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					Sampling in Marketing Research




                                 1
                        Basics of sampling I

   A sample is a           Samples offer many benefits:
    “part of a whole         Save costs: Less expensive to study the
    to show what the          sample than the population.
    rest is like”.           Save time: Less time needed to study the
   Sampling helps to         sample than the population .
    determine the            Accuracy: Since sampling is done with
    corresponding             care and studies are conducted by skilled
    value of the              and qualified interviewers, the results are
    population and            expected to be accurate.
    plays a vital role in
                             Destructive nature of elements: For some
    marketing
                              elements, sampling is the way to test, since
    research.
                              tests destroy the element itself.
                                                                             2
                    Basics of sampling II

Limitations of Sampling             Sampling Process
   Demands more rigid control
    in undertaking sample        Defining the   Developing
    operation.                    population    a sampling
                                                   Frame
   Minority and smallness in
    number of sub-groups often
    render study to be            Specifying    Determining
    suspected.                     Sample         Sample
                                   Method           Size
   Accuracy level may be
    affected when data is
    subjected to weighing.
   Sample results are good      SELECTING THE SAMPLE
    approximations at best.

                                                              3
       Sampling: Step 1                          Sampling: Step 2
      Defining the Universe                  Establishing the Sampling
                                                        Frame
   Universe or population is the
    whole mass under study.                 A sample frame is the list of all
                                             elements in the population
   How to define a universe:
                                             (such as telephone directories,
    » What constitutes the units of
                                             electoral registers, club
      analysis (HDB apartments)?
                                             membership etc.) from which
    » What are the sampling units
                                             the samples are drawn.
      (HDB apartments occupied in
      the last three months)?               A sample frame which does not
                                             fully represent an intended
    » What is the specific designation
                                             population will result in frame
      of the units to be covered (HDB
                                             error and affect the degree of
      in town area)?
                                             reliability of sample result.
    » What time period does the data
      refer to (December 31, 1995)
                                                                                 4
                     Step - 3
           Determination of Sample Size
   Sample size may be determined by using:
    » Subjective methods (less sophisticated methods)
       – The rule of thumb approach: eg. 5% of population
       – Conventional approach: eg. Average of sample sizes of
         similar other studies;
       – Cost basis approach: The number that can be studied
         with the available funds;
    » Statistical formulae (more sophisticated methods)
       – Confidence interval approach.

                                                                 5
  Conventional approach of Sample size determination using
     Sample sizes used in different marketing research studies

           TYPE OF STUDY                 MINIMUM           TYPICAL
                                           SIZE             RANGE
Identifying a problem (e.g.market
segmentation)                                 500          1000-2500
Problem-solving (e.g., promotion)             200           300-500
Product tests                                 200           300-500
Advertising (TV, Radio, or print Media
per commercial or ad tested)                  150            200-300
Test marketing                                200            300-500
Test market audits                             10             10-20
                                         stores/outlets   stores/outlets
Focus groups                               2 groups        4-12 groups

                                                                           6
    Sample size determination using statistical formulae:
              The confidence interval approach

   To determine sample sizes using statistical formulae,
    researchers use the confidence interval approach based on the
    following factors:
     » Desired level of data precision or accuracy;
     » Amount of variability in the population (homogeneity);
     » Level of confidence required in the estimates of population values.
   Availability of resources such as money, manpower and time
    may prompt the researcher to modify the computed sample
    size.
   Students are encouraged to consult any standard marketing
    research textbook to have an understanding of these formulae.
                                                                             7
                         Step 4:
             Specifying the sampling method
   Probability Sampling
    » Every element in the target population or universe [sampling
      frame] has equal probability of being chosen in the sample for
      the survey being conducted.
    » Scientific, operationally convenient and simple in theory.
    » Results may be generalized.
   Non-Probability Sampling
    » Every element in the universe [sampling frame] does not have
      equal probability of being chosen in the sample.
    » Operationally convenient and simple in theory.
    » Results may not be generalized.

