research methodology - isp-infinite possibilities · 2016. 8. 17. · lecture 12 sampling &...

LECTURE 12

SAMPLING & PROBABILITY

DISTRIBUTIONS

Mazhar Hussain

Dept of Computer Science

ISP,Multan

[email protected]

1

RESEARCH

METHODOLOGY

ROAD MAP

Introduction

Chosing your research problem

Chosing your research advisor

Literature Review

Plagiarism

Variables in Research

Construction of Hypothesis

Research Design

Writing Research Proposal

Writing your Thesis

Data Collection

Data Representation

Sampling and Distributions

Paper Writing

Ethics of Research

2

SAMPLING

How to find average student age in the

university?

Ask each student and compute the average

Randomly select 3 to 4 students from each discipline

and find their average age – Estimation of the

average age of student in the university

3

SAMPLING

Why sampling?

Efforts and resources required to carry out the study

on the population

Examples

Average income of families living in a city

Results of an election

Opinion about the a problem

4

SAMPLING

5

Sampling is the process of selcetion a few (a

sample) from a bigger group (the sampling

population) to become the basis for estimating

or predicting the prevalence of an unknown

piece of information, situation or outcome

regarding the bigger group

RECAP – MEAN & STANDARD DEVIATION

6

Mean/Average

Standard Deviation

On the average, how far the data values are from the

mean

POPULATION VS SAMPLE

7

8

Karl Friedrich Gauss 1777-1855

Gaussian

Distribution

GAUSSIAN/NORMAL PROBABILITY

DISTRIBUTION

9

Most of the naturally occurring processes can be

modeled by a bell shaped curve


DISTRIBUTION

The Gaussian probability distribution is perhaps

the most used distribution in all of science.

Sometimes it is called the ―bell shaped curve‖ or

normal distribution.

10

2

2

( )

21

( )2

x

p x e

= mean of distribution

= standard deviation of distributionx is a continuous variable (-∞x ∞

2( , )N


DISTRIBUTION

11

The area within +/- σ is ≈ 68%

The area within +/- 2σ is ≈ 95%

The area within +/- 2σ is ≈ 99.7%


DISTRIBUTION

Probability (P) of x being in the range [a, b] is

given by an integral:

12

2

2

( )

21

( ) ( )2

xb b

a a

P a x b p x dx e dx

95% of area within 2 Only 5% of area outside 2

Gaussian pdf with =0 and =1


DISTRIBUTION

13

Standard Normal Distribution

http://en.wikipedia.org/wiki/Image:Normal_Distribution_PDF.svg

STANDARD NORMAL DISTRIBUTION

Normal distribution with mean of zero and

standard deviation of one

Since mean and standard deviation define any

normal distribution…

Standard normal distribution can be used for any

normally distributed variable by converting mean

to zero and standard deviation to one—z scores

14

Z SCORES

By itself, a raw score or X value provides very little

information about how that particular score

compares with other values in the distribution.

A score of X = 53, for example, may be a relatively

low score, or an average score, or an extremely

high score depending on the mean and standard

deviation for the distribution from which the score

was obtained.

If the raw score is transformed into a z-score,

however, the value of the z-score tells exactly

where the score is located relative to all the other

scores in the distribution. 15

Z SCORES

The process of changing an X value into a z-score

involves creating a signed number, called a z-

score, such that

The sign of the z-score (+ or –) identifies whether the

X value is located above the mean (positive) or below

the mean (negative).

The numerical value of the z-score corresponds to the

number of standard deviations between X and the

mean of the distribution.

Thus, a score that is located two standard deviations

above the mean will have a z-score of +2.00

16

Z SCORES

In addition to knowing the basic definition of a z-

score and the formula for a z-score, it is useful to

be able to visualize z-scores as locations in a

distribution.

Remember, z = 0 is in the center (at the mean),

and the extreme tails correspond to z-scores of

approximately –2.00 on the left and +2.00 on the

right.

Although more extreme z-score values are

possible, most of the distribution is contained

between z = –2.00 and z = +2.00.17

Z SCORES

z-score for a sample value in a data set is obtained by

subtracting the mean of the data set from the value

and dividing the result by the standard deviation of

the data set.

NOTE: When computing the value of the z-score,

the data values can be population values or sample

values. Hence we can compute either a population z-

score or a sample z-score.

