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Sampling Techniques

Sampling: Step 1Defining the Universe

• Universe or population is the whole mass under study.

Sampling: Step 2Establishing the Sampling

Frame

• A sample frame is the list of all elements in the• 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 d i i f h i b

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 designation of the units to be covered (HDB in town area)?

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

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 - 3Determination 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)– Statistical formulae (more sophisticated methods)• Confidence interval approach.

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

TYPE OF STUDY MINIMUM TYPICALTYPE OF STUDY MINIMUMSIZE

TYPICALRANGE

Identifying a problem (e.g.marketsegmentation) 500 1000-2500Problem-solving (e.g., promotion) 200 300-500Product tests 200 300-500Advertising (TV, Radio, or print Media

i l d t t d) 150 200 300per 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:The confidence interval approach

• To determine sample sizes using statistical formulae, researchers use the confidence interval approach based on theresearchers 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 samplemay 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.

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.

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Sampling methods

Classification of Sampling Methods

Probability samples

Systematic Stratified

Non‐probability samples

Convenience Snowball

ClusterSimple random

Judgement Quota

Probability sampling

Four types of probability sampling

• Appropriate for homogeneous population– Simple random sampling

• Requires the use of a random number table.

– Systematic sampling

• Appropriate for heterogeneous population– Stratified sampling

• Use of random number table may be necessary

• Requires the sample frame only,

• No random number table is necessary

– Cluster sampling• Use of random number

table may be necessary

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Non-probability sampling

• Four types of non-probability sampling techniquestechniques – Very simple types, based on subjective criteria

• Convenient sampling• Judgmental sampling

– More systematic and formal• Quota samplingQuota sampling

– Special type• Snowball Sampling

Simple Random Sampling

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

random sampling• Simplest method

of probability sampling

1 37 75 10 49 98 66 03 86 34 80 98 44 22 22 45 83 53 86 23 512 50 91 56 41 52 82 98 11 57 96 27 10 27 16 35 34 47 01 36 083 99 14 23 50 21 01 03 25 79 07 80 54 55 41 12 15 15 03 68 564 70 72 01 00 33 25 19 16 23 58 03 78 47 43 77 88 15 02 55 675 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 26 457 83 76 95 25 70 60 13 32 52 11 87 38 49 01 82 84 99 02 64 008 58 90 07 84 20 98 57 93 36 65 10 71 83 93 42 46 34 61 44 019 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

d 11 34 99 06 21 22 38 22 32 85 26 37 00 62 27 74 46 02 61 59 8112 02 26 92 27 95 87 59 38 18 30 95 38 36 78 23 20 19 65 48 5013 43 04 25 36 00 45 73 80 02 61 31 10 06 72 39 02 00 47 06 9814 92 56 51 22 11 06 86 88 77 86 59 57 66 13 82 33 97 21 31 6115 67 42 43 26 20 60 84 18 68 48 85 00 00 48 35 48 57 63 38 84

Need 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

li f St t ith i l b 1 01 001 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 beeng y selected.5. Repeat the selection process until the required number of sample elements is selected.

How to Use a Table of Random Numbers to Select a Sample

Your marketing research lecturer wants to randomly select 20 students fromyour 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 99Singh, 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 76Starting point:

How to use random number table to select a random sample

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 into

g p 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.

the sample. #87 – Tan Teck WahStep 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 selectedearlier (e.g., 90, 06 in this example) simply skip over it and choose the next number.

Types of Probability Sampling Designs

– Simple Random Sampling

S li h l i d b• Sampling where you sample cases using random numbers• Each unit in the sampling frame gets a number, from 1 to N• Consult a random number table or use a random number

generator to select units for observation

– For example:

• If you have a population of 100, consult a random number table with two columns of units, i.e., from 00 to 99

• Keep sampling until you have a sample of the desired size

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Systematic sampling

• Very similar to simple random sampling with one exception.• In systematic sampling only one random number is needed throughout the

entire sampling processentire 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

i i i• 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.E l 250 000 i h h b k d i d l i f 2500Example: 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).

– Systematic Sampling

• Sampling where every “kth” case is selected

Types of Probability Sampling Designs

• Sampling where every kth case is selected• Given a sampling frame, decide on the sample size• This sets the sampling ratio and k, the sampling interval

For example:• If you have 10,000 in a population & want a sample of

1000…th ti i 1/10 d k 10• …the ratio is 1/10 and k=10

• Randomize the order of cases in the sampling frame• Use a random number table to select the first case• Sample every kth case thereafter

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Stratified sampling I

A three-stage process:• Step 1- Divide the population into

homogeneous, mutually exclusive

Stratified samples can be:• Proportionate: involving

the selection of sample g , yand 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

pelements 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 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.

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 )

Selection of a proportionate Stratified Sample

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)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 )

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 42

Selection of a proportionate stratified sample II

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

0.2

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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 numbers

Selection of a proportionate stratified sample III

are 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 n = 20 x f = 20 X 0 2 = 4 For this stratumstratum 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)

Cluster sampling

• Is a type of sampling in which clusters or groups of elements are sampled at the same timeelements 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 Others1 00, 22, 40, 64, 82 06, 35, 66 02, 42

01, 24, 43, 67, 85 07, 44, 68 12, 462 03, 26, 45, 69, 86 10, 47, 72 17, 52

04, 29, 48, 70, 89 13, 51, 77 18, 603 05, 30, 49, 71, 91 15, 53, 78 21, 65

08, 31, 50, 73, 93 19, 56, 80 23, 744 09, 32, 54, 75, 94 20, 58, 83 28, 84

11, 34, 55, 76, 96 25, 59, 87 38, 885 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. ClubMembers 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 membersfrom each of the five clusters. In this case, the sample will be different from that shown in step 2above.

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Stratified Sampling vs Cluster Sampling

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

i t f b t t h1. The target population is sub-

di id d i t l b finto a few subgroups or strata, eachcontaining a large number of elements.

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 time3. 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.

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 newYour 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 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).

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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.

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 variousattrib tes of the specified control characteristics the distrib tion pattern of theattributes 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 Errorh h l h h l f l f h

To understand the concepts of sampling error and nonsampling error.

Sampling And Non‐sampling Errors

The error that results when the same sample is not perfectly representative of the population.

Two types of sampling error:

μ +‐ εs εns+‐X = X = sample mean 

μ = true population mean

εs = sampling error

εns = non‐sampling error

Sampling Errorh h l h h l f l f h

To understand the concepts of sampling error and nonsampling error.

Sampling And Nonsampling Errors

The error that results when the same sample is not perfectly representative of the population.

• Administrative error: problems in the execution of the sample

• Random error: due to chance and cannot be avoided

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Sampling vs non-sampling errors

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

Very small sample Size

Larger sample size

Still larger sample

Complete census

Choosing probability vs. non-probability sampling

Probability Evaluation Criteria Non-probabilitysampling 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