Sampling Methods Guide

SYED MD. SAJJAD KABIRSYED MD. SAJJAD KABIR UNIVERSITY OF CHITTAGONGUNIVERSITY OF CHITTAGONG
Reference Book:Reference Book:
(2016). Basic Gu(2016). Basic Gui
Research: An IntResearch: An Int
Approach for AllApproach for All
Book Zone PublicaBook Zone Publica
ISBN: 978-984-ISBN: 978-984-
Chittagong-4203Chittagong-4203,
Bangladesh.Bangladesh.
smskabir218@gmsmskabir218@gm
smskabir@psy.jnusmskabir@psy.jnu

Sample and Sampling DesignSample and Sampling Design
All Disciplines. Book Zone Publication, ISBN: 978-984-33-9565-8, Chittagong-4203, Bangladesh. smskabir218@gmail.com; smskabir@psy.jnu.ac.bdAll Disciplines. Book Zone Publication, ISBN: 978-984-33-9565-8, Chittagong-4203, Bangladesh. smskabir218@gmail.com; smskabir@psy.jnu.ac.bd
 Concept of SamplingConcept of Sampling
 Purpose of SamplingPurpose of Sampling
 Stages of Sampling ProcessStages of Sampling Process
 Types of Sampling –Types of Sampling –
• ProbabilityProbability
• Non-probability SamplingNon-probability Sampling
 Sampling Error and BiasSampling Error and Bias
 Determination of Sample Size.Determination of Sample Size.

Concept of SamplingConcept of Sampling
PopulationPopulation: Total of items about which: Total of items about which
information is desired. It can beinformation is desired. It can be
classified into two categories- finite andclassified into two categories- finite and
infinite.infinite.
SampleSample: It is part of the population: It is part of the population
that represents the characteristics ofthat represents the characteristics of
the population.the population.
SamplingSampling: It is the process of: It is the process of
obtaining information about an entireobtaining information about an entire
population by examining only a part ofpopulation by examining only a part of
Population
Population
SampleSample
3

Sampling UnitSampling Unit: Elementary units/group of such: Elementary units/group of such
units which besides being clearly defined,units which besides being clearly defined,
identifiable and observable, are convenientidentifiable and observable, are convenient
for purpose of sampling.for purpose of sampling.
Sampling FrameSampling Frame: A list containing all sampling: A list containing all sampling
units is known as sampling frame. Samplingunits is known as sampling frame. Sampling
frame consists of a list of items from whichframe consists of a list of items from which
the sample is to be drawn.the sample is to be drawn.
Sample SurveySample Survey: An investigation in which: An investigation in which
elaborate information is collected on a sampleelaborate information is collected on a sample
basis is known as sample survey.basis is known as sample survey.
4

StatisticStatistic: Characteristics of the sample. For: Characteristics of the sample. For
example, sample Mean, proportion, etc.example, sample Mean, proportion, etc.
ParameterParameter: Characteristics of the population.: Characteristics of the population.
For example, population Mean, proportion, etc.For example, population Mean, proportion, etc.
Sampling with and without replacementSampling with and without replacement::
Sampling schemes may beSampling schemes may be without replacementwithout replacement
('WOR' - no element can be selected more('WOR' - no element can be selected more
than once in the same sample) orthan once in the same sample) or withwith
replacementreplacement ('WR' - an element may appear('WR' - an element may appear
multiple times in the one sample).multiple times in the one sample).
5

Sample DesignSample Design: The plans and methods: The plans and methods
to be followed in selecting sample fromto be followed in selecting sample from
the target population and the estimationthe target population and the estimation
technique formula for computing thetechnique formula for computing the
sample statistics.sample statistics.
Sampled PopulationSampled Population: The population,: The population,
which we actually sample, is the sampledwhich we actually sample, is the sampled
population. It is also called surveypopulation. It is also called survey
population.population.
Target PopulationTarget Population: A target population: A target population
is the entire group about whichis the entire group about which
information is desired and conclusion isinformation is desired and conclusion is
SAMPLESAMPLE
STUDY POPULATION
STUDY POPULATION
TARGET POPULATION
TARGET POPULATION
6