18

Z SCORES

The Sample z-score for a value x is given by the

following formula:

Where is the sample mean and s is the sample

standard deviation.

19

x xz

s

x

Z SCORES

The Population z-score for a value x is given by

the following formula:

Where is the population mean and is the

population standard deviation.

20

xz

EXAMPLE

Example: What is the z-score for the value of 14

in the following sample values?

3 8 6 14 4 12 7 10

21

Thus, the data value of 14 is 1.57 standard deviations above the mean of 8, since the z-score is positive.

EXAMPLE

Dot Plot of the data points with the location of

the mean and the data value of 14.

22

Z SCORE & PROBABILITY

What is the probability of finding a value

between 100 and 110?

23

How to calculate

this area using z

scores?

Z SCORE CHART

24

0.9394

Reading area under curve for z=1.55


25

Probability of z>1.55 (Area in tail)

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

-3.0 -2.0 -1.0 0.0 1.0 2.0 3.0

1.55

P=.0606

0.9394

P=1-0.9394

P=0.0606


26

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

-3.0 -2.0 -1.0 0.0 1.0 2.0 3.0

-1.55 1.55

P=.0606+.0606

P=.1212

Probability of z>1.55 + z


27

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

-3.0 -2.0 -1.0 0.0 1.0 2.0 3.0

1.55

P=.5-.0606=.4394

Probability of z>0 and z

EXAMPLE: 50 MEASURES OF POLLUTION

28

V a l u e F r e q u e n c y

2 0 0

2 5 3

3 0 5

3 5 6

4 0 8

4 5 1 3

5 0 5

5 5 6

6 0 3

6 5 1

M o r e 0

Histogram

0

2

4

6

8

10

12

14

20 25 30 35 40 45 50 55 60 65

Mor

e

Value

Fre

que

ncy

68.40 88.9


Probability value > 45

29

•

4372.88.9

68.4045

z

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

-3 -2 -1 0 1 2 3

.4372P=.3300


Probability from 35 to 45

30

•5749.

88.9

68.4035

z

4372.88.9

68.4045

z

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

-3 -2 -1 0 1 2 3

-.5749 .4372

P=.5-.3300=.1700P=.5-.2843=.2157

P=.2157+.1700=.3857

31

Sampling

SAMPLING

Pros

Saves time

Resources – financial, human

Cons

Not exact value for the population

An estimate or prediction

Compromise on accuracy of findings

32

SAMPLING – TERMINOLOGY

Examples

Average student age in the university

Average income of families living in a city

Results of an election

Population or study population (N)

The university students, families living in the city,

electors

Sample

The small group of students, families or electors you

chose to collect the required information33


Sample size (n)

The number of entities in your sample

Sampling design or strategy

The way you select the students, families or electors

Sampling unit or sampling element

Each student, family or elector in your study

Sample statistics

Your findings based on infomration obtained from

your sample34


Population Parameters

Aim of research – find answers to research question

for study population not the sample

Use sample statistics to estimate answers to research

questions in study population

Estimates arrived at from sample statistics –

population parameters

Saturation Point

When no new information is coming from your

respondents

35


Sampling Frame

A list identifying each student, family or elector in

the study population

36

PRINCIPLES OF SAMPLING

Example – Four individuals A,B,C, D

A = 18 years

B = 20 years

C = 23 years

D = 25 years

Average age

(18+20+23+25) / 4 = 21.5 years

Use a sample of two indivudals to estimate the

average age of your study population (4

individuals)37


How many possible combinations of two

individuals?

