Introductory Sampling Theory. Various types of distributions zPopulation zSample zSampling z(Normal)

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Presentation transcript:

Introductory Sampling Theory

Various types of distributions zPopulation zSample zSampling z(Normal)

Measures of central tendency zMode zMedian zMean

Symbols zN = size of sample zX = a “score” zX = mean z  = summation

Mean z“Average” zFormula

Formula for mean

Variability zHow measures spread out zRange zDeviations yDifference between the mean and the score

Variability zHow measures spread out zRange zDeviations yDifference between the mean and the score

Variance z“The mean of the squared deviations”

Variance

Standard Deviation

Various types of distributions zPopulation zSample zSampling z(Normal)

Population Distribution zDistribution of the attributes of a population or universe. zMay have any shape. y“Skewed” left or right yFlat or peaked

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.

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

Normal Distribution zSymmetrical zDefined by standard deviations (standard errors) zCan predict what proportion of cases will fall within a specified range of values

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

Standard error of the mean

Five types of sampling zRandom (or simple random) zStratified random zCluster sampling zSystematic zArea probability

Random zEvery subject is known zEvery subject has equal or know probability of selection

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

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

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

Systematic random zSelection of every nth name zUsually quicker

Cluster zDone for efficiency zPopulation is broken down into smaller groups zUseful when no sampling frame is available

Area zCombines cluster and systematic zBased on geography