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SSAAMMPPLLIINNGG
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A method by which someA method by which some
unitsunits/items of a given/items of a givenpopulationpopulation/occurrence are/occurrence areselected as representativesselected as representatives
of the entire population.of the entire population.
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Term used in SamplingTerm used in Sampling
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PopulationPopulation
Totalnumberof units/people/Totalnumberof units/people/occurrencesunderstudy.occurrencesunderstudy.
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ElementElement
Individualmember/unitofIndividualmember/unitofpopulationpopulation
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PopulationPopulationvsvs
Sample frameSample frameA known list of elements fromA known list of elements from
which the sample is actuallywhich the sample is actually
drawn.drawn.
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SampleSampleRepresentative partoftheRepresentative partofthe
whole/populationunderwhole/populationunder
study.study.
Subsetofthe populationthat
representsthe entire population. Theyhave similarcharacteristicsof
population.
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SubjectSubject
Individual member ofIndividual member ofsamplesample
Representativeness of SampleRepresentativeness of Sample
MeanMean PopulationPopulation u Sample xu Sample x
St. deviation PopulationSt. deviation Population Sample s Sample s
Variance PopulationVariance Population 22 Sample sSample s22
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a.a. Reducescosts,labourandtimeReducescosts,labourandtime
b.b. Quality Management/SupervisionQuality Management/Supervision
c.c. Accuracyand Reliabilityof ResultsAccuracyand Reliabilityof Results
d.d. Samplingmay be the only way (bulbs)Samplingmay be the only way (bulbs)
DemingDeming arguesthatthe qualityofstudyisoftenarguesthatthe qualityofstudyisoften
better withbetter withsamplingsampling than withthan withcensuscensus..
Furtherhe saysthatitisgoodtointerviewFurtherhe saysthatitisgoodtointerview
few inanicer wayfew inanicer way thanthantocover everybodytocover everybody inin
population.population.
Whysampling?
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1010
When Is CensusWhen Is Census
Appropriate?Appropriate? PopulationPopulation sizesize itselfitself isis quitequite smallsmall
InformationInformation isis neededneeded fromfrom everyeveryindividualindividual inin thethe populationpopulation
CostCost ofof makingmaking anan incorrectincorrect decisiondecision isis
highhigh SamplingSampling errorserrors areare highhigh
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1111
When Is SampleWhen Is Sample
Appropriate?Appropriate? SampleSample sizesize isis largelarge
BothBoth cost cost andand timetime associatedassociated withwith obtainingobtaininginformationinformation fromfrom thethe populationpopulation isis highhigh
QuickQuick decisiondecision isis neededneeded
InIn aa givengiven timetime period,period, moremore timetime cancan bebe spentspent ononeacheach interview,interview, therebythereby increasingincreasing responseresponse qualityquality
EasierEasier toto managemanage surveyssurveys ofof smallersmaller samplessamples andandalsoalso exerciseexercise qualityquality controlcontrol inin thethe interviewinterview processprocess
PopulationPopulation beingbeing dealtdealt withwith isis homogeneoushomogeneous
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Which of the following situations most obviouslyWhich of the following situations most obviouslycalls for the use of an appropriate samplingcalls for the use of an appropriate sampling
strategy?strategy?a. The principal wants to find out how frequently thea. The principal wants to find out how frequently the
parents of the children in the school agree with theparents of the children in the school agree with thedisciplinary strategies applied by the teachers.disciplinary strategies applied by the teachers.
There are 1000 children in the school.There are 1000 children in the school.
b. The principal wants to find out what percentage ofb. The principal wants to find out what percentage ofthe 1000 children in the school buy their lunch atthe 1000 children in the school buy their lunch atschool on a given day (rather than bringing theirschool on a given day (rather than bringing theirown lunch).own lunch).
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The SamplingDesignProcessThe SamplingDesignProcess
Define the Population
Determine the Sampling Frame
Select Sampling Technique(s)
D
etermine the Sample Size
Execute the Sampling Process
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Sampling MethodsSampling MethodsProbability:
In which each and every member of thepopulation gets equal/non zero chance to become
the part of the sample.
Used when we know our elements
OR
population frame
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Nonprobability:
In which everymember/unitfromthe populationdoesnotget equal
chance of beingselectedinthesample.
Used when we do not know our elementsUsed when we do not know our elements OROR
population framepopulation frame
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SamplingSampling
Probability
Simple Random stratifiedcluster
nonsystematic
systematic
Non Probability
quota
snowball
judgment
convenience
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ProbabilitysamplingmethodsProbabilitysamplingmethods
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Random Sampling MethodRandom Sampling Method
It is divided in to :
A. Systematic and
B. Non systematic
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2
0
Simple Random SamplingSimple Random Sampling
Also called
random sampling
Simplest method
of probabilitysampling
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 9811
57 96 2710
271
6 35 34 4701
36 08
3 99 14 23 50 21 01 03 25 79 07 80 54 55 41 12 15 15 03
68 56
4 70 72 01 00 33 25 19 16 23 58 03 78 47 43 77 88 15 02
55 67
5 18 46 06 49 47 32 58 08 75 29 63 66 89 09 22 35 97 74
30 80
6 65 76 34 11 33 60 95 03 53 72 06 78 28 14 51 78 76 4526 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
1056 8
192 73 4
0
07 2
0
05 26 63 57 86 48 5
159
15 46
09
75 64
Need to useNeed to use
Random
Number Table
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2
1
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 0912 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 sample
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Systematic Random Sampling:
In which an initial starting point is selectedby a random process and than every nth
number is selected.