38

A and B

A and C

A and D

B and C

B and D

C and D


A+B = 18+20 = 38/2 = 19.0 years

A+C = 18+23 = 41/2 = 20.5 years

A+D = 18+25 = 43/2 = 21.5 years

B+C = 20+23 = 43/2 = 21.5 years

B+D = 20+25 = 45/2 = 22.5 years

C+D = 23+25 = 48/2 = 24.0 years

In two cases – no difference between sample

statistics and population parameters

Difference – Sampling error39


Sample Sample

Statistics

Population

Parameters

Difference

1 19.0 21.5 -2.5

2 20.5 21.5 -1.5

3 21.5 21.5 0.0

4 21.5 21.5 0.0

5 22.5 21.5 +1.0

6 24 21.5 +2.5

40


Principle I

41

In majority of cases of sampling, there will

be a difference between sample statistics

and the true population parameters which

is attribuatable to the selection of the units

in the sample


Instead of samples of two – take a sample of

three

Four possible combinations

A+B+C = 18+20+23 = 61/3 = 20.33 years

A+B+D = 18+20+25 = 63/3 = 21.00 years

A+C+D = 18+23+25 = 66/3 = 22.00 years

B+C+D = 20+23+25 = 68/3 = 22.67 years

42


43

Sample Sample

Statistics

Population

Parameters

Difference

1 20.33 21.5 -1.17

2 21.00 21.5 -0.5

3 22.00 21.5 +0.5

4 22.67 21.5 +1.17


44

Sample Sample

Statistics

Population

Parameters

Difference

1 20.33 21.5 -1.17

2 21.00 21.5 -0.5

3 22.00 21.5 +0.5

4 22.67 21.5 +1.17

Sample Sample

Statistics

Population

Parameters

Difference

1 19.0 21.5 -2.5

2 20.5 21.5 -1.5

3 21.5 21.5 0.0

4 21.5 21.5 0.0

5 22.5 21.5 +1.0

6 24 21.5 +2.5

-2.5 to +2.5

-1.17 to +1.17


The gap between sample statistics and population parameters is reduced

Principle II

45

The greater the sample size, the more

accurate will be the estimate of the true

population statistics


Same Example – Different Data

A =18 years

B = 26 years

C = 32 years

D = 40 years

Variable (age) – markedly different

46


Estimate average using

Samples of two

Samples of three

Difference in the average age:

Sample size of 2: -7.00 to +7.00 years

Sample size of 3: -3.67 to +3.67 years

Range of difference is greater than previously

calculated

47


Principle III

48

The greater the difference in the variable

under study in a population for a given

sample size, the greater will be the

difference between the sample statistics

and the true population parameters

FACTORS AFFECTING THE INFERENCE

Principles suggest that two factors may influence

the degree of certainity about the inferences

drawn from a sample

Size of sample

Larger the sample size, the more accurate will be the

findings

The extent of variation in the sampling population

Greater the variation in the study population w.r.t. the

chracteristics under study, the greater will be the

uncertainity for a given sample size

49

AIMS IN SELECTING A SAMPLE

Achieve maximum precision in your estimate

Avoid bias in selection

Bias can occur if: Non-random sampling – consciously or unconsciously affected

by human choice

Sampling frame does not cover the sampling population

accurately or completely

A section of sampling population is impossible to find or

refuses to cooperate

50

SAMPLING METHODS

Probability Sampling

Used to generate random/non-biased samples

required for conducting inferential analyses

Non-probability Sampling

Used mostly in qualitative analysis

Mixed Sampling

51

SAMPLING METHODS



Mixed Sampling

52

PROBABILITY SAMPLING

Each element in the population has an equal and independent chance of selection in the sample

Equal:

Probability of selection of each element is the same

Choice is not affected by other considerations –human preferences

Independent:

Choice of one element is not dependent upon the choice of another element

Selection or rejection of one element does not affect the inclusion or exclusion of another 53


Example – Equal Chance

80 students in the class

20 refuse to participate in your study

Each of 80 students (population) does not have an

equal chance of selection

Sample is not representative of your class

54


Example – Independence

Three close friends in the class

One is selected – Two are not

Refuses to participate without friends

Forced to chose all three or none

Not independent sampling

55

Inferences drawn from random samples

can be generalized to the total sampling

population


Simple Random Sampling

Fishbowl draw

Computer program

Table of random numbers

Stratified Sampling

Proportional

Disproportional

Cluster Sampling

56

SIMPLE RANDOM SAMPLING

The Fishbowl Draw

Small population

Number each element on separate slips of paper for

each element

Put them in a box

Pick out one by one until you get desired sample size

Similar to lotteries

Computer Program

Write a program to select a random sample

57

SIMPLE RANDOM SAMPLING


58

Random

Number Table

59

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.

60

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

Your supervisor 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

61

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. #42 – 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 end of the row, then down to the next row row; move left to the end, then down to the next row, and so on.