                                                                       8
                Probability sampling
              Four types of probability sampling

   Appropriate for                        Appropriate for
    homogeneous population                  heterogeneous population
    » Simple random sampling                » Stratified sampling
       – Requires the use of a random           – Use of random number
         number table.                            table may be necessary
    » Systematic sampling                   » Cluster sampling
       – Requires the sample frame              – Use of random number
         only,                                    table may be necessary
       – No random number table is
         necessary


                                                                           9
             Non-probability sampling

   Four types of non-probability sampling
    techniques
    » Very simple types, based on subjective criteria
       – Convenient sampling
       – Judgmental sampling
    » More systematic and formal
       – Quota sampling
    » Special type
       – Snowball Sampling
                                                        10
               Simple Random Sampling

                              1    2    3 4       5    6    7    8    9 10 11 12 13 14 15 16 17 18 19 20
   Also called random
    sampling             1    37   75   10   49   98   66   03 86 34 80 98 44 22 22                 45   83   53   86   23   51
                         2    50   91   56   41   52   82   98 11 57 96 27 10 27 16                 35   34   47   01   36   08
   Simplest method of   3    99   14   23   50   21   01   03 25 79 07 80 54 55 41                 12   15   15   03   68   56
    probability          4    70   72   01   00   33   25   19 16 23 58 03 78 47 43                 77   88   15   02   55   67
                         5    18   46   06   49   47   32   58 08 75 29 63 66 89 09                 22   35   97   74   30   80
    sampling
                          6   65   76   34   11   33   60   95   03   53   72   06   78   28   14   51   78   76   45   26   45
                          7   83   76   95   25   70   60   13   32   52   11   87   38   49   01   82   84   99   02   64   00
                          8   58   90   07   84   20   98   57   93   36   65   10   71   83   93   42   46   34   61   44   01
                          9   54   74   67   11   15   78   21   96   43   14   11   22   74   17   02   54   51   78   76   76
                         10   56   81   92   73   40   07   20   05   26   63   57   86   48   51   59   15   46   09   75   64
      Need to use
      Random             11   34   99   06   21   22   38 22 32 85 26 37 00 62 27 74 46 02 61 59 81
                         12   02   26   92   27   95    87 59 38 18 30 95 38 36 78 23 20 19 65 48 50
      Number Table       13   43   04   25   36   00   45 73 80 02 61 31 10 06 72 39 02 00 47 06 98
                         14   92   56   51   22   11   06 86 88 77 86 59 57 66 13 82 33 97 21 31 61
                         15   67   42   43   26   20   60 84 18 68 48 85 00 00 48 35 48 57 63 38 84


                                                                                                                                  11
      How to Use Random Number Tables

________________________________________________
1. Assign a unique number to each population element in the
   sampling frame. Start with serial number 1, or 01, or 001,
   etc. upwards depending on the number of digits required.
2. Choose a random starting position.
3. Select serial numbers systematically across rows or down
   columns.
4. Discard numbers that are not assigned to any population
   element and ignore numbers that have already been
   selected.
5. Repeat the selection process until the required number of
   sample elements is selected.


                                                                12
   How to Use a Table of Random Numbers to Select a Sample
    Your marketing research lecturer wants to randomly select 20 students from
your class of 100 students. Here is how he can do it using a random number table.
Step 1: Assign all the 100 members of the population a unique number.You may
identify each element by assigning a two-digit number. Assign 01 to the first name
on the list, and 00 to the last name. If this is done, then the task of selecting the
sample will be easier as you would be able to use a 2-digit random number table.
     NAME                       NUMBER      NAME                  NUMBER
     Adam, Tan                    01        Tan Teck Wah             42
     ………………                                 ……………………                 …
     Carrol, Chan                 08        Tay Thiam Soon           61
     ……………….                      …         ………………..                 …
     Jerry Lewis                  18        Teo Tai Meng             87
     ……………….                      …         ………………….                 …
     Lim Chin Nam                 26        ……………………                 …
     ……………….                      …         Yeo Teck Lan             99
     Singh, Arun                  30        Zailani bt Samat         00

                                                                                        13
        How to use random number table to select a random sample
Step 2: Select any starting point in the Random Number Table and find the first number that
     corresponds to a number on the list of your population. In the example below, # 08 has been
     chosen as the starting point and the first student chosen is Carol Chan.