Example:Example:
If we want to have a sample size of 50If we want to have a sample size of 50houses from the population of 500, thenhouses from the population of 500, then
we can have sample from every 10we can have sample from every 10thth
house.house.
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Stratified Sampling MethodStratified Sampling Method
A probability sampling technique thatuses two step process to partition into
subpopulation or strata .
Divide samplingframe intohomogeneousDivide samplingframe intohomogeneoussubgroups (strata) e.g. agesubgroups (strata) e.g. age--group,group,occupation etc.occupation etc.
Drawrandomsample in eachstrata.Drawrandomsample in eachstrata.Used for large population without distance e.g Study of
Students of Diff Departments of Karachi University.
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Steps Involved in Stratified Sampling
1. Divide the population into stratas or groups.
2. Identify the population in each strata.
3. Select the number of respondents eitherproportionately or disproportionately.
4. Select final respondents by applying simplerandom sampling method
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Total Population
M
ale 60
Female
40
10% = 6
10% = 4
100 students: 10%
Selecting Numbers of Respondents by
Proportionate ( Size )
Larger the size of the group the more we select,
the smaller the size of strata the less we select.
Strata-1
Strata-2
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Cluster Sampling
Same asstratified, butusedwhenthepopulationislarge anddispersed, e.gstudyof Faculty MembersinUniversitiesofPakistanorstudyofthe farmersofPakistanwhoarecultivatingwheat.
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Cluster Sampling
Faculty Members in Pak Universities
Punjab Sindh NWFP Balochistan
Male Female Male Female Male Female Male Female
enior Junior Qualified Non qualified
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Nonprobability Sampling.Nonprobability Sampling.
Each and every member from the population
does not get the equal chance of being
selected in the sample.
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ConvenienceConvenience
Here the samplesare drawnontheconvenience ofthe researcher.
Accordingtomost convenientlocation,time, etc. respondentsare selected.
Convenience samplingmaymisrepresentthe population.
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JudgmentJudgment
In judgmentsampling researcheruseshis/ herown educatedguessor
judgmentto identifywhowill be in
the sample.
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Snow ballSnow ball
It is commonly used when it is difficult toidentify members of the desired population.
Make contact with one or two respondents in
the population. Ask these respondents to
identify further new respondents and so on.
And this process of obtaining data by initial
respondent , and then from referral to referral iscalled as snow ball.
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QuotaQuota
The quota sample establishes a specific quotaor percentage for various types of individualsto be interviewed.
This can be included in prob and non probsampling.
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Quota sampling may be viewed as two-stage restricted
judgmental sampling.
The first stage consists of developing control categories, orquotas, of population elements (male and female).
In the second stage, sample elements are selected based on
convenience or judgment (if it is non prob sampling).
Population Composition
Sample
Control Characteristic Number Percentage 200Male 600 60 120
Female 400 40 80
____ ____ ____
1000 100 200
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Strength and weakness of sampling techniquesStrength and weakness of sampling techniques
Convenience
Judgmental
Quota
Snow Ball
strengthstrength weaknessweakness
Least expensive, least timeLeast expensive, least timeconsuming, most convenientconsuming, most convenient
Selection biasness, sample isSelection biasness, sample isnot representative of (P)not representative of (P)
L
ow cost, convenient , lessL
ow cost, convenient , lesstime consumingtime consumingD
oesnt allow generalization,D
oesnt allow generalization,subjective instead of objectivesubjective instead of objective
Sample can be controlledSample can be controlledfrom certain characteristics.from certain characteristics.
Selection bias, no assuranceSelection bias, no assuranceof representative.of representative.
Can estimate rareCan estimate rarecharacteristicscharacteristics
Time consumingTime consuming
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StrengthandweaknessofsamplingtechniquesStrengthandweaknessofsamplingtechniques
StrengthStrength WeaknessWeakness
Easily understood, results areEasily understood, results areprojectableprojectable
Difficult to constructDifficult to constructsampling frame, expensive,sampling frame, expensive,lower precision, no assurancelower precision, no assuranceof representativeof representative
Can increase representativeCan increase representativeness, easier to implement, thanness, easier to implement, thanSrs, Sampling frame notSrs, Sampling frame notnecessary.necessary.
Can decrease representativeCan decrease representative
Includes all importantIncludes all importantsubpopulation, precision.subpopulation, precision.
Difficult to select relevantDifficult to select relevantstratification variable,stratification variable,expensive,not feasible toexpensive,not feasible toverify many variables.verify many variables.
