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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
   you get access to?




                         7
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?




                      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



  Who is in your study?
                          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




                                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                    Average = 3.72
                   sample




                                                     20
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




                                     24
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




                                                                                                                                                            25
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




                                                                                                                                                            26
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




                                                       10
                                                                                                                              ...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



                                                   31
Simple Random Sampling
 Example
     :
 People who subscribe Novin Pezeshki last
  year
 People who visit our site
 draw a simple random sample of n/N




                                         32
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
        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)
                                                37
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


                                           41
Systematic Random Sampling
 Assumes that the population is randomly
  ordered
 Advantages - easy; may be more precise
  than simple random sample
 Example - Residents study




                                            42
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
                                               43
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

 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



                                         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

                                       54
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.
                                             57
Quota Sampling

   select people nonrandomly according to
    some quotas




                                             61
                        Sampling

Random                              Non Random


           Simple                          Haphazard

         Systematic                        Convenience

           Cluster                         Modal Instance

        Multi Stage                         Purposive

          Stratified                          Expert

                                             Snowball
Proportionate    Disproportionate
                                           Heterogeneity

                                                 Quota
                                                            64
65

				
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