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Sampling in Marketing ResearchSampling in Marketing Research

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Basics of sampling IBasics of sampling I

A sample is a “part of a whole to show what the rest is like”.

Sampling helps to determine the corresponding value of the population and plays a vital role in marketing research.

Samples offer many benefits: Save costs: Less expensive to study the

sample than the population. Save time: Less time needed to study the

sample than the population . Accuracy: Since sampling is done with

care and studies are conducted by skilled and qualified interviewers, the results are expected to be accurate.

Destructive nature of elements: For some elements, sampling is the way to test, since tests destroy the element itself.

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Basics of sampling IIBasics of sampling II

Limitations of Sampling Demands more rigid

control in undertaking sample operation.

Minority and smallness in number of sub-groups often render study to be suspected.

Accuracy level may be affected when data is subjected to weighing.

Sample results are good approximations at best.

Sampling Process

Defining the population

Developing a sampling

Frame

DeterminingSample

Size

SpecifyingSample Method

SELECTING THE SAMPLE

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Sampling: Step 1Defining the Universe

Universe or population is the whole mass under study.

How to define a universe:» What constitutes the units of

analysis (HDB apartments)?

» What are the sampling units (HDB apartments occupied in the last three months)?

» What is the specific designation of the units to be covered (HDB in town area)?

» What time period does the data refer to (December 31, 1995)

Sampling: Step 2Establishing the Sampling

Frame

A sample frame is the list of all elements in the population (such as telephone directories, electoral registers, club membership etc.) from which the samples are drawn.

A sample frame which does not fully represent an intended population will result in frame error and affect the degree of

reliability of sample result.

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Step - 3Step - 3Determination of Sample SizeDetermination 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.

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Conventional approach of Sample size determination using

Sample sizes used in different marketing research studies

TYPE OF STUDY MINIMUM

SIZE

TYPICAL

RANGE

Identifying a problem (e.g.marketsegmentation) 500 1000-2500Problem-solving (e.g., promotion) 200 300-500

Product tests 200 300-500

Advertising (TV, Radio, or print Mediaper commercial or ad tested) 150 200-300Test marketing 200 300-500Test market audits 10

stores/outlets10-20

stores/outletsFocus groups 2 groups 4-12 groups

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Sample size determination using statistical formulae: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.

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Step 4: Step 4: Specifying the sampling methodSpecifying 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.

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Probability samplingProbability sampling

Appropriate for homogeneous population» Simple random sampling

– Requires the use of a random number table.

» Systematic sampling– Requires the sample frame

only,

– No random number table is necessary

Appropriate for heterogeneous population» Stratified sampling

– Use of random number table may be necessary

» Cluster sampling– Use of random number

table may be necessary

Four types of probability sampling

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Non-probability samplingNon-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

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Simple Random SamplingSimple Random Sampling

Also called random sampling

Simplest method of probability sampling

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

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

3 99 14 23 50 21 01 03 25 79 07 80 54 55 41 12 15 15 03 68 56

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

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

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

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

Need to useNeed to useRandom Number Table

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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.

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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 mayidentify each element by assigning a two-digit number. Assign 01 to the first nameon the list, and 00 to the last name. If this is done, then the task of selecting thesample 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

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Step 2: Select any starting point in the Random Number Table and find the first number thatcorresponds to a number on the list of your population. In the example below, # 08 has beenchosen as the starting point and the first student chosen is Carol Chan.

10 09 73 25 33 7637 54 20 48 05 6408 42 26 89 53 1990 01 90 25 29 0912 80 79 99 70 8066 06 57 47 17 3431 06 01 08 05 45

Step 3: Move to the next number, 42 and select the person corresponding to that number intothe 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 #19Step 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.

Starting point: move right to the endof the row, then downto the next row row;move left to the end,then down to the nextrow, and so on.

How to use random number table to select a random sample

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Systematic samplingSystematic 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 entiredirectory [sampling frame], and select his sample.

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Example: How to Take a Systematic Sample

Step 1: Select a listing of the population, say the City Telephone Directory, from which tosample. 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 thedesired 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 nameyou 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).

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Stratified sampling IStratified sampling I

A three-stage process:

Step 1- Divide the population into homogeneous, mutually exclusive and collectively exhaustive subgroups or strata using some stratification variable;

Step 2- Select an independent simple random sample from each stratum.

Step 3- Form the final sample by consolidating all sample elements chosen in step 2.

May yield smaller standard errors of estimators than does the simple random sampling. Thus precision can be gained with smaller sample sizes.

Stratified samples can be:

Proportionate: involving the selection of sample elements from each stratum, such that the ratio of sample elements from each stratum to the sample size equals that of the population elements within each stratum to the total number of population elements.

Disproportionate: the sample is disproportionate when the above mentioned ratio is unequal.

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To select a proportionate stratified sample of 20 members of the Island Video Club which has100 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 groups00 (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 )

Selection of a proportionate Stratified Sample

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Step 2: Sub-divide the club members into three homogeneous sub-groups or strata by thelanguage groups: English, Mandarin and others.

EnglishLanguage Mandarin Language Other Language Stratum Stratum Stratum .00 22 40 64 82 06 35 66 02 4201 24 43 67 85 07 44 68 12 4603 26 45 69 86 10 47 72 17 5204 29 48 70 89 13 51 77 18 6005 30 49 71 91 15 53 78 21 6508 31 50 73 93 19 56 80 23 7409 32 54 75 94 20 58 83 28 8411 34 55 76 96 25 59 87 38 8814 36 57 79 97 27 61 92 39 9016 37 63 81 99 33 62 98 41 95

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

f = n = 20 = 1 = N 100 5

where n = sample size and N = population size

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Selection of a proportionate stratified sample II

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

Next, determine the number of sample elements (n2) from the Mandarin languagestratum. In this example, n2 = 30 x f = 30 X 0.2 = 6. By using a simple randomsampling method as before, members having numbers 10,15, 27, 51, 59, 87 areselected 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 ultimatestratified 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)

Selection of a proportionate stratified sample III

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Cluster samplingCluster 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.

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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.

ClusterNo. 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.

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Stratified Sampling vs Cluster Sampling

Stratified Sampling Cluster Sampling1. The target population is sub-divided

into a few subgroups or strata, eachcontaining a large number of elements.

1. The target population is sub-divided into a large number ofsub-population or clusters, eachcontaining a few elements.

2. Within each stratum, the elements arehomogeneous. However, high degree ofheterogeneity exists between strata.

2. Within each cluster, the elementsare heterogeneous. Betweenclusters, there is a high degree ofhomogeneity.

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.

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AREA SAMPLING

A common form of cluster sampling where clusters consist of geographic areas, such asdistricts, housing blocks or townships. Area sampling could be one-stage, two-stage, ormulti-stage.

How to Take an Area Sample Using SubdivisionsYour 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 beinterviewed. 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 housingblocks 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 thechosen 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).

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Non-probability samplesNon-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.

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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 thegeneral population in country X in terms of each control characteristics is examined.

ControlCharacteristics 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

__________________________________________________________________________________

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Sampling vs non-sampling errorsSampling vs non-sampling errors

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

Very small samVery small sampleple SizeSize

Larger sLarger sample sizeample size

SStill larger sampletill larger sample

Complete censusComplete census

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Choosing probability vs. non-probability samplingChoosing 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