sampling +ch+11

8/7/2019 Sampling +Ch+11

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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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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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