SAMPLING BREAKDOWNSAMPLING BREAKDOWN
search: An Introductory Approach for All Disciplines. Book Zone Publication, ISBN: 978-984-33-9565-8, Chittagong-4203, Ba

Basic purpose of sampling is to provide anBasic purpose of sampling is to provide an
estimate of the population parameter and toestimate of the population parameter and to
test the hypothesis.test the hypothesis.
Advantages of sampling are -Advantages of sampling are -
• Save time and money.Save time and money.
• Enable collection of comprehensive data.Enable collection of comprehensive data.
• Enable more accurate measurement.Enable more accurate measurement.
• Sampling remains the only way when populationSampling remains the only way when population
contains infinitely many members.contains infinitely many members.
• In certain situation, sampling is the only way ofIn certain situation, sampling is the only way of
data collection [pathological status of blood, boilingdata collection [pathological status of blood, boiling
status of rice, etc.].status of rice, etc.].
Purpose of SamplingPurpose of Sampling
8

Stages of Sampling ProcessStages of Sampling Process
Sampling process comprises several stages-Sampling process comprises several stages-
1.1. Define the population.Define the population.
2. Specifying the sampling frame.2. Specifying the sampling frame.
3. Specifying the sampling unit.3. Specifying the sampling unit.
4. Selection of the sampling method.4. Selection of the sampling method.
5. Determination of sample size.5. Determination of sample size.
6. Specifying the sampling plan.6. Specifying the sampling plan.
7. Selecting the sample.7. Selecting the sample.
9

Types/ Procedures/ Approaches/Types/ Procedures/ Approaches/
Methods/ Techniques of SamplingMethods/ Techniques of Sampling
Two basic approaches to sampling: Probability Sampling andTwo basic approaches to sampling: Probability Sampling and
Non-probability Sampling.Non-probability Sampling.

PROBABILITY SAMPLINGPROBABILITY SAMPLING
 It is also known as random sampling or chanceIt is also known as random sampling or chance
sampling.sampling.
 Sample is taken in such a manner that each and everySample is taken in such a manner that each and every
unit of the population has an equal and positive chanceunit of the population has an equal and positive chance
of being selected.of being selected.
Major random sampling procedures are -Major random sampling procedures are -
 Simple Random Sample Simple Random Sample
 Systematic Random Sample Systematic Random Sample
 Stratified Random Sample, and Stratified Random Sample, and
 Cluster/ Multistage Sample.Cluster/ Multistage Sample.
10

Each member of the population isEach member of the population is
numbered. Then, a given size of thenumbered. Then, a given size of the
sample is drawn with the help of asample is drawn with the help of a
random number chart. The other way israndom number chart. The other way is
to do a lottery.to do a lottery.
Write all the numbers on small, uniformWrite all the numbers on small, uniform
pieces of paper, fold the papers, putpieces of paper, fold the papers, put
them in a container and take out thethem in a container and take out the
required lot in a random manner from therequired lot in a random manner from the
container as is done in the kitty parties.container as is done in the kitty parties.
 It is relatively simple to implement but theIt is relatively simple to implement but the
final sample may miss out small sub groups.final sample may miss out small sub groups.

ProbabilitySamplingProbabilitySampling
Simple Random SampleSimple Random Sample
11

It also requires numberingIt also requires numbering
the entire population.the entire population.
Then every nth numberThen every nth number
(say every 5th or 10th(say every 5th or 10th
number, as the case maynumber, as the case may
be) is selected tobe) is selected to
constitute the sample.constitute the sample.
It is easier and moreIt is easier and more
likely to representlikely to represent
different subgroups.different subgroups.
Systematic Random SampleSystematic Random Sample
12

At first, the population is firstAt first, the population is first
divided into groups or stratadivided into groups or strata
each of which is homogeneouseach of which is homogeneous
with respect to the givenwith respect to the given
characteristic feature.characteristic feature.
From each strata, then,From each strata, then,
samples are drawn at random.samples are drawn at random.
This way, it is possible thatThis way, it is possible that
different categories in thedifferent categories in the
population are fairlypopulation are fairly
represented in the sample.represented in the sample.
Stratified Random SampleStratified Random Sample
13

