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Prof. AradhyaProf. Aradhya 11

Collection of DataCollection of Data

CensusCensus SamplingSampling

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Essentials of SamplingEssentials of Sampling

R epresentative nessR epresentative ness

Adequacy AdequacyIndependenceIndependenceHomogeneityHomogeneity

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Pr inciples of samplingPr inciples of sampling

Principle of statistical regularityPrinciple of statistical regularity

Principle of Inertia of large numbersPrinciple of Inertia of large numbers

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METHODS OF SA MPLINGMETHODS OF SA MPLING

R ANDOM SAMPLING NONR ANDOM SAMPLINGR ANDOM SAMPLING NONR ANDOM SAMPLING

SIMPLE OR R ESRT ICT ED DELIBER AT ESIMPLE OR R ESRT ICT ED DELIBER AT EUNR ESTR ICT ED SAMPLING CONVENIENCEUNR ESTR ICT ED SAMPLING CONVENIENCESAMPLING QUOT ASAMPLING QUOT A

SELFSELFSELECT EDSELECT ED

SNOWSNOW--BALLINGBALLING

STR AT IFIED SYST EMAT IC CLUST ER MULT ISTR AT IFIED SYST EMAT IC CLUST ER MULT I--ST AGEST AGE

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SAMPLINGSAMPLING

R andom sampling also referred to asR andom sampling also referred to as probability sampling probability samplingIt does not mean haphazard or hit orIt does not mean haphazard or hit ormiss methodmiss methodEvery item has equal chance of beingEvery item has equal chance of beingincludedincluded

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Random SamplingRandom Sampling

MethodsMethods::

1) Lottery method1) Lottery method2) T ables of random numbers:2) T ables of random numbers:a) T ippet s random tablesa) T ippet s random tablesb) Fisher s and Yates tablesb) Fisher s and Yates tables

c) Kendall and Smithc) Kendall and Smithd) R and Corporationd) R and Corporation

3) Software packages3) Software packages

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Random SamplingRandom Sampling

A A-- Simple or Unrestricted samplingSimple or Unrestricted samplingEach and every item has equal andEach and every item has equal and

independent chance of being in theindependent chance of being in thesamplesampleNo personal biasNo personal biasNo discretion or preferenceNo discretion or preferenceR eplacement of sampling unit R eplacement of sampling unit

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Simple o r Un r est r icted samplingSimple o r Un r est r icted sampling

Each unit is returned to the population, beforeEach unit is returned to the population, beforedrawing the next sampledrawing the next sampleProbability of every item isProbability of every item is - - 1 / N 1 / N Otherwise, Population is reduced for successiveOtherwise, Population is reduced for successivestagesstages--

next item will have probability of 1 / Nnext item will have probability of 1 / N- -1 ,1 ,next will be 1/Nnext will be 1/N--2 ,2 ,

1 / N 1 / N--3 3

When the slip is returned to the drum before drawingWhen the slip is returned to the drum before drawingthe next slip, the size of population is samethe next slip, the size of population is same

1000- 0 =10001000-1 =999

1000-2 =9981000-3 =9971000-4 =9961000-5 =9951000-6 =994

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B) Rest r icted SamplingB) Rest r icted Sampling

1) Stratified random sampling1) Stratified random samplinga) Proportionate stratified samplinga) Proportionate stratified samplingb) Disproportionate stratifiedb) Disproportionate stratified

samplingsampling2) Systematic sampling2) Systematic sampling3) Multi3) Multi--stage samplingstage sampling4) Cluster sampling4) Cluster sampling

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St r atified r andom samplingSt r atified r andom sampling

N is divided into groups according to N is divided into groups according tohomogeneityhomogeneity

Adopted when there are heterogeneous Adopted when there are heterogeneousfeaturesfeatures

For example, to study the consumptionFor example, to study the consumption

pattern of Belgaum, the city is divided into apattern of Belgaum, the city is divided into anumber of groups / wardsnumber of groups / wardsSamples are taken from each wardSamples are taken from each ward

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Types of st r atified samplingTypes of st r atified sampling

Proportionate stratified randomProportionate stratified randomsampling:sampling:

sample is in proportion to the sizesample is in proportion to the sizeof subof sub--populationpopulationDisproportionate stratified randomDisproportionate stratified randomsampling:sampling:

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2 ) Systematic sampling ( Equal inte rv al2 ) Systematic sampling ( Equal inte rv alsampling o r Quasi r andom sampling o r k )sampling o r Quasi r andom sampling o r k )

Sample is formed by selecting oneSample is formed by selecting one

unit at random and then selectingunit at random and then selectingadditional units at evenly spacedadditional units at evenly spacedintervals.intervals.