Starting point:                    10 09 73 25 33 76
 move right to the end
of the row, then down              37 54 20 48 05 64
to the next row row;               08 42 26 89 53 19
move left to the end,              90 01 90 25 29 09
then down to the next
row, and so on.                    12 80 79 99 70 80
                                   66 06 57 47 17 34
                                   31 06 01 08 05 45
Step 3: Move to the next number, 42 and select the person corresponding to that number into
     the sample. #87 – Tan Teck Wah
Step 4: Continue to the next number that qualifies and select that person into the sample.
     # 26 -- Jerry Lewis, followed by #89, #53 and #19
Step 5: After you have selected the student # 19, go to the next line and choose #90. Continue
     in the same manner until the full sample is selected. If you encounter a number selected
     earlier (e.g., 90, 06 in this example) simply skip over it and choose the next number.
                                                                                                 14
                       Systematic sampling
 Very similar to simple random sampling with one exception.
 In systematic sampling only one random number is needed throughout the
  entire sampling process.
 To use systematic sampling, a researcher needs:
         [i] a sampling frame of the population; and is needed.
         [ii] a skip interval calculated as follows:
       Skip interval = population list size
                        Sample size
 Names are selected using the skip interval.
 If a researcher were to select a sample of 1000 people using the local telephone
  directory containing 215,000 listings as the sampling frame, skip interval is
  [215,000/1000], or 215. The researcher can select every 215th name of the entire
  directory [sampling frame], and select his sample.
                                                                                     15
                      Example: How to Take a Systematic Sample
Step 1: Select a listing of the population, say the City Telephone Directory, from which to
     sample. Remember that the list will have an acceptable level of sample frame error.

Step 2: Compute the skip interval by dividing the number of entries in the directory by the
     desired sample size.
     Example: 250,000 names in the phone book, desired a sample size of 2500,
               So skip interval = every 100th name

Step 3: Using random number(s), determine a starting position for sampling the list.
     Example: Select: Random number for page number. (page 01)
               Select: Random number of column on that page. (col. 03)
              Select: Random number for name position in that column (#38, say, A..Mahadeva)

Step 4: Apply the skip interval to determine which names on the list will be in the sample.
     Example: A. Mahadeva (Skip 100 names), new name chosen is A Rahman b Ahmad.

Step 5: Consider the list as “circular”; that is, the first name on the list is now the initial name
     you selected, and the last name is now the name just prior to the initially selected one.
     Example: When you come to the end of the phone book names (Zs), just continue on
               through the beginning (As).
                                                                                                       16
                        Stratified sampling I
        A three-stage process:               Stratified samples can be:
   Step 1- Divide the population into          Proportionate: involving the
    homogeneous, mutually exclusive              selection of sample elements
    and collectively exhaustive subgroups        from each stratum, such that
    or strata using some stratification          the ratio of sample elements
    variable;                                    from each stratum to the
   Step 2- Select an independent simple         sample size equals that of the
    random sample from each stratum.             population elements within
   Step 3- Form the final sample by             each stratum to the total
    consolidating all sample elements            number of population
    chosen in step 2.                            elements.
   May yield smaller standard errors of        Disproportionate: the sample
    estimators than does the simple random       is disproportionate when the
    sampling. Thus precision can be gained       above mentioned ratio is
    with smaller sample sizes.                   unequal.
                                                                                  17
             Selection of a proportionate Stratified Sample
To select a proportionate stratified sample of 20 members of the Island Video Club which has
100 members belonging to three language based groups of viewers i.e., English (E), Mandarin
(M) and Others (X).

Step 1: Identify each member from the membership list by his or her respective language groups
        00 (E )         20   (M)     40   (E )    60   (X)     80   (M)
        01 (E )         21   (X)     41   (X)     61   (M)     81   (E )
        02 ( X )        22   (E )    42   (X)     62   (M)     82   (E )
        03 (E )         23   (X)     43   (E )    63   (E )    83   (M)
        04 (E )         24   (E )    44   (M)     64   (E )    84   (X)
        05 (E )         25   (M)     45   (E )    65   (X)     85   (E )
        06 (M)          26   (E )    46   (X)     66   (M)     86   (E )
        07 (M)          27   (M)     47   (M)     67   (E )    87   (M)
        08 (E )         28   (X)     48   (E )    68   (M)     88   (X)
        09 (E )         29   (E )    49   (E )    69   (E )    89   (E )
        10 (M)          30   (E )    50   (E )    70   (E )    90   (X)
        11 (E )         31   (E )    51   (M)     71   (E )    91   (E )
        12 ( X )        32   (E )    52   (X)     72   (M)     92   (M)
        13 (M)          33   (M)     53   (M)     73   (E )    93   (E )
        14 (E )         34   (E )    54   (E )    74   (X)     94   (E )
        15 (M)          35   (M)     55   (E )    75   (E )    95   (X)
        16 (E )         36   (E )    56   (M)     76   (E )    96   (E )
        17 ( X )        37   (E )    57   (E )    77   (M)     97   (E )
        18 ( X )        38   (X)     58   (M)     78   (M)     98   (M)
        19 (M)          39   (X)     59   (M)     79   (E )    99   (E )
                                                                                                 18
       Selection of a proportionate stratified sample II