 In some cases, the selectionIn some cases, the selection
of units may pass throughof units may pass through
various stages, before finallyvarious stages, before finally
reach sample of study.reach sample of study.
 For this, a State, e.g., may beFor this, a State, e.g., may be
divided into districts, districtsdivided into districts, districts
into blocks, blocks into villages,into blocks, blocks into villages,
and villages into identifiableand villages into identifiable
groups of people, and thengroups of people, and then
taking the random or quotataking the random or quota
sample from each group.sample from each group.
 This design is used for large-scaleThis design is used for large-scale
surveys spread over large areas.surveys spread over large areas.
Cluster/ Multistage SampleCluster/ Multistage Sample
14

Non-Probability SamplingNon-Probability Sampling
 It is a non-random and subjective method ofIt is a non-random and subjective method of
sampling where the selection of the populationsampling where the selection of the population
elements comprising the sample depends on theelements comprising the sample depends on the
personal judgment.personal judgment.
 In this sampling method some elements of theIn this sampling method some elements of the
population have no chance of selection (these arepopulation have no chance of selection (these are
sometimes referred to as 'out ofsometimes referred to as 'out of
coverage'/'under covered').coverage'/'under covered').
 Because the selection of elements is nonrandom,Because the selection of elements is nonrandom,
non-probability sampling does not allow thenon-probability sampling does not allow the
estimation of sampling errors.estimation of sampling errors. 15

Non-Probability SamplingNon-Probability Sampling
Non-probability sampling includes –Non-probability sampling includes –
 Accidental/Convenience/Accidental/Convenience/
Opportunity/Availability/Opportunity/Availability/
Haphazard/ GrabHaphazard/ Grab
 Quota samplingQuota sampling
 Judgment/ Subjective/ PurposiveJudgment/ Subjective/ Purposive
 Snowball samplingSnowball sampling
16

Non-ProbabilitySamplingNon-ProbabilitySampling
Convenience/ Accidental SamplingConvenience/ Accidental Sampling
 Sample population selected because itSample population selected because it
is readily available and convenient.is readily available and convenient.
 Researcher using such sample cannotResearcher using such sample cannot
scientifically make generalizationsscientifically make generalizations
about the total population because itabout the total population because it
would not be representative enough.would not be representative enough.
It is most useful for pilot testing.It is most useful for pilot testing.
 Population is unknown, method forPopulation is unknown, method for
selecting cases is haphazard, and theselecting cases is haphazard, and the
cases studied probably don’tcases studied probably don’t
represent any population you couldrepresent any population you could
come up with.come up with.
17

Quota SamplingQuota Sampling
 Population is first segmented into mutuallyPopulation is first segmented into mutually
exclusive sub-groups, just as in stratifiedexclusive sub-groups, just as in stratified
sampling.sampling.
 Then judgment is used to select theThen judgment is used to select the
subjects or units from each segmentsubjects or units from each segment
based on a specified proportion.based on a specified proportion.
For example, an interviewer may be toldFor example, an interviewer may be told
to sample 200 females and 300 malesto sample 200 females and 300 males
between the age of 45 and 60.between the age of 45 and 60.
 In quota sampling the selection of theIn quota sampling the selection of the
sample is non-random.sample is non-random.
 Samples may be biased because notSamples may be biased because not
everyone gets a chance of selection.everyone gets a chance of selection.
 Quota versus probability has been aQuota versus probability has been a
matter of controversy for many years.matter of controversy for many years.
18

Subjective or Purposive or Judgment SamplingSubjective or Purposive or Judgment Sampling
 Sample is selected with definite purpose inSample is selected with definite purpose in
view and the choice of the sampling unitsview and the choice of the sampling units
depends entirely on the discretion anddepends entirely on the discretion and
judgment of the investigator.judgment of the investigator.
 It suffers from drawbacks of favoritismIt suffers from drawbacks of favoritism
and nepotism depending upon the beliefsand nepotism depending upon the beliefs
and prejudices of the investigator and thusand prejudices of the investigator and thus
does not give a representative sample ofdoes not give a representative sample of
the population.the population.
 It is seldom used and cannot beIt is seldom used and cannot be
recommended for general use.recommended for general use.
 If the investigator is experienced andIf the investigator is experienced and
skilled and this sampling is carefullyskilled and this sampling is carefully
applied, then judgment samples may yieldapplied, then judgment samples may yield
valuable results.valuable results.
SampleSampleSampleSample
PopulationPopulation19

