Introductory Sampling Theory

Various types of distributions

PopulationSampleSampling(Normal)

Measures of central tendency

ModeMedianMean

Symbols

N = size of sampleX = a “score”X = mean = summation

Mean

“Average”Formula

Formula for mean

Formula for mean

NX

X

Variability

How measures spread outRangeDeviations

Difference between the mean and the score

Variability

How measures spread outRangeDeviations

Difference between the mean and the score

XX

Variance

“The mean of the squared deviations”

Variance

N

?

X

Variance

1

22

N

XXsx

Standard Deviation

1

2

N

XXsx

Various types of distributions

PopulationSampleSampling(Normal)

Population Distribution

Distribution of the attributes of a population or universe.

May have any shape. “Skewed” left or right Flat or peaked

Sample Distribution

Distribution of the attributes of a sample drawn from a specified population or universe

Shape will approximate the population or universe distribution

The larger the sample size, the closer the approximation, in all likelihood.

Sampling Distribution

Distribution of the means (could be other statistics) of all possible samples

Theoretical distribution since all possible samples cannot be drawn

Will always be normal, because of the laws of probability

Normal Distribution

SymmetricalDefined by standard deviations

(standard errors)Can predict what proportion of cases

will fall within a specified range of values

Relation among distributions

Never know the population characteristics Population characteristics are “parameters” That’s why research is done

Sample distribution shows characteristics Can guess at what the population

characteristics are Larger sample size give greater precision and

confidence

Standard error of the mean

nxsxs

Five types of sampling

Random (or simple random)Stratified randomCluster samplingSystematicArea probability

Random

Every subject is knownEvery subject has equal or know

probability of selection

Random

Advantages: Don’t have to know the characteristics of a

population Tends to be completely representative

Disadvantages: Complete list is difficult to obtain Always a chance of drawing a misleading

sample Needs a larger sample size

Stratified random

Population classified into two or more strata

Sample drawn from each oneCases drawn in proportion to

representation in populationCases can be oversampled, if needed

Stratified random

Advantages: Can be sure no relevant group is omitted Greater precision possible with lower

sample sizeDisadvantages:

Need to know about the population Proportions must be known Difficulty in locating cases

Systematic random

Selection of every nth nameUsually quicker

Cluster

Done for efficiencyPopulation is broken down into

smaller groupsUseful when no sampling frame is

available

Area

Combines cluster and systematicBased on geography