDefined by standard deviations (standard errors) zCan predict what proportion of cases will fall within a specified range of values
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Relation among distributions zNever know the population characteristics yPopulation characteristics are “parameters” yThat’s why research is done zSample distribution shows characteristics yCan guess at what the population characteristics are yLarger sample size give greater precision and confidence
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Variance z“The mean of the squared deviations”
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Variance
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Standard Deviation
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Standard error of the mean
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Determining Sample Size
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Factors affecting sample size zVariability zConfidence level zPrecision
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confidence precision 2 n =(variability)
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confidence precision 2 n =(pq)
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Five types of sampling zRandom (or simple random) zStratified random zCluster sampling zSystematic zArea probability
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Random zEvery subject is known zEvery subject has equal or know probability of selection
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Random zAdvantages: yDon’t have to know the characteristics of a population yTends to be completely representative zDisadvantages: yComplete list is difficult to obtain yAlways a chance of drawing a misleading sample yNeeds a larger sample size
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Stratified random zPopulation classified into two or more strata zSample drawn from each one zCases drawn in proportion to representation in population zCases can be oversampled, if needed
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Stratified random zAdvantages: yCan be sure no relevant group is omitted yGreater precision possible with lower sample size zDisadvantages: yNeed to know about the population yProportions must be known yDifficulty in locating cases
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Systematic random zSelection of every nth name zUsually quicker
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Cluster zDone for efficiency zPopulation is broken down into smaller groups zUseful when no sampling frame is available
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Area zCombines cluster and systematic zBased on geography
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