Purposive sampling strategies that can be used in qualitativePurposive sampling strategies that can be used in qualitative
studies are given below. Each strategy serves a particularstudies are given below. Each strategy serves a particular
data gathering and analysis purpose.data gathering and analysis purpose.
• Extreme Case SamplingExtreme Case Sampling: It focuses on cases that are: It focuses on cases that are
rich in information because they are unusual orrich in information because they are unusual or
special in some way. e.g. the only community in aspecial in some way. e.g. the only community in a
region that prohibits felling of trees. region that prohibits felling of trees.
• Maximum Variation SamplingMaximum Variation Sampling: Aims at capturing the: Aims at capturing the
central themes that cut across participant variations.central themes that cut across participant variations.
e.g. persons of different age, gender, religion ande.g. persons of different age, gender, religion and
marital status in an area protesting against childmarital status in an area protesting against child
marriage.marriage.
• Homogeneous SamplingHomogeneous Sampling: Picks up a small sample with: Picks up a small sample with
similar characteristics to describe some particularsimilar characteristics to describe some particular
sub-group in depth. e.g. firewood cutters or snakesub-group in depth. e.g. firewood cutters or snake
charmers or bonded laborers.charmers or bonded laborers.
20

• Typical Case SamplingTypical Case Sampling: Uses one or: Uses one or
more typical cases (individuals,more typical cases (individuals,
families / households) to provide afamilies / households) to provide a
local profile. The typical cases arelocal profile. The typical cases are
carefully selected with the co-carefully selected with the co-
operation of the local people/operation of the local people/
extension workers.extension workers.

• Critical Case SamplingCritical Case Sampling: Looks for: Looks for
critical cases that can make a pointcritical cases that can make a point
quite dramatically. e.g. farmers whoquite dramatically. e.g. farmers who
have set up an unusually high yieldhave set up an unusually high yield
record of a crop. record of a crop.
21

• Chain SamplingChain Sampling: Begins by asking people,: Begins by asking people,
“who knows a lot about ________”. By“who knows a lot about ________”. By
asking a number of people, you can identifyasking a number of people, you can identify
specific kinds of cases e.g. critical,specific kinds of cases e.g. critical,
typical, extreme etc. typical, extreme etc.
• Criterion SamplingCriterion Sampling: Reviews and studies: Reviews and studies
cases that meet some pre-set criterion ofcases that meet some pre-set criterion of
importance e.g. farming households whereimportance e.g. farming households where
women take the decisions. women take the decisions.
Purposive sampling is best used with small numbersPurposive sampling is best used with small numbers
of individuals/groups which may well be sufficientof individuals/groups which may well be sufficient
for understanding human perceptions, problems,for understanding human perceptions, problems,
needs, behaviors and contexts, which are the mainneeds, behaviors and contexts, which are the main
justification for a qualitative audience research.justification for a qualitative audience research.22

Snowball SamplingSnowball Sampling
• In this method researcher identifies oneIn this method researcher identifies one
member of some population of interest, speaksmember of some population of interest, speaks
to him/her, and then asks that person toto him/her, and then asks that person to
identify others in the population that theidentify others in the population that the
researcher might speak to. This person isresearcher might speak to. This person is
then asked to refer the researcher to yetthen asked to refer the researcher to yet
another person, and so on.another person, and so on.

• This sampling technique is used against lowThis sampling technique is used against low
incidence or rare populations.incidence or rare populations.
• Small sample sizes and low costs are the clearSmall sample sizes and low costs are the clear
advantages of snowball sampling.advantages of snowball sampling.
• Sample may not represent a cross-section ofSample may not represent a cross-section of
the total population. It may also happen thatthe total population. It may also happen that
visitors to the site or interviewers may refusevisitors to the site or interviewers may refuse
to disclose the names of those whom theyto disclose the names of those whom they
know.know. 23