Step 2: Sub-divide the club members into three homogeneous sub-groups or strata by the
language groups: English, Mandarin and others.
EnglishLanguage      Mandarin Language     Other Language
    Stratum            Stratum               Stratum    .
00 22 40 64 82        06 35 66                02 42
01 24 43 67 85        07 44 68                12 46
03 26 45 69 86        10 47 72                17 52
04 29 48 70 89        13 51 77                18 60
05 30 49 71 91        15 53 78                21 65
08 31 50 73 93        19 56 80                23 74
09 32 54 75 94        20 58 83                28 84
11 34 55 76 96        25 59 87                38 88
14 36 57 79 97        27 61 92                39 90
16 37 63 81 99        33 62 98                41 95


1. Calculate the overall sampling fraction, f, in the following manner:

           f = n = 20 = 1 =         0.2
               N 100    5
           where n = sample size and N = population size

                                                                                         19
        Selection of a proportionate stratified sample III

 Determine the number of sample elements (n1) to be selected from the English
  language stratum. In this example, n1 = 50 x f = 50 x 0.2 =10. By using a simple
  random sampling method [using a random number table] members whose numbers
  are 01, 03, 16, 30, 43, 48, 50, 54, 55, 75, are selected.

 Next, determine the number of sample elements (n2) from the Mandarin language
  stratum. In this example, n2 = 30 x f = 30 X 0.2 = 6. By using a simple random
  sampling method as before, members having numbers 10,15, 27, 51, 59, 87 are
  selected from the Mandarin language stratum.

 In the same manner, the number of sample elements (n3) from the „Other language‟
  stratum is calculated. In this example, n3 = 20 x f = 20 X 0.2 = 4. For this stratum,
  members whose numbers are 17, 18, 28, 38 are selected‟

 These three different sets of numbers are now aggregated to obtain the ultimate
  stratified sample as shown below.
  S = (01, 03, 10, 15, 16, 17, 18, 27, 28, 30, 38, 43, 48, 50, 51, 54, 55, 59, 75, 87)
                                                                                          20
                      Cluster sampling

   Is a type of sampling in which clusters or groups of
    elements are sampled at the same time.
   Such a procedure is economic, and it retains the
    characteristics of probability sampling.
   A two-step-process:
     » Step 1- Defined population is divided into number of mutually
        exclusive and collectively exhaustive subgroups or clusters;
     » Step 2- Select an independent simple random sample of clusters.
   One special type of cluster sampling is called area sampling, where
    pieces of geographical areas are selected.



                                                                          21
         Example : One-stage and two-stage Cluster sampling
Consider the same Island Video Club example involving 100 club members:

 Step 1: Sub-divide the club members into 5 clusters, each cluster containing 20 members.
            Cluster
             No.           English         Mandarin     Others
               1      00, 22, 40, 64, 82   06, 35, 66   02, 42
                      01, 24, 43, 67, 85   07, 44, 68   12, 46
              2       03, 26, 45, 69, 86   10, 47, 72   17, 52
                      04, 29, 48, 70, 89   13, 51, 77   18, 60
              3       05, 30, 49, 71, 91   15, 53, 78   21, 65
                      08, 31, 50, 73, 93   19, 56, 80   23, 74
              4       09, 32, 54, 75, 94   20, 58, 83   28, 84
                      11, 34, 55, 76, 96   25, 59, 87   38, 88
              5       14, 36, 57, 79, 97   27, 61, 92   39, 90
                      16, 37, 63, 81, 99   33, 62, 98   41, 95


 Step 2: Select one of the 5 clusters. If cluster 4 is selected, then all its elements (i.e. Club
  Members with numbers 09, 11, 32, 34, 54, 55, 75, 76, 94, 96, 20, 25, 58, 59, 83, 87, 28, 38, 84,
  88) are selected.

 Step 3: If a two-stage cluster sampling is desired, the researcher may randomly select 4 members
  from each of the five clusters. In this case, the sample will be different from that shown in step 2
  above.                                                                                                 22
               Stratified Sampling vs Cluster Sampling

             Stratified Sampling                      Cluster Sampling
1. The target population is sub-divided    1. The target population is sub-
   into a few subgroups or strata, each       divided into a large number of
   containing a large number of elements.     sub-population or clusters, each
                                              containing a few elements.
2. Within each stratum, the elements are 2. Within each cluster, the elements
   homogeneous. However, high degree of       are heterogeneous. Between
   heterogeneity exists between strata.       clusters, there is a high degree of
                                              homogeneity.
3. A sample element is selected each time. 3. A cluster is selected each time.
4. Less sampling error.                    4. More prone to sampling error.
5. Objective is to increase precision.     5. Objective is to increase sampling
                                                efficiency by decreasing cost.


