# Sampling by yurtgc548

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```									Sampling

1
Sampling Issues
Sampling Terminology

Probability in Sampling

Probability Sampling Designs

Non-Probability Sampling Designs

Sampling Distribution

2
Sampling
Terminology

3
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     selection is systematic or
Sampling            haphazard, but not random

4
Groups in Sampling
Who do you want
to generalize to?

5
Groups in Sampling

The Theoretical
Population

6
Groups in Sampling
The Theoretical
Population

What population can

7
Groups in Sampling

The Theoretical
Population

The Study
Population

8
Groups in Sampling
The Theoretical
Population

The Study
Population

How can you get

9
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

11
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

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Statistical Terms in Sampling
Variable                    1   2   3   4   5

responsibility

18
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

21
Statistical Terms in Sampling
Variable                 1   2   3   4   5

response

Statistic                Average = 3.72
sample

Parameter                 Average = 3.75
population

22
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.
                       This class would in be
A sample is a subset of elementsnot thea
to represent all
population chosengood sample of it. Persian
                       Dentists, we are the
Quality of the sample = quality of more
inference           interested in research
methodology, so we are
                       different!!
Would this class be a good representation of
all Persian Doctors? Why or why not?
23
The Sampling Distribution
sample    sample      sample

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The Sampling Distribution
sample                                              sample                                              sample
5                                                   5                                                   5

0                                                   0                                                   0

5                                                   5                                                   5

0                                                   0                                                   0

3.0   3.2   3.4   3.6   3.8   4.0   4.2   4.4       3.0   3.2   3.4   3.6   3.8   4.0   4.2   4.4       3.0   3.2   3.4   3.6   3.8   4.0   4.2   4.4

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The Sampling Distribution
sample                                              sample                                              sample
5                                                   5                                                   5

0                                                   0                                                   0

5                                                   5                                                   5

0                                                   0                                                   0

3.0   3.2   3.4   3.6   3.8   4.0   4.2   4.4       3.0   3.2   3.4   3.6   3.8   4.0   4.2   4.4       3.0   3.2   3.4   3.6   3.8   4.0   4.2   4.4

Average                                             Average                                             Average

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The Sampling Distribution
sample                                                           sample                                                        sample
5                                                              5                                                               5

0                                                              0                                                               0

5                                                              5                                                               5

0                                                              0                                                               0

3.0   3.2   3.4   3.6   3.8   4.0   4.2   4.4                  3.0   3.2     3.4     3.6   3.8   4.0   4.2     4.4             3.0   3.2   3.4   3.6   3.8   4.0   4.2   4.4

Average                                                        Average                                                         Average
15

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...is the distribution
The Sampling                                                                                                                  of a statistic across
Distribution...                                        5
an infinite number
0                                                                            of samples 27
3.0       3.2     3.4         3.6     3.8   4.0     4.2         4.4
Random Sampling

28
Types of Probability Sampling
Designs
 Simple Random Sampling
 Stratified Sampling
 Systematic Sampling
 Cluster Sampling
 Multistage Sampling

29
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

30
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
•   f=n/N is the sampling fraction

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Simple Random Sampling
Example
:
 People who subscribe Novin Pezeshki last
year
 draw a simple random sample of n/N

32
Simple Random Sampling

List of Residents

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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
N1, N2, N3, ... Ni such that N1 + N2 +
... + Ni = N, then do simple random
sample of n/N in each strata

35
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.

36
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   medical   Non-clinical

Strata

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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

41
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
N = 100   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
17   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   99
25   50   75   100
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Systematic Random Sampling
1    26   51   76
2    27   52   77
3    28   53   78
N = 100   4    29   54   79
5    30   55   80
6    31   56   81
7    32   57   82
want n = 20    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
17   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   99
25   50   75   100
44
Systematic Random Sampling
1    26   51   76
2    27   52   77
3    28   53   78
N = 100   4    29   54   79
5    30   55   80
6    31   56   81
7    32   57   82
want n = 20    8    33   58   83
9    34   59   84
10   35   60   85
11   36   61   86
N/n = 5    12   37   62   87
13   38   63   88
14   39   64   89
15   40   65   90
16   41   66   91
17   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   99
25   50   75   100
45
Systematic Random Sampling
1    26   51   76
2    27   52   77
3    28   53   78
N = 100   4    29   54   79
5    30   55   80
6    31   56   81
7    32   57   82
want n = 20    8    33   58   83
9    34   59   84
10   35   60   85
11   36   61   86
N/n = 5   12   37   62   87
13   38   63   88
14   39   64   89
15   40   65   90
select a random number from 1-5:    16   41   66   91
17   42   67   92
chose 4                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   99
25   50   75   100
46
Systematic Random Sampling
1    26   51   76
2    27   52   77
3    28   53   78
N = 100    4    29   54   79
5    30   55   80
6    31   56   81
7    32   57   82
want n = 20      8    33   58   83
9    34   59   84
10   35   60   85
11   36   61   86
N/n = 5     12   37   62   87
13   38   63   88
14   39   64   89
15   40   65   90
select a random number from 1-5:         16   41   66   91
17   42   67   92
chose 4                     18   43   68   93
19   44   69   94
20   45   70   95
21   46   71   96
22   47   72   97
start with #4 and take every 5th unit   23   48   73   98
24   49   74   99
25   50   75   100
47
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.

48
Cluster Random Sampling

especially when you have a wide
geographic area to cover
 Example: Randomly sample from city
blocks and measure all homes in selected
blocks

49
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.
50
Multi-Stage Sampling
 Cluster random sampling can be multi-
stage
 Any combinations of single-stage methods

51
Multi-Stage Sampling
c
• hoosing students from medical schools:

 Select all schools, then sample within
schools
 Sample schools, then measure all
students
 Sample schools, then sample students

52
Nonrandom
Sampling Designs

53
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

55
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.

56
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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Sampling

Random                              Non Random

Simple                          Haphazard

Systematic                        Convenience

Cluster                         Modal Instance

Multi Stage                         Purposive

Stratified                          Expert

Snowball
Proportionate    Disproportionate
Heterogeneity

Quota
64
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