SomeOtherSamplingMethodsSomeOtherSamplingMethods
Matched Random SamplingMatched Random Sampling:: AssigningAssigning
participants to groups in which pairs ofparticipants to groups in which pairs of
participants are first matched on someparticipants are first matched on some
characteristic and then individually assignedcharacteristic and then individually assigned
randomly to groups.randomly to groups.
Procedure for Matched random sampling can be -Procedure for Matched random sampling can be -
(a)(a)Two samples in which the members areTwo samples in which the members are
clearly paired, or are matched explicitly byclearly paired, or are matched explicitly by
the researcher. For example, IQthe researcher. For example, IQ
measurements or pairs of identical twins.measurements or pairs of identical twins.
(b)(b)Those samples in which the same attribute,Those samples in which the same attribute,
or variable, is measured twice on eachor variable, is measured twice on each
subject, under different circumstances.subject, under different circumstances.
Commonly called repeated measures. Commonly called repeated measures.
24

Mechanical Sampling:Mechanical Sampling: It is typicallyIt is typically
used in sampling solids, liquids andused in sampling solids, liquids and
gases, using devices such as grabs,gases, using devices such as grabs,
scoops etc. Care is needed inscoops etc. Care is needed in
ensuring that the sample isensuring that the sample is
representative of the frame.representative of the frame.
Line-intercept Sampling:Line-intercept Sampling: It is aIt is a
method of sampling elements in amethod of sampling elements in a
region whereby an element isregion whereby an element is
sampled if a chosen line segment,sampled if a chosen line segment,
called a “transect”, intersects thecalled a “transect”, intersects the
element.element. 25

Panel Sampling:Panel Sampling: First selecting a groupFirst selecting a group
of participants through a randomof participants through a random
sampling and then asking that groupsampling and then asking that group
for the same information againfor the same information again
several times over a period of time.several times over a period of time.
Each participant is given the sameEach participant is given the same
survey or interview at two or moresurvey or interview at two or more
time points; each period of datatime points; each period of data
collection is called a “wave”.collection is called a “wave”.
This sampling methodology is oftenThis sampling methodology is often
chosen for large scale or nation-widechosen for large scale or nation-wide
studies.studies.
26

Rank SamplingRank Sampling:: A non-probability sample isA non-probability sample is
drawn and ranked. The highest value isdrawn and ranked. The highest value is
chosen as the first value of the targetedchosen as the first value of the targeted
sample. Another sample is drawn andsample. Another sample is drawn and
ranked, the second highest value is chosenranked, the second highest value is chosen
for the targeted sample. The process isfor the targeted sample. The process is
repeated until the lowest value of therepeated until the lowest value of the
targeted sample is chosen. This samplingtargeted sample is chosen. This sampling
method can be used in forestry to measuremethod can be used in forestry to measure
the average diameter of the trees.the average diameter of the trees.
Voluntary Sample:Voluntary Sample: It is made up of peopleIt is made up of people
who self-select into the survey. Thiswho self-select into the survey. This
sample is chosen by the viewers, not by thesample is chosen by the viewers, not by the
survey administrator.survey administrator.
27

Sampling Errors and Biases:Sampling Errors and Biases: Sampling errorsSampling errors
and biases are induced by the sample design. They include-and biases are induced by the sample design. They include-
Selection BiasSelection Bias: When the true: When the true
selection probabilities differ fromselection probabilities differ from
those assumed in calculating thethose assumed in calculating the
results.results.
Random Sampling ErrorRandom Sampling Error: Random: Random
variation in the results due to thevariation in the results due to the
elements in the sample being selectedelements in the sample being selected
at random.at random.
Sampling Error and Survey BiasSampling Error and Survey Bias
28

Non-sampling Error:Non-sampling Error: Impact the final surveyImpact the final survey
estimates, caused by problems in data collection,estimates, caused by problems in data collection,
processing, or sample design. They include-processing, or sample design. They include-
●●Over-coverageOver-coverage ●●Under-coverageUnder-coverage
●●Measurement errorMeasurement error ●●Processing errorProcessing error
●●Non-responseNon-response:: Two major types of non-Two major types of non-
response:response: unit non-responseunit non-response andand item non-item non-
responseresponse. Reasons for this problem include. Reasons for this problem include
improperly designed surveys, over-surveying (orimproperly designed surveys, over-surveying (or
survey fatigue), and participants hold multiple e-survey fatigue), and participants hold multiple e-
mail addresses, which they don’t use anymore ormail addresses, which they don’t use anymore or
don’t check regularly.don’t check regularly.
29

