7/30/2019 10 Sampling

1/6

11/14/20

Sampling TechniquesAdvanced Research Methods

Muhammad Zaki Rashidi

Overview

Sampling techniques

Determination of sample size

Probability sampling

Simple random sampling Stratified random sampling

Systematic sampling

Cluster sampling

Non-probability sampling Quota, judgment, convenience sampling

Snowball sampling

Errors in sampling

Table of sample size

2

Basics 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 marketingresearch.

Samples offer many benefits:

Save costs:Less expensive to study thesample than the population.

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

Accuracy:Since sampling is done withcare and studies are conducted byskilled and qualified interviewers, theresults are expected to be accurate.

Destructive nature of elements:Forsome elements, sampling is the way totest, since tests destroy the elementitself.

Basics of sampling II

Limitations ofSampling

Demands more rigidcontrol in undertakingsample operation.

Minority and smallnessin number of sub-groupsoften render study to besuspected.

Accuracy level may beaffected when data issubjected to weighing.

Sample results are goodapproximations at best.

Sampling Process

Defining the

population

Developing

a sampling

Frame

Determining

Sample

Size

Specifying

Sample

Method

SELECTING THE SAMPLE

Sampling: Step 1

Defining 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 ofall elements in thepopulation (such astelephone directories,electoral registers, club

membership etc.) fromwhich the samples are

drawn.

A sample frame which doesnot fully represent anintended population willresult inframe error andaffect the degree of reliability

of sample result.

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.

7/30/2019 10 Sampling

2/6

11/14/20

Choice of Sample Size - Large

PopulationsSample Sizes

% Margin of Error 95% Confidence 99% Confidence

1 9,604 16,590

2 2,401 4,148

3 1,068 1,844

4 601 1,037

5 385 664

6 267 461

7 196 339

8 151 260

9 119 250

10 97 166

Source :Parker & Rea, Designing and Conducting Research

Table 1

Choice of Sample Size - Small Populations

Sample Sizes

95% Level of Confidence 99% Level of Confidence

N 3% 5% 10% 3% 5% 10%

500 250 218 81 250 250 124

1000 500 278 88 500 399 143

1500 624 306 91 750 460 150

2,000 696 323 92 959 498 154

3,000 788 341 94 1,142 544 158

5,000 880 357 95 1,347 586 161

10,000 965 370 96 1,556 622 164

20,000 1,014 377 96 1,687 642 165

50,000 1,045 382 96 1,777 655 166

100,000 1,058 383 96 1,809 659 166

Source : Parker & Rea, Designing and Conducting Research

Table 2

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 1000-2500

Problem-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 200 300-500

Test market audits 10stores/outlets 10-20stores/outletsFocus groups 2 groups 4-12 groups

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 marketingresearch 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.

Probability 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

7/30/2019 10 Sampling

3/6

11/14/20

Non-probability sampling

Four types of non-probability samplingtechniques

Very simple types, based on subjective criteria Convenient sampling

Judgmental sampling

More systematic and formal

Quota sampling

Special type

Snowball Sampling

Simple 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 36 083 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 use

Random

Number Table

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.

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

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.

10 09 73 25 33 76

37 54 20 48 05 64

08 42 26 89 53 19

90 01 90 25 29 09

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.

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 sampleSystematic 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 [samplingframe], and select his sample.

7/30/2019 10 Sampling

4/6

11/14/20

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 100

th

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).

Stratified sampling I

A three-stage process:

Step 1- Divide the population intohomogeneous, mutually exclusiveand collectively exhaustive

subgroups or strata using somestratification variable;

Step 2- Select an independentsimple random sample from eachstratum.

Step 3- Form the final sample byconsolidating all sample elementschosen in step 2.

May yield smaller standard errors ofestimators than does the simplerandom sampling. Thus precision canbe gained with smaller sample sizes.

Stratified samples can be:

Proportionate: involvingthe selection of sampleelements from each

stratum, such that the ratioof sample elements fromeach stratum to the samplesize equals that of thepopulation elements withineach stratum to the totalnumber of populationelements.

Disproportionate: thesample is disproportionatewhen the above mentionedratio is unequal.