                                                                                23
                                     AREA SAMPLING
 A common form of cluster sampling where clusters consist of geographic areas, such as
  districts, housing blocks or townships. Area sampling could be one-stage, two-stage, or
  multi-stage.
How to Take an Area Sample Using Subdivisions
     Your company wants to conduct a survey on the expected patronage of its new outlet in a new
housing estate. The company wants to use area sampling to select the sample households to be
interviewed. The sample may be drawn in the manner outlined below.
___________________________________________________________________________________
Step 1: Determine the geographic area to be surveyed, and identify its subdivisions. Each
     subdivision cluster should be highly similar to all others. For example, choose ten housing
     blocks within 2 kilometers of the proposed site [say, Model Town ] for your new retail outlet;
     assign each a number.
Step 2: Decide on the use of one-step or two-step cluster sampling. Assume that you decide to
      use a two-stage cluster sampling.
Step 3: Using random numbers, select the housing blocks to be sampled. Here, you select 4
     blocks randomly, say numbers #102, #104, #106, and #108.
Step 4: Using some probability method of sample selection, select the households in each of the
     chosen housing block to be included in the sample. Identify a random starting point (say,
     apartment no. 103), instruct field workers to drop off the survey at every fifth house
     (systematic sampling).
                                                                                                      24
                         Non-probability samples

   Convenience sampling
    » Drawn at the convenience of the researcher. Common in exploratory research.
      Does not lead to any conclusion.
   Judgmental sampling
    » Sampling based on some judgment, gut-feelings or experience of the researcher.
      Common in commercial marketing research projects. If inference drawing is not
       necessary, these samples are quite useful.
   Quota sampling
    » An extension of judgmental sampling. It is something like a two-stage judgmental
      sampling. Quite difficult to draw.
   Snowball sampling
    » Used in studies involving respondents who are rare to find. To start with, the
      researcher compiles a short list of sample units from various sources. Each of
      these respondents are contacted to provide names of other probable respondents.
                                                                                         25
                                                        Quota Sampling
 To select a quota sample comprising 3000 persons in country X using three control
  characteristics: sex, age and level of education.
 Here, the three control characteristics are considered independently of one another.
  In order to calculate the desired number of sample elements possessing the various
  attributes of the specified control characteristics, the distribution pattern of the
  general population in country X in terms of each control characteristics is examined.
    Control
    Characteristics        Population                     Distribution                 Sample Elements       .

       Gender: ....        Male......................     50.7%      Male              3000 x 50.7% = 1521
       .................   Female ..................      49.3%      Female            3000 x 49.3% = 1479

       Age: .........      20-29 years ...........        13.4%      20-29 years       3000 x 13.4% = 402
       .................   30-39 years ...........        53.3%      30-39 years       3000 x 52.3% = 1569
       .................   40 years & over ....           33.3%      40 years & over   3000 x 34.3% = 1029

      Religion: ..       Christianity ...........    76.4% Christianity 3000 x 76.4% = 2292
       ................. Islam ..................... 14.8% Islam        3000 x 14.8% = 444
       ................. Hinduism ..............     6.6%  Hinduism     3000 x 6.6% = 198
       ................. Others ...................   2.2% Others       3000 x 2.2% = 66
    _________________________________________________________________________________
_
                                                                                                                 26
        Sampling vs non-sampling errors


Sampling Error [SE]   Non-sampling Error [NSE]

            Very small sample Size
                  Larger sample size

                        Still larger sample

                              Complete census




                                                 27
     Choosing probability vs. non-probability sampling

 Probability          Evaluation Criteria        Non-probability
  sampling                                          sampling
  Conclusive           Nature of research            Exploratory

Larger sampling       Relative magnitude         Larger non-sampling
      errors             sampling vs.                   error
                      non-sampling error

     High             Population variability            Low
[Heterogeneous]                                     [Homogeneous]

   Favorable        Statistical Considerations       Unfavorable

     High             Sophistication Needed              Low

Relatively Longer           Time                   Relatively shorter

     High               Budget Needed                    Low

                                                                        28

				
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