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Sampling

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Statistic. responsibility. Average = 3.72. sample. 21. 1 2 3 4 ... is the distribution of a statistic across an infinite number of samples. 28. Random Sampling ... – PowerPoint PPT presentation

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Title: Sampling


1
Sampling
2
Sampling Issues
Sampling Terminology
Probability in Sampling
Probability Sampling Designs
Non-Probability Sampling Designs
Sampling Distribution
3
Sampling Terminology
4
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
5
Groups in Sampling
Who do you want to generalize to?
6
Groups in Sampling
The Theoretical Population
7
Groups in Sampling
The Theoretical Population
What population can you get access to?
8
Groups in Sampling
The Theoretical Population
The Study Population
9
Groups in Sampling
The Theoretical Population
The Study Population
How can you get access to them?
10
Groups in Sampling
The Theoretical Population
The Study Population
The Sampling Frame
11
Groups in Sampling
The Theoretical Population
The Study Population
The Sampling Frame
Who is in your study?
12
Groups in Sampling
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
Where Can We Go Wrong?
The Theoretical Population
The Study Population
The Sampling Frame
The Sample
17
Statistical Terms in Sampling
Variable
18
Statistical Terms in Sampling
Variable
1 2 3 4 5
responsibility
19
Statistical Terms in Sampling
Variable
1 2 3 4 5
responsibility
Statistic
20
Statistical Terms in Sampling
Variable
1 2 3 4 5
responsibility
Statistic
Average 3.72
sample
21
Statistical Terms in Sampling
Variable
1 2 3 4 5
responsibility
Statistic
Average 3.72
sample
Parameter
22
Statistical Terms in Sampling
Variable
1 2 3 4 5
response
Statistic
Average 3.72
sample
Parameter
Average 3.75
population
23
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!!
24
The Sampling Distribution
25
The Sampling Distribution
26
The Sampling Distribution
Average
Average
Average
27
The Sampling Distribution
Average
Average
Average
...is the distribution of a statistic across an
infinite number of samples
The Sampling Distribution...
28
Random Sampling
29
Types of Probability Sampling Designs
  • Simple Random Sampling
  • Stratified Sampling
  • Systematic Sampling
  • Cluster Sampling
  • Multistage Sampling

30
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

31
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

32
Simple Random Sampling
Example
  • People who subscribe Novin Pezeshki last year
  • People who visit our site
  • draw a simple random sample of n/N

33
Simple Random Sampling
List of Residents
34
Simple Random Sampling
List of Residents
Random Subsample
35
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

36
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.

37
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)

38
Stratified Random Sampling
List of Residents
39
Stratified Random Sampling
List of Residents
surgical
Non-clinical
medical
Strata
40
Stratified Random Sampling
List of Residents
surgical
Non-clinical
medical
Strata
Random Subsamples of n/N
41
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

42
Systematic Random Sampling
  • Assumes that the population is randomly ordered
  • Advantages - easy may be more precise than
    simple random sample
  • Example - Residents study

43
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
44
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
45
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
46
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
47
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
48
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.

49
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

50
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.

51
Multi-Stage Sampling
  • Cluster random sampling can be multi-stage
  • Any combinations of single-stage methods

52
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

53
Nonrandom Sampling Designs
54
Types of nonrandom samples
  • Accidental, haphazard, convenience
  • Modal Instance
  • Purposive
  • Expert
  • Quota
  • Snowball
  • Heterogeneity sampling

55
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

56
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.

57
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.

58
Modal Instance Sampling
  • Sample for the typical case
  • Typical medical students age?
  • Typical socioeconomic class?
  • Problem may not represent the modal group
    proportionately

59
Purposive Sampling
  • Might sample several pre-defined groups (e.g.,
    patients who does not attend at follow up visits)
  • Deliberately sampling an extreme group

60
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

61
Quota Sampling
  • select people nonrandomly according to some quotas

62
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

63
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

64
Sampling
Random
Non Random
Haphazard
Simple
Convenience
Systematic
Modal Instance
Cluster
Purposive
Multi Stage
Expert
Stratified
Snowball
Proportionate
Disproportionate
Heterogeneity
Quota
65
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