1 sampling. 2 sampling issues sampling terminology probability in sampling probability sampling...

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SamplingSampling

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Sampling IssuesSampling Issues

Sampling TerminologySampling TerminologySampling TerminologySampling Terminology

Probability in SamplingProbability in SamplingProbability in SamplingProbability in Sampling

Probability Sampling DesignsProbability Sampling DesignsProbability Sampling DesignsProbability Sampling Designs

Non-Probability Sampling DesignsNon-Probability Sampling DesignsNon-Probability Sampling DesignsNon-Probability Sampling Designs

Sampling DistributionSampling DistributionSampling DistributionSampling Distribution

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Sampling TerminologySampling Terminology

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Two Major Types of Sampling MethodsTwo Major Types of Sampling Methods

uses some form of random selection

requires that each unit have a known (often equal) probability of being selected

selection is systematic or haphazard, but not random

Probability SamplingProbability SamplingProbability SamplingProbability Sampling

Non-Probability Non-Probability SamplingSampling

Non-Probability Non-Probability SamplingSampling

azi

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Who do you want Who do you want to generalize to?to generalize to?Who do you want Who do you want to generalize to?to generalize to?

Groups in SamplingGroups in Sampling

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The Theoretical The Theoretical PopulationPopulation


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What population can What population can you get access to?you get access to?

What population can What population can you get access to?you get access to?

Groups in SamplingGroups in SamplingThe Theoretical The Theoretical

PopulationPopulationThe Theoretical The Theoretical

PopulationPopulation

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The Study The Study PopulationPopulationThe Study The Study PopulationPopulation

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How can you get How can you get access to them?access to them?How can you get How can you get access to them?access to them?





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The Sampling The Sampling FrameFrame


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Who is in your study?Who is in your study?Who is in your study?Who is in your study?







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The SampleThe SampleThe SampleThe Sample

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Where Can We Go Wrong?Where Can We Go Wrong?The Theoretical The Theoretical







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Statistical Terms in SamplingStatistical Terms in SamplingVariableVariableVariableVariable

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11 22 33 44 55


responsibilityresponsibility

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StatisticStatisticStatisticStatistic


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Average = 3.72Average = 3.72samplesample

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11 22 33 44 55



ParameterParameterParameterParameter


Average = 3.72Average = 3.72samplesample

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ParameterParameterParameterParameter

responseresponse

Average = 3.72Average = 3.72

Average = 3.75Average = 3.75

samplesample

populationpopulation

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Statistical Inference

Statistical inference: make generalizations about a population from a sample.

A population is the set of all the elements of interest in a study.

A sample is a subset of elements in the population chosen to represent it.

Quality of the sample = quality of the inference

Would this class be a good representation of all Persian Doctors? Why or why not?

This class would not be a good sample of all Persian Dentists, we are more interested in research methodology, so we are different!!

This class would not be a good sample of all Persian Dentists, we are more interested in research methodology, so we are different!!

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samplesample samplesample samplesample

The Sampling DistributionThe Sampling Distribution

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The Sampling DistributionThe Sampling Distributionsamplesample

4.44.24.03.83.63.43.23.0

5

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5

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samplesample

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5

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5

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samplesample

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5

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5

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The Sampling DistributionThe Sampling Distributionsamplesample

4.44.24.03.83.63.43.23.0

5

0

5

0

samplesample

4.44.24.03.83.63.43.23.0

5

0

5

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samplesample

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AverageAverageAverageAverage AverageAverageAverageAverage AverageAverageAverageAverage

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The Sampling DistributionThe Sampling Distribution

samplesample

4.44.24.03.83.63.43.23.0

5

0

5

0

samplesample

4.44.24.03.83.63.43.23.0

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5

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samplesample

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AverageAverageAverageAverage AverageAverageAverageAverage AverageAverageAverageAverage

4.44.24.03.83.63.43.23.0

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10

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The Sampling The Sampling Distribution...Distribution...The Sampling The Sampling Distribution...Distribution...

......is the distribution is the distribution of a statistic across of a statistic across an infinite number an infinite number

of samplesof samples

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Random SamplingRandom Sampling

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Types of Probability Sampling DesignsTypes of Probability Sampling Designs

Simple Random Sampling Stratified Sampling Systematic Sampling Cluster Sampling Multistage Sampling

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Some DefinitionsSome Definitions

N = the number of cases in the sampling frame

n = the number of cases in the sample

NCn = the number of combinations (subsets) of n from N

f = n/N = the sampling fraction

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Simple Random SamplingSimple Random Sampling• Objective - select n units out of N such

that every NCn has an equal chance

• Procedure - use table of random numbers, computer random number generator or mechanical device

• can sample with or without replacement

• f=n/N is the sampling fraction

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Simple Random SamplingSimple Random Sampling

People who subscribe Novin Pezeshki last year

People who visit our site draw a simple random sample of n/N

ExampleExample::

ExampleExample::

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List of ResidentsList of ResidentsList of ResidentsList of Residents

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List of ResidentsList of ResidentsList of ResidentsList of Residents

Random SubsampleRandom SubsampleRandom SubsampleRandom Subsample

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Stratified Random SamplingStratified Random Sampling• sometimes called "proportional" or

"quota" random sampling

• Objective - population of N units divided into non-overlapping strata N1, N2, N3, ... Ni such that N1 + N2 + ... + Ni = N, then do simple random sample of n/N in each strata

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Stratified Sampling The population is first divided into groups called strata. If

stratification is evident Example: medical students; preclinical, clerckship, internship

Best results when low intra strata variance and high inter strata variance

A simple random sample is taken from each stratum. Advantage: If strata are homogeneous, this method is

“more precise” than simple random sampling of same sample size

As precise but with a smaller total sample size. If there is a dominant strata and it is relatively small, you

can enumerate it, and sample the rest.