TABLE OF RANDOM NUMBERS

Suppose you are using a table like this:

62

TABLE OF RANDOM NUMBERS

Sampling population – 256 individuals

Numbered from 1 to 256

You chose to select 10% - 25 individuals

Randomly select any starting point

Pick last three digits of the number

Select the valid ones (001-256) and skip the

invalid numbers (257-999)

63

DRAWING A RANDOM SAMPLE

Two ways of selecting a random sample

Sampling without replacement

Sampling with replacement

Example

20 students to be selected out of 80

First student is selected – Probability 1/80

For second student – 79 left, Probability 1/79

By the time you select the 20th – Probability 1/61

64

DRAWING A RANDOM SAMPLE

Sampling without replacement

Contrary to randomization – Each element should

have equal probability of selection

Sampling with replacement

Selected element is replaced in the population

If it is selected again – it is discarded

65



Fishbowl draw

Computer program


Stratified Sampling

Proportional

Disproportional

Cluster Sampling

66

STRATIFIED SAMPLING

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.

67

STRATIFIED SAMPLING

Example

Stratify on the basis of gender

Two groups – male and female

Select random samples from each group

68

STRATIFIED SAMPLING

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.

69

70

To select a 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 l ist 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 )

71

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

72

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)



Fishbowl draw

Computer program


Stratified Sampling

Proportional

Disproportional

Cluster Sampling

73

CLUSTER SAMPLING

Simple Random, Symmetric and Stratified

sampling – based on researcher’s ability to

identify each element in population

Small population size – easy

Large population – country

Cluster sampling

74

CLUSTER SAMPLING

Divide population into clusters

Select elements wihtin each cluster

Cluster formation

Geographical proximity

Common characteristic – similar to stratified

sampling

75

STRATIFIED VS CLUSTER SAMPLING

In startified sampling the target population is

sub-divided into a few subgroups or strata, each

containing a large number of elements.

In cluster sampling, the target population is sub-

divided into a large number of sub-population or

clusters, each containing a few elements.

76

77

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).

SAMPLING METHODS



Mixed Sampling

78

NON-PROBABILITY SAMPLING

Do not follow probability theory

Useful when the number of elements in

population is unknown or cannot be individually

identified

Four common designs

Quota Sampling

Accidental Sampling

Judgemental Sampling

Snowball Sampling

79

QUOTA SAMPLING

Main consideration – ease of access to sample

population

Guided by some visible chracteristic of study

population – age, gender etc.

Sample selection – location convenient to the

researcher

Whenever a person with required characteristic

is seen – asked to participate in the study

Process continues until the required number of

respondents (quota) is reached

80

QUOTA SAMPLING - EXAMPLE

Average age of male students in the university

Select a sample of 20 male students

You decide to stand at the entrance of the

university - convenient

Whenever a male student arrives – ask his age

When you get 20 – Target is achieved

81

QUOTA SAMPLING

Advantages

Convenient

Less expensive

Disadvantages

Not probability based

May not be generalized to the population

82

ACCIDENTAL SAMPLING

Also based on convenience

Quota sampling – include people with some

obvious characteristic

Accidental sampling – no such attempt

Common in market research and newspaper

reporters

Since you just pick up the people – may not get

the required information

83

JUDGEMENTAL SAMPLING

Judgement of the researcher as to who can

provide the best information to achieve the

objectives of the study

Sampling based on some judgment, gut-feelings

or experience of the researcher.

84

SNOWBALL SAMPLING

Sample selection using network

Start with few individuals or organizations and

collect the information

They are then asked to identify other

participants – people selected by them become a

part of sample

The process continues……

85

SAMPLING METHODS



Mixed Sampling

86

MIXED SAMPLING

Systematic sampling

Divide the frame into segments or intervals

Select one element from first interval using SRS

Select elements from subsequent intervals

depending upon the element selected from the

first interval

Example

5th element selected from first element

Select the 5th from each interval

87

SYSTEMATIC SAMPLING

88

To use systematic sampling, a researcher needs:

[i] A sampling frame of the population; .

[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.

89

Example: How to Take a Systematic Sample

Step 1: Select a listing of the population, say the City Telephone Directory, from which to

sample. 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 init ial 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).

CREDITS

Chapter 12, Research Methodology, Ranjit

Kumar

Sampling in Market Research - APMF

90

research methodology - isp-infinite possibilities · 2016. 8. 17. · lecture 12 sampling &...

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