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 )

Selection of a proportionate Stratified Sample

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 =N 100 5

where n = sample size and N = population size

0.2

Selection of a proportionate stratified sample II

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 numbersare 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)

Selection of a proportionate stratified sample III

Cluster sampling

Is a type of sampling in which clusters or groups ofelements are sampled at the same time.

Such a procedure is economic, and it retains thecharacteristics of probability sampling.

A two-step-process:

Step 1- Defined population is divided into number ofmutually exclusive and collectively exhaustive subgroups orclusters;

Step 2- Select an independent simple random sample ofclusters.

One special type of cluster sampling is called area sampling, wherepieces of geographical areas are selected.

7/30/2019 10 Sampling

5/6

11/14/20

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

0 1, 24 , 4 3, 67 , 8 5 0 7, 44 , 6 8 1 2, 46

2 03, 26, 45, 69, 86 10, 47, 72 17, 52

0 4, 29 , 4 8, 70 , 8 9 1 3, 51 , 7 7 1 8, 60

3 05, 30, 49, 71, 91 15, 53, 78 21, 65

0 8, 31 , 5 0, 73 , 9 3 1 9, 56 , 8 0 2 3, 74

4 09, 32, 54, 75, 94 20, 58, 83 28, 84

1 1, 34 , 5 5, 76 , 9 6 2 5, 59 , 8 7 3 8, 88

5 14, 36, 57, 79, 97 27, 61, 92 39, 90

1 6, 37 , 6 3, 81 , 9 9 3 3, 62 , 9 8 4 1, 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.

Stratified Sampling vs Cluster Sampling

Stratified Sampling Cluster Sampling

1.The target population is sub-divided

into a few subgroups or strata, each

containing a large number of elements.

1.The target population is sub-

divided into a large number of

sub-population or clusters, eachcontaining a few elements.

2.Within each stratum, the elements are

homogeneous. However, high degree of

heterogeneity exists between strata.

2.Within each cluster, the elements

are heterogeneous. Between

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.Object ive i s 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 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).

Non-probability samples

Convenience sampling

Drawn at the convenience of the researcher. Common in exploratoryresearch. Does not lead to any conclusion.

Judgmental sampling

Sampling based on some judgment, gut-feelings or experience of theresearcher. 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-stagejudgmental 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 otherprobable 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 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

A ge : .. .. .. .. . 2 0-2 9 ye ar s .. .. .. ... .. 1 3. 4% 2 0-2 9 y ea rs 3 00 0 x 1 3. 4% = 4 0 2

. .. .. .. .. .. .. .. .. 3 0-3 9 ye ar s .. .. .. ... .. 5 3. 3% 3 0-3 9 y ea rs 3 00 0 x 52 .3 % = 15 69

. .. .. .. .. .. .. .. .. 4 0 y ea rs & o ve r .. .. 3 3. 3% 4 0 y ea rs & o ve r 3 00 0 x 3 4. 3% = 1 02 9

R el ig io n: .. C hri st ia ni ty .. .. .. ... .. 7 6. 4% C hr is ti an ity 3 00 0 x 7 6. 4% = 2 29 2

................. Is la m..................... 14.8% Islam 3000 x 14.8% = 4 44

................. Hinduism .............. 6.6% Hinduism 3000 x 6 .6% = 1 98

. .. .. .. .. .. .. .. .. O th ers . .. .. ... .. .. .. .. .. . 2 .2 % O th ers 3 00 0 x 2 .2 % = 6 6

__________________________________________________________________________________

Sampling vs non-sampling errors

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

Very small sampleSize

Larger sample size

Still larger sample

Complete census

7/30/2019 10 Sampling

6/6

11/14/20

Choosing probability vs. non-probability sampling

Probability Evaluation Criteria Non-probabilitysampling sampling

Conclusive Nature of research Exploratory

Larger sampling Relative magnitude Larger non-

samplingerrors sampling vs. error

non-sampling error

High Population variability Low

[Heterogeneous][Homogeneous]

Favorable Statistical Considerations Unfavorable

High Sophistication Needed Low

Relatively Longer Time Relativelyshorter

High Budget Needed Low

THANK YOU

32