Bias Due to Measurement Error:Bias Due to Measurement Error: The bias thatThe bias that
results from problems in the measurement process.results from problems in the measurement process.
Leading Questions:Leading Questions: The wording of the questionThe wording of the question
may be loaded in some way to unduly favor onemay be loaded in some way to unduly favor one
response over another.response over another.
Social Desirability:Social Desirability: Responses may be biasedResponses may be biased
toward what people believe is socially desirable.toward what people believe is socially desirable.
 Increasing the sample size tends to reduce theIncreasing the sample size tends to reduce the
sampling error.sampling error.
 Large sample size cannot correct for theLarge sample size cannot correct for the
methodological problems (under-coverage, non-methodological problems (under-coverage, non-
response bias, etc.) that produce survey bias.response bias, etc.) that produce survey bias.
30

Generally the larger the sample size,Generally the larger the sample size,
the better is the estimation.the better is the estimation.
Always larger sample sizes cannot beAlways larger sample sizes cannot be
used in view of time and budgetused in view of time and budget
constraints.constraints.
When a probability sample reaches aWhen a probability sample reaches a
certain size, the precision of ancertain size, the precision of an
estimator cannot be significantlyestimator cannot be significantly
increased by increasing the sample sizeincreased by increasing the sample size
any further.any further.
Determination of Sample SizeDetermination of Sample Size
31

DeterminationofSampleSizeDeterminationofSampleSize
Sample Size for Estimating a MeanSample Size for Estimating a Mean
For Infinite/ Unknown Population SizeFor Infinite/ Unknown Population Size
The confidence interval for the universeThe confidence interval for the universe
mean, μ, is given by-mean, μ, is given by-
X ± Z . σ/√nX ± Z . σ/√n
Where, X = Sample mean; σ = Population standard deviation; Z = The value of theWhere, X = Sample mean; σ = Population standard deviation; Z = The value of the
standard normal variate at a given confidence level; n = Size of samplestandard normal variate at a given confidence level; n = Size of sample
The margin of error isThe margin of error is
e = Z .e = Z . σσ/√n; or, n e/√n; or, n e22
= Z= Z22
σσ22
ZZ22
σσ22
n =n =
ee22
Where n is the first approximation of the sample size.Where n is the first approximation of the sample size.
32

Sample Size for Estimating a MeanSample Size for Estimating a Mean
For Finite PopulationFor Finite Population
In case of finite population the confidence interval forIn case of finite population the confidence interval for
μ is given by, X ± Z .σ/√n .√(N-n)/(N-1)μ is given by, X ± Z .σ/√n .√(N-n)/(N-1)
Where, √(N-n)/(N-1) is the finite population multiplier andWhere, √(N-n)/(N-1) is the finite population multiplier and
all other terms mean the same thing as stated above. Ifall other terms mean the same thing as stated above. If
the precision is taken as equal to ‘e’, then we have-the precision is taken as equal to ‘e’, then we have-
e = Z. σ/√n. √(N-n)/(N-1)e = Z. σ/√n. √(N-n)/(N-1)
or, eor, e22
= Z= Z22
.σ.σ22
/n .(N-n)/ (N-1)/n .(N-n)/ (N-1)
or, (N – 1) eor, (N – 1) e22
+ Z+ Z22
. σ. σ22
= (Z= (Z22
.σ.σ22
. N)/n. N)/n
ZZ22
. σ. σ22
. N. N
n =n =
(N – 1) e(N – 1) e22
+ Z+ Z22
. σ. σ22
Where, N = Size of population; n = Size of sample;Where, N = Size of population; n = Size of sample;
e = Acceptable error; σ = Standard deviation of population;e = Acceptable error; σ = Standard deviation of population;
Z = Standard normal variate at a given confidence level.Z = Standard normal variate at a given confidence level.
33

EXAMPLEEXAMPLE
Determine the size of the sample for
estimating the per capita income for the
universe with N=5000 on the basis of the
following information.
 The standard deviation of per capita income
on the basis of past records = 0.75.
 The estimate should be within 5% error of
the true income with 95% confidence level.
Will there be a change in the size of the
sample if we assume infinite population in the
given case? If so, explain by how much?
34