Cost effective ,Cost effective ,
easy implementeasy implement
Low statistical efficiencyLow statistical efficiency
Simple
Random
Systematic
Stratified
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PrincipalPrincipal WachelWachel wanted to find out the true feelings of the children in hiswanted to find out the true feelings of the children in hiselementary school regarding his school lunch program. Since this would best beelementary school regarding his school lunch program. Since this would best bedone through a personal interview, he decided to find a sample of 50 of the 281done through a personal interview, he decided to find a sample of 50 of the 281children and interview them himself. Listed below are several strategies forchildren and interview them himself. Listed below are several strategies for
drawing such a sample. Classify each as one of the following samplingdrawing such a sample. Classify each as one of the following samplingstrategies:strategies:
a. Random.a. Random.b. Systematic.b. Systematic.c. Quota.c. Quota.
d. Stratified.d. Stratified.e. Biased.e. Biased.
(1) _____ The children sat at tables with five children at each table. There were(1) _____ The children sat at tables with five children at each table. There weretwo lunch periods. He selected five tables from each of the two periods andtwo lunch periods. He selected five tables from each of the two periods andasked the children from those tables to talk to him one at a time during lunch.asked the children from those tables to talk to him one at a time during lunch.(The children simply brought their trays to the table where Mr.(The children simply brought their trays to the table where Mr. WachelWachelinterviewed them, and then returned to a different table. Mr.interviewed them, and then returned to a different table. Mr. WachelWachel felt thatfelt thatthis would keep them from briefing one another on what the questions werethis would keep them from briefing one another on what the questions wereabout.) He chose the tables in such a way as to get the proper proportions ofabout.) He chose the tables in such a way as to get the proper proportions ofchildren from each grade level and of boys and girls.children from each grade level and of boys and girls.
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(2) _____ Mr. Wachel finds a chart that shows the location of each table andchair, but that does not list the children's names. He numbers each chair onthe chart and then uses a table of random numbers to select chairs. He doesthis in such a way as to include children from both periods. He then interviewsthe children who happen to be sitting in those chairs. To account for absent
children, he assigns their names to empty seats and gets their opinions whenthey come back to school. He completes all the interviews (except for theabsentees) in one day.
(3) _____ Mr. Wachel finds a list of the locker numbers for all the children inthe school. He starts with the first locker and takes every other locker until he
has 50. He then interviews the children to whom these lockers belong. Heinterviews them separately by calling them one at a time out of their morningclasses.
(4) _____ Mr. Wachel gets a list of all the children in the school arranged byclasses. He starts with one of the first grades and selects a number between 1
and 10 at random. He then takes every tenth name from the lists at random.(When he finishes one list, he merely continues to the next.) He individuallyinterviews all the children selected in this manner.
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Sample Size:Sample Size:
Factorstodetermine sample sizeFactorstodetermine sample size1. Cost2. Time
3. Importance of decision4. Reliability requirements5. Population size6. Nature of the problem
7. Diversity of population
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Sample size:Sample size:
It is believed that larger the sample size,It is believed that larger the sample size,greater the extent of the reliability ofgreater the extent of the reliability of
data.data.
The size of sample depends on:The size of sample depends on:
-- The characteristics of populationThe characteristics of population-- the type of info requiredthe type of info required
-- The cost involved etcThe cost involved etc
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Roscoe (1975)Roscoe (1975) proposes the following rule of thumb:proposes the following rule of thumb:
i.i. Sample size larger than 30 and less than 500 areSample size larger than 30 and less than 500 areappropriate for most of the research.appropriate for most of the research.
ii.ii. Having a sample size of 5000 is not necessarilyHaving a sample size of 5000 is not necessarilybetter than having a sample size of 500.better than having a sample size of 500.
iii.iii. In UK, national surveys of house wives buyingIn UK, national surveys of house wives buying
habits, a sample size of 2000 was used and samehabits, a sample size of 2000 was used and samedone in Europe.done in Europe.
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Example:Example:
In UK, more thanIn UK, more than 10 mln ballots10 mln ballots wereweremailed, of whichmailed, of which 3 million were returned3 million were returned..
Of these,Of these, 41% supported Theature41% supported Theature andand55% favored opponent55% favored opponent..
But in actual Theature won.But in actual Theature won.
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Sample Sizes Usedin Research StudiesSample Sizes Usedin Research Studiespe Stud inimum Size T pical Ran e
Pr blemidenti icati nresearche mar etp tential
500 1,000 2,500
Pr blem-s l in research e
pricin
200 300-500
Pr ducttests 200 300-500
Testmar etin studies 200 300-500
TV, radi , rprintad ertisin perc mmercial radtested
150 200-300
Test-mar etaudits 10 st res 10-20 st res
cus r ups 2 r ups -12 r ups
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Type Iandtype IIErrorType Iandtype IIErrorIfwe have the sample size toosmall,theIfwe have the sample size toosmall,the
sampling errormight be solargesampling errormight be solarge(hypotheseswhichisactuallytrue will be(hypotheseswhichisactuallytrue will berejected)Itiscalledtype II error.rejected)Itiscalledtype II error.
The other errorthe researchermakesistoThe other errorthe researchermakesistoacceptthe hypothesis,whenitisactuallyacceptthe hypothesis,whenitisactuallyfalse. Thisisknownastype II error.false. Thisisknownastype II error.
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