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Stratified Sampling - Purposes:Stratified Sampling - Purposes:

• to insure representation of each strata - oversample smaller population groups

• sampling problems may differ in each strata

• increase precision (lower variance) if strata are homogeneous within (like blocking)

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Stratified Random SamplingStratified Random SamplingList of ResidentsList of ResidentsList of ResidentsList of Residents

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StrataStrataStrataStrata

surgicalsurgical Non-clinicalNon-clinicalmedicalmedical

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Random Subsamples of n/NRandom Subsamples of n/NRandom Subsamples of n/NRandom Subsamples of n/N

StrataStrataStrataStrata

surgicalsurgical Non-clinicalNon-clinicalmedicalmedical

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Systematic Random SamplingSystematic Random Sampling

number units in population from 1 to N decide on the n that you want or need N/n=k the interval size randomly select a number from 1 to k then take every kth unit

Procedure:Procedure:Procedure:Procedure:

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Systematic Random SamplingSystematic Random Sampling

Assumes that the population is randomly ordered

Advantages - easy; may be more precise than simple random sample

Example - Residents study

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Systematic Random SamplingSystematic Random Sampling1 26 51 762 27 52 773 28 53 784 29 54 795 30 55 806 31 56 817 32 57 828 33 58 839 34 59 8410 35 60 8511 36 61 8612 37 62 8713 38 63 8814 39 64 8915 40 65 9016 41 66 9117 42 67 9218 43 68 9319 44 69 9420 45 70 9521 46 71 9622 47 72 9723 48 73 9824 49 74 9925 50 75 100

N = 100N = 100N = 100N = 100

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N = 100N = 100N = 100N = 100

want n = 20want n = 20want n = 20want n = 20

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N = 100N = 100N = 100N = 100


N/n = 5N/n = 5N/n = 5N/n = 5

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N = 100N = 100N = 100N = 100


N/n = 5N/n = 5N/n = 5N/n = 5

select a random number from 1-5: select a random number from 1-5: chose 4chose 4


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N = 100N = 100N = 100N = 100


N/n = 5N/n = 5N/n = 5N/n = 5



start with #4 and take every 5th unitstart with #4 and take every 5th unitstart with #4 and take every 5th unitstart with #4 and take every 5th unit

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Cluster Sampling

The population is first divided into clusters A cluster is a small-scale version of the

population (i.e. heterogeneous group reflecting the variance in the population.

Take a simple random sample of the clusters. All elements within each sampled (chosen)

cluster form the sample.

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Cluster Random SamplingCluster Random Sampling

Advantages - administratively useful, especially when you have a wide geographic area to cover

Example: Randomly sample from city blocks and measure all homes in selected blocks

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Cluster Sampling vs. Stratified Sampling Stratified sampling seeks to divide the sample

into heterogeneous groups so the variance within the strata is low and between the strata is high.

Cluster sampling seeks to have each cluster reflect the variance in the population…each cluster is a “mini” population. Each cluster is a mirror of the total population and of each other.

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Multi-Stage SamplingMulti-Stage Sampling

Cluster random sampling can be multi-stage

Any combinations of single-stage methods

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Multi-Stage SamplingMulti-Stage Sampling

Select all schools, then sample within schools

Sample schools, then measure all students

Sample schools, then sample students

�choosing students from medical schools:choosing students from medical schools:�choosing students from medical schools:choosing students from medical schools:

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Nonrandom Sampling DesignsNonrandom Sampling Designs

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Types of nonrandom samplesTypes of nonrandom samples

Accidental, haphazard, convenience Modal Instance Purposive Expert Quota Snowball Heterogeneity sampling

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Accidental or Haphazard SamplingAccidental or Haphazard Sampling

“Man on the street” Medical student in the library available or accessible clients volunteer samples

•Problem: we have no evidence

for representativeness

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Convenience Sampling

The sample is identified primarily by convenience.

It is a nonprobability sampling technique. Items are included in the sample without known probabilities of being selected.

Example: A professor conducting research might use student volunteers to constitute a sample.

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Convenience Sampling

Advantage: Relatively easy, fast, often, but not always, cheap

Disadvantage: It is impossible to determine how representative of the population the sample is. Try to offset this by

collecting large sample

size.

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Quota SamplingQuota Sampling

select people nonrandomly according to some quotas

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Sampling

Random Non Random

Simple

Systematic

Cluster

Multi Stage

Stratified

Proportionate Disproportionate

Haphazard

Convenience

Modal Instance

Purposive

Expert

Snowball

Heterogeneity

Quota

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