Used when a complete list is availableUsed when a complete list is availableT he list is prepared in alphabetical orT he list is prepared in alphabetical ornumerical order and serially numberednumerical order and serially numbered

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Systematic samplingSystematic sampling- - continuedcontinued

T he first item is selected at randomT he first item is selected at randomT hen the remaining items are selected at k T hen the remaining items are selected at k

intervalintervalk is the sample interval, which is selected ask is the sample interval, which is selected asfollows:follows:k =k = Size of UniverseSize of Universe == NN

Size of Sample nSize of Sample n

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Systematic samplingSystematic sampling- -continuedcontinued

Also known as equal interval sampling Also known as equal interval samplingor quasi random sampling as theor quasi random sampling as thesubsequent units are presubsequent units are pre- -determineddeterminedMerits:Merits: 1) Simple and convenient to1) Simple and convenient toadopt adopt

2) More efficient than simple random2) More efficient than simple random3) T ime, cost and work3) T ime, cost and work- - become smallerbecome smaller

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Systematic samplingSystematic sampling- -continuedcontinued

Demerits :Demerits : 1) not truly a random method1) not truly a random methodas there are pre determined intervalsas there are pre determined intervals

2) Problem of representativeness as2) Problem of representativeness asthere may be a hidden periodicitiesthere may be a hidden periodicities( every k th worker may be a well paid)( every k th worker may be a well paid)

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MultiMulti--stage samplingstage sampling

Sampling is carried out at severalSampling is carried out at severalstagesstagesSample is taken from previous stageSample is taken from previous stagesamplesample

Sample of one stage becomesSample of one stage becomespopulation for next stagepopulation for next stage

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MultiMulti--stage samplingstage sampling

Merits :Merits :1) Flexibility1) Flexibility2) No bias2) No bias3) Cost and efforts are less as N 3) Cost and efforts are less as N

becomes smaller in successive stagesbecomes smaller in successive stagesDemerits:Demerits: 1)Less accurate1)Less accurate2) More work2) More work3) Not representative as stratified3) Not representative as stratified

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C luste r samplingC luste r sampling

Primarily selection of groups rather thanPrimarily selection of groups rather thanindividualsindividuals

Population is divided into groupsPopulation is divided into groupsGroups are mutually exclusive andGroups are mutually exclusive and

collectively exhaustive collectively exhaustive

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C luste r samplingC luste r sampling - - continuedcontinued

Merits :Merits :1) Easier and Practical1) Easier and Practical

Demerits :Demerits : 1) Difficulty in clustering1) Difficulty in clustering2) Unequal2) Unequal

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N on r andom samplingN on r andom sampling

1)1) Purposive or Judgment samplingPurposive or Judgment samplingalso known as Deliberate sampling It is aalso known as Deliberate sampling It is a

conscious selection by an investigator onconscious selection by an investigator onhis own judgment.his own judgment.It requires deep and thorough knowledge andIt requires deep and thorough knowledge and

experience. Interviewer requiresexperience. Interviewer requiresawareness of the characteristics of theawareness of the characteristics of the

population.population.Samples vary from investigator toSamples vary from investigator toinvestigatorinvestigator

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P u r posi v e o r Judgment samplingP u r posi v e o r Judgment sampling

Merits :Merits : 1) used in solving economic and1) used in solving economic andbusiness problemsbusiness problems

2) No missing characteristics2) No missing characteristics3) Properties of population are known3) Properties of population are known4) Appropriate for pilot surveys4) Appropriate for pilot surveys5) Motivation to the investigator5) Motivation to the investigator

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P u r posi v e o r Judgment samplingP u r posi v e o r Judgment sampling

Demerits :Demerits :1) not scientific1) not scientific2) Personal prejudice2) Personal prejudice3) Difficult to calculate sampling errors3) Difficult to calculate sampling errors4) Inclination or convenience , but not 4) Inclination or convenience , but not

judgment judgment 5) Comparison of work is difficult 5) Comparison of work is difficult

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C on v enience samplingC on v enience samplingalso known as chunkalso known as chunk

Chunk is a fraction of population whichChunk is a fraction of population whichis selected neither by probability noris selected neither by probability norby judgment, but by convenience.by judgment, but by convenience.

