Sampling

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Sampling
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Sampling Issues
Sampling Terminology
Probability in Sampling
Probability Sampling Designs
Non-Probability Sampling Designs
Sampling Distribution
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Sampling Terminology
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Two 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 Sampling
Non-Probability Sampling
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Groups in Sampling
Who do you want to generalize to?
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Groups in Sampling
The Theoretical Population
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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
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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
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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
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Where Can We Go Wrong?
The Theoretical Population
The Study Population
The Sampling Frame
The Sample
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Where Can We Go Wrong?
The Theoretical Population
The Study Population
The Sampling Frame
The Sample
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Where Can We Go Wrong?
The Theoretical Population
The Study Population
The Sampling Frame
The Sample
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Where Can We Go Wrong?
The Theoretical Population
The Study Population
The Sampling Frame
The Sample
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Statistical Terms in Sampling
Variable
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Statistical Terms in Sampling
Variable
1 2 3 4 5
responsibility
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Statistical Terms in Sampling
Variable
1 2 3 4 5
responsibility
Statistic
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Statistical Terms in Sampling
Variable
1 2 3 4 5
responsibility
Statistic
Average 3.72
sample
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Statistical Terms in Sampling
Variable
1 2 3 4 5
responsibility
Statistic
Average 3.72
sample
Parameter
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Statistical Terms in Sampling
Variable
1 2 3 4 5
response
Statistic
Average 3.72
sample
Parameter
Average 3.75
population
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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!!
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The Sampling Distribution
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The Sampling Distribution
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The Sampling Distribution
Average
Average
Average
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The Sampling Distribution
Average
Average
Average
...is the distribution of a statistic across an
infinite number of samples
The Sampling Distribution...
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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
• NCn 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 NCn has an equal chance
• Procedure - use table of random numbers,
  computer random number generator or mechanical
  device
• can sample with or without replacement
• fn/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
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Simple Random Sampling
List of Residents
Random Subsample
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Stratified 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

• 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
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Stratified Random Sampling
List of Residents
surgical
Non-clinical
medical
Strata
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Stratified Random Sampling
List of Residents
surgical
Non-clinical
medical
Strata
Random Subsamples of n/N
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Systematic Random Sampling
Procedure

• number units in population from 1 to N
• decide on the n that you want or need
• N/nk 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
1 26 51 76 2 27 52 77 3 28 53 78 4 29 54 79 5
30 55 80 6 31 56 81 7 32 57 82 8 33 58 83 9 34
59 84 10 35 60 85 11 36 61 86 12 37 62 87 13
38 63 88 14 39 64 89 15 40 65 90 16 41 66 91 1
7 42 67 92 18 43 68 93 19 44 69 94 20 45 70 95
21 46 71 96 22 47 72 97 23 48 73 98 24 49 74 9
9 25 50 75 100
N 100
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Systematic Random Sampling
1 26 51 76 2 27 52 77 3 28 53 78 4 29 54 79 5
30 55 80 6 31 56 81 7 32 57 82 8 33 58 83 9 34
59 84 10 35 60 85 11 36 61 86 12 37 62 87 13
38 63 88 14 39 64 89 15 40 65 90 16 41 66 91 1
7 42 67 92 18 43 68 93 19 44 69 94 20 45 70 95
21 46 71 96 22 47 72 97 23 48 73 98 24 49 74 9
9 25 50 75 100
N 100
want n 20
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Systematic Random Sampling
1 26 51 76 2 27 52 77 3 28 53 78 4 29 54 79 5
30 55 80 6 31 56 81 7 32 57 82 8 33 58 83 9 34
59 84 10 35 60 85 11 36 61 86 12 37 62 87 13
38 63 88 14 39 64 89 15 40 65 90 16 41 66 91 1
7 42 67 92 18 43 68 93 19 44 69 94 20 45 70 95
21 46 71 96 22 47 72 97 23 48 73 98 24 49 74 9
9 25 50 75 100
N 100
want n 20
N/n 5
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Systematic Random Sampling
1 26 51 76 2 27 52 77 3 28 53 78 4 29 54 79 5
30 55 80 6 31 56 81 7 32 57 82 8 33 58 83 9 34
59 84 10 35 60 85 11 36 61 86 12 37 62 87 13
38 63 88 14 39 64 89 15 40 65 90 16 41 66 91 1
7 42 67 92 18 43 68 93 19 44 69 94 20 45 70 95
21 46 71 96 22 47 72 97 23 48 73 98 24 49 74 9
9 25 50 75 100
N 100
want n 20
N/n 5
select a random number from 1-5 chose 4
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Systematic Random Sampling
1 26 51 76 2 27 52 77 3 28 53 78 4 29 54 79 5
30 55 80 6 31 56 81 7 32 57 82 8 33 58 83 9 34
59 84 10 35 60 85 11 36 61 86 12 37 62 87 13
38 63 88 14 39 64 89 15 40 65 90 16 41 66 91 1
7 42 67 92 18 43 68 93 19 44 69 94 20 45 70 95
21 46 71 96 22 47 72 97 23 48 73 98 24 49 74 9
9 25 50 75 100
N 100
want n 20
N/n 5
select a random number from 1-5 chose 4
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 populationeach
  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

• choosing students from medical schools

• 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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Modal Instance Sampling

• Sample for the typical case
• Typical medical students age?
• Typical socioeconomic class?
• Problem may not represent the modal group
  proportionately

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Purposive Sampling

• Might sample several pre-defined groups (e.g.,
  patients who does not attend at follow up visits)
• Deliberately sampling an extreme group

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Expert Sampling

• Have a panel of experts make a judgment about the
  representativeness of your sample
• Advantage at least you can say that expert
  judgment supports the sampling
• Problem the experts may be wrong

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Quota Sampling

• select people nonrandomly according to some quotas

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Snowball Sampling

• one person recommends another, who recommends
  another, who recommends another, etc.
• good way to identify hard-to-reach populations
• for example, adolescents who abuse recreational
  drugs

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Heterogeneity Sampling

• make sure you include all sectors - at least
  several of everything - don't worry about
  proportions (like in quota sampling)
• for instance, when brainstorming issues across
  stakeholder groups

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