Sampling

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Sampling Issues

Sampling Terminology Probability in Sampling Probability Sampling Designs Non-Probability Sampling Designs Sampling Distribution 2

Sampling Terminology

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Two Major Types of Sampling Methods

Probability Sampling uses some form of random selection requires that each unit have a known (often equal) probability of being selected Non-Probability Sampling selection is systematic or haphazard, but not random 4

Groups in Sampling

Who do you want to generalize to?

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Groups in Sampling

The Theoretical Population 6

Groups in Sampling

The Theoretical Population What population can you get access to?

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Groups in Sampling

The Theoretical Population The Study Population 8

Groups in Sampling

The Theoretical Population The Study Population How can you get access to them?

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Groups in Sampling

The Theoretical Population The Study Population The Sampling Frame 10

Groups in Sampling

The Theoretical Population The Study Population The Sampling Frame Who is in your study?

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Groups in Sampling

The Theoretical Population The Study Population The Sampling Frame The Sample 12

Where Can We Go Wrong?

The Theoretical Population The Study Population The Sampling Frame The Sample 13

Where Can We Go Wrong?

The Theoretical Population The Study Population The Sampling Frame The Sample 14

Where Can We Go Wrong?

The Theoretical Population The Study Population The Sampling Frame The Sample 15

Where Can We Go Wrong?

The Theoretical Population The Study Population The Sampling Frame The Sample 16

Statistical Terms in Sampling

Variable 17

Statistical Terms in Sampling

Variable 1 2 3 4 5 responsibility 18

Statistical Terms in Sampling

Variable 1 2 3 4 5 responsibility Statistic 19

Statistical Terms in Sampling

Variable 1 2 3 4 5 responsibility Statistic sample Average = 3.72

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Statistical Terms in Sampling

Variable 1 2 3 4 5 responsibility Statistic sample Average = 3.72

Parameter 21

Statistical Terms in Sampling

Variable 1 2 3 4 5 response Statistic sample Average = 3.72

Parameter population Average = 3.75

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Statistical Inference  S

tatistical 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 interested in research methodology, so we are Would this class be a good representation of all Persian Doctors? Why or why not?

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The Sampling Distribution

sample sample sample 24

The Sampling Distribution

sample

5 0 5 0 3.0

3.2

3.4

3.6

3.8

4.0

4.2

4.4

sample

5 0 5 0 3.0

3.2

3.4

3.6

3.8

4.0

4.2

4.4

sample

5 0 5 0 3.0

3.2

3.4

3.6

3.8

4.0

4.2

4.4

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The Sampling Distribution

sample

5 0 5 0 3.0

3.2

3.4

3.6

3.8

4.0

4.2

4.4

sample

5 0 5 0 3.0

3.2

3.4

3.6

3.8

4.0

4.2

4.4

sample

5 0 5 0 3.0

3.2

3.4

3.6

3.8

4.0

4.2

4.4

Average Average Average 26

The Sampling Distribution

sample

5 0 5 0 3.0

3.2

3.4

3.6

3.8

4.0

4.2

4.4

sample

5 0 5 0 3.0

3.2

3.4

3.6

3.8

4.0

4.2

4.4

sample

5 0 5 0 3.0

3.2

3.4

3.6

3.8

4.0

4.2

4.4

Average The Sampling Distribution...

Average Average

15 10 5 0 3.0

3.2

3.4

3.6

3.8

4.0

4.2

4.4

...is the distribution of a statistic across an infinite number of samples 27

Random Sampling

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Types of Probability Sampling Designs  Simple Random Sampling  Stratified Sampling  Systematic Sampling  Cluster Sampling  Multistage Sampling

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Some Definitions  N = the number of cases in the sampling frame  n = the number of cases in the sample  N C n = the number of combinations (subsets) of n from N  f = n/N = the sampling fraction

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Simple Random Sampling • • Objective - select n units out of N such that every N C n 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 Sampling

Example



:

People who subscribe Novin Pezeshki last year  People who visit our site  draw a simple random sample of n/N

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Simple Random Sampling

List of Residents 33

Simple Random Sampling

List of Residents Random Subsample 34

Stratified Random Sampling • sometimes called "proportional" or "quota" random sampling • Objective - population of N units divided into non-overlapping strata N 1 , N 2 , N 3 , ... N i ... + N i such that N 1 + N 2 + = 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: • 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 Sampling

List of Residents 38

Stratified Random Sampling

List of Residents surgical medical Non-clinical Strata 39

Stratified Random Sampling

List of Residents surgical medical Non-clinical Strata Random Subsamples of n/N 40

Systematic Random Sampling

Procedure:

 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

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Systematic 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 Sampling

N = 100

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Systematic Random Sampling

N = 100 want n = 20

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Systematic Random Sampling

N = 100 want n = 20 N/n = 5

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Systematic Random Sampling

N = 100 want n = 20 N/n = 5 select a random number from 1-5: chose 4

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Systematic Random Sampling

chose 4 N = 100 want n = 20 N/n = 5 select a random number from 1-5: start 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 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 Sampling  Cluster random sampling can be multi stage  Any combinations of single-stage methods

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Multi-Stage Sampling  Select all schools, then

sample

within schools  Sample schools, then measure

all

students  Sample schools, then

sample

students

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Nonrandom Sampling Designs

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Types of nonrandom samples  Accidental, haphazard, convenience  Modal Instance  Purposive  Expert  Quota  Snowball  Heterogeneity sampling

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Accidental 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 Sampling  select people nonrandomly according to some quotas

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Random Simple Systematic Cluster Multi Stage Stratified Proportionate Sampling Non Random Disproportionate Haphazard Convenience Modal Instance Purposive Expert Snowball Heterogeneity Quota 64

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