Determination of Sample Size -Determination of Sample Size - SOLUTIONSOLUTION
N=5000, σ = 0.75, e = .05, Z= 1.96N=5000, σ = 0.75, e = .05, Z= 1.96
The sample size can be worked out as under -The sample size can be worked out as under -
ZZ22
. σ. σ22
. N (1.96)2. (0.75)2. 5000. N (1.96)2. (0.75)2. 5000
n = =n = =
(N – 1) e(N – 1) e22
+ Z+ Z22
.. ΣΣ22
4999 (.05)2 + (1.96)2. (0.75)24999 (.05)2 + (1.96)2. (0.75)2
10804.510804.5
= = 737= = 737
14.658414.6584
But if we take population to be infinite, the sample sizeBut if we take population to be infinite, the sample size
will be worked out as under -will be worked out as under -
ZZ22
σσ2 (1.96)2 (1.96)22
. (0.75). (0.75)22
n = = =864n = = =864
ee22
(.05)(.05)22
Thus, in case of infinite population the sample size becomesThus, in case of infinite population the sample size becomes
larger.larger. 35

Sample Size when Estimating aSample Size when Estimating a
Percentage or ProportionPercentage or Proportion
In Case of Infinite PopulationIn Case of Infinite Population
The confidence interval for the universeThe confidence interval for the universe
proportion, p, is given by –proportion, p, is given by –
p ± Z .√pq/np ± Z .√pq/n
Where, p = Sample proportion; Z =The value of theWhere, p = Sample proportion; Z =The value of the
standard normal variate at a given confidence level; n =standard normal variate at a given confidence level; n =
Size of sample.Size of sample.
The acceptable error, ‘e’ can be explained asThe acceptable error, ‘e’ can be explained as
--e = Z. √pq/n or, ee = Z. √pq/n or, e22
= Z= Z22
. p. q/n. p. q/n
ZZ22
. p. q. p. q
n =n =
ee22
36

Sample Size when Estimating a Percentage/ProportionSample Size when Estimating a Percentage/Proportion
In Case of Finite PopulationIn Case of Finite Population
ZZ22
. p. q. N. p. q. N
n =n =
(N-1) e(N-1) e22
+ Z+ Z22
. p. q. p. q
Where,Where, nn == Sample sizeSample size;; zz = The= The value of the standardvalue of the standard
variatevariate at a given confidence level and to be worked outat a given confidence level and to be worked out
from table showing area under Normal Curve. It would befrom table showing area under Normal Curve. It would be
considered standard normal deviate atconsidered standard normal deviate at 95%95% confidence levelconfidence level
==1.961.96;; pp == Sample proportionSample proportion, which may either be based on, which may either be based on
personal judgment, experience or may be result of a pilotpersonal judgment, experience or may be result of a pilot
study. In absence of such estimation one method may be tostudy. In absence of such estimation one method may be to
take the value oftake the value of p=0.50p=0.50 in which casein which case ‘‘nn’’ will be thewill be the
maximum and the sample will yield at least the desiredmaximum and the sample will yield at least the desired
precision.precision. qq == 1-p1-p.. ee == Acceptable margin of errorAcceptable margin of error (the(the
precision), usually consideredprecision), usually considered 0.050.05.. NN == Size of populationSize of population..
37

Adjustment of Sample SizeAdjustment of Sample Size
After the sample size is calculated, if it is found thatAfter the sample size is calculated, if it is found that
it represents a sizeable fraction of the population, thenit represents a sizeable fraction of the population, then
the adjustment is made by introducing the finitethe adjustment is made by introducing the finite
population correction. The final sample of size ‘n’ is thenpopulation correction. The final sample of size ‘n’ is then
obtained as -obtained as -
nn
n' =n' =
nn
1 +1 +
NN
Where, N is the population size. In general, if a sampleWhere, N is the population size. In general, if a sample
represents 5 percent or more of the population, therepresents 5 percent or more of the population, the
adjustment is made by the finite population correction.adjustment is made by the finite population correction.
38

Thursday, February 1, 2018Thursday, February 1, 2018
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search: An Introductory Approach for All Disciplines. Book Zone Publication, ISBN: 978-984-33-9565-8, Chittagong-4203, Ba

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