Samples are drawn from readilySamples are drawn from readilyavailable lists such as automobilesavailable lists such as automobilesregistration, telephone directory, etcregistration, telephone directory, etc

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C on v enience samplingC on v enience sampling

Convenience sample is not random,Convenience sample is not random,although samples are drawn at although samples are drawn at random from the lists.random from the lists.

Good for Pilot studiesGood for Pilot studies

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Quota samplingQuota sampling

It is a type of judgment samplingIt is a type of judgment samplingQuotas are set up on characteristicsQuotas are set up on characteristicssuch as income group, age, politicalsuch as income group, age, politicalaffiliation, religious affiliation ,etcaffiliation, religious affiliation ,etcT he interviewer is asked to interview aT he interviewer is asked to interview a

certain number of persons in thecertain number of persons in thequota. He is free to chose any personquota. He is free to chose any personin the given quota.in the given quota.

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Quota samplingQuota sampling- - continuedcontinued

For example:For example:In a T V survey, the interviewer is told to interviewIn a T V survey, the interviewer is told to interview

any 500 persons and out of every 100 followingany 500 persons and out of every 100 followingshould be the composition:should be the composition:

2020 -- StudentsStudents1010 HousewivesHousewives2525 Office goersOffice goers

1515 ChildrenChildren2020 -- FarmersFarmers1010 -- BusinessmenBusinessmen

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Snowball sampleSnowball sample

R esearcher asks the respondent forR esearcher asks the respondent fornames of other individuals who arenames of other individuals who arealso to be surveyedalso to be surveyedT he difficulty isT he difficulty is close friends orclose friends orcolleagues tend to behave in the samecolleagues tend to behave in the same

wayway

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STE P S IN SAMPLING P ROC ESSSTE P S IN SAMPLING P ROC ESS

DEFINE POPULAT ION

SPECIFY SAMPLING FR AME

SPECIFY SAMPLING MET HOD

DET ER MINE SAMPLE SIZE

SPECIFY SAMPLE PLAN

SELECT SAMPLE & COLLECT INFOR MAT ION

ANALYZE DAT A & R EPORT R ESULT S

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Size of sampleSize of sample

No hard and fast ruleNo hard and fast ruleDepends on subject, time, cost andDepends on subject, time, cost and

accuracyaccuracyConsiderationsConsiderations1)1) Size of populationSize of population2)2) Accuracy desired Accuracy desired3)3) Homogeneity / heterogeneityHomogeneity / heterogeneity

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Size of sampleSize of sample- -continuedcontinued

4) Nature of study4) Nature of study- - intensive,intensive,continuous, technical, generalcontinuous, technical, general

5) Practical considerations5) Practical considerations- - time,time,finance, personnelfinance, personnel

6) T ype of sampling6) T ype of sampling- - stratified, etcstratified, etc7) Size of questionnaire7) Size of questionnaire8) Question on questionnaire8) Question on questionnaire

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Size of sampleSize of sample- -continuedcontinued

SamplingSamplingErrorsErrors

Sample SizeSample Size

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Ma r keting conditions affecting samplingMa r keting conditions affecting sampling

Some characteristics of marketing populationSome characteristics of marketing population: :a)a) Population is nether uniform norPopulation is nether uniform nor

concentratedconcentratedb)b) Characteristics of people are not simple asCharacteristics of people are not simple as

there are so many factorsthere are so many factorsc)c)

Data on desired characteristics are nonData on desired characteristics are non- -existent , or inaccurateexistent , or inaccurated)d) Identity of specific population is difficult Identity of specific population is difficult

3.1 sampling

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