Sample &Sampling Sample &Sampling DesignDesign

DR.G.SINGARAVELUDR.G.SINGARAVELUAssociate ProfessorAssociate Professor

UGC-ASCUGC-ASCBHARATHIAR UNIVERSITY BHARATHIAR UNIVERSITY

COIMBATORECOIMBATORE

DEFINITIONSDEFINITIONS

Population-totality of the objects or Population-totality of the objects or individuals regarding inferences are individuals regarding inferences are

made in a sampling study.made in a sampling study.

Sample-smaller representation of a Sample-smaller representation of a large whole.large whole.

Sampling- is a process of selecting a Sampling- is a process of selecting a subset of randomised number of the subset of randomised number of the members of the population of a studymembers of the population of a study

Sampling frame /Source list -complete list of all the Sampling frame /Source list -complete list of all the members/ units of the population from which each members/ units of the population from which each sampling unit sampling unit

Sample design / sample plan-is a definite plan for obtaining Sample design / sample plan-is a definite plan for obtaining a sample from a given population.a sample from a given population.

Sampling unit-is a geographical one (state,district)Sampling unit-is a geographical one (state,district)

Sample size-number of items selected for the studySample size-number of items selected for the study

Sampling Error-is the difference between population value Sampling Error-is the difference between population value and sample value.and sample value.

Sampling distribution-is the relative frequency distribution of Sampling distribution-is the relative frequency distribution of samples.samples.

CENSUS/SAMPLINGCENSUS/SAMPLINGCensus-collection of data from Census-collection of data from

whole population.whole population.

Sampling is taking any portion of a Sampling is taking any portion of a population or universe as population or universe as

representative of that representative of that population.population.

Sampling method has been using Sampling method has been using in social science research since in social science research since

1754 by A.L.BOWLEY1754 by A.L.BOWLEY

Indispensable of sampling in Indispensable of sampling in ResearchResearch

Saves lot of timeSaves lot of timeProvides accuracyProvides accuracyControls unlimited dataControls unlimited dataStudies individualStudies individualReduces costReduces costGives greater speed /helps to complete in Gives greater speed /helps to complete in stipulated timestipulated timeAssists to collect intensive and exhaustive dataAssists to collect intensive and exhaustive dataOrganises conveniencesOrganises conveniences

Steps in Sampling Process / Steps in Sampling Process / ProceduresProcedures

Define the population (element,units,extent and Define the population (element,units,extent and time)time)Specify sampling frame(Telephone directory)Specify sampling frame(Telephone directory)Specify sampling unit (retailers, our Specify sampling unit (retailers, our product,students,unemployed)product,students,unemployed)Specify sampling method/techniqueSpecify sampling method/techniqueDetermine sampling sizeDetermine sampling sizeSpecify sampling size-(optimum sample)Specify sampling size-(optimum sample)Specify sampling planSpecify sampling planSelect the sampleSelect the sample

PRINCIPLES OF SAMPLINGPRINCIPLES OF SAMPLING

Two important principlesTwo important principles

Principles of Statistical Regularity-random Principles of Statistical Regularity-random (sufficient representative of the sample),(sufficient representative of the sample),

Principles of Large Numbers-(steadiness , Principles of Large Numbers-(steadiness , stability and consistency)stability and consistency)

Principles are referred to as the laws of Principles are referred to as the laws of samplingsampling

Good samplingGood sampling

The sample should be true representative of The sample should be true representative of universe.universe.

No bias in selecting sampleNo bias in selecting sample

Quality of the sample should be sameQuality of the sample should be same

Regulating conditions should be same for all Regulating conditions should be same for all individualindividual

Sampling needs to be adequateSampling needs to be adequate

Estimate the sampling errorEstimate the sampling error

Sample study should be applicable to all itemsSample study should be applicable to all items

Preparing a sampling designPreparing a sampling design

Type of universe (set of objects) Type of universe (set of objects) Finite/Non-finiteFinite/Non-finite

Sampling unit (district,school,products)Sampling unit (district,school,products)

Sampling frameSampling frame

Sampling sizeSampling size

Sampling techniqueSampling technique

Methods of samplingMethods of sampling

Bloomers and LindquistBloomers and LindquistProbability Probability Non ProbabilityNon Probability Random/simple QuotaRandom/simple QuotaStratified random PurposiveStratified random PurposiveCluster AccidentalCluster AccidentalSystematic IncidentalSystematic Incidental MultistageMultistageProportionate Snow ballProportionate Snow ball

Probability Probability

Probability samplingProbability sampling technique is one technique is one in which every unit in the population has a in which every unit in the population has a chance of being selected in the sample chance of being selected in the sample

This probability can be accurately This probability can be accurately determined. determined.

Nonprobability samplingNonprobability sampling

Nonprobability samplingNonprobability sampling is any sampling is any sampling method where some elements of the population method where some elements of the population have have nono chance of selection (these are chance of selection (these are sometimes referred to as 'out of sometimes referred to as 'out of coverage'/'undercovered'), or where the coverage'/'undercovered'), or where the probability of selection can't be accurately probability of selection can't be accurately determined.determined. It involves the selection of elements based on It involves the selection of elements based on assumptions regarding the population of interest, assumptions regarding the population of interest, which forms the criteria for selection. which forms the criteria for selection. The selection of elements is non randomThe selection of elements is non random

. .

Simple random sampling Simple random sampling

In a In a simple random samplesimple random sample ('SRS') of a given size, all ('SRS') of a given size, all such subsets of the frame are given an equal probability. such subsets of the frame are given an equal probability. Method of chance selection. Lottery method,Tippet’s Method of chance selection. Lottery method,Tippet’s table, Kendall and Babington smith, Fisher and Yate’s table, Kendall and Babington smith, Fisher and Yate’s numbers.numbers.Simple random sampling with replacement:- equal Simple random sampling with replacement:- equal probability selection of each unit=1/N (Monte-Carlo probability selection of each unit=1/N (Monte-Carlo simulation)simulation)Simple random without replacement -varying probability Simple random without replacement -varying probability selection of each. First unit=1/N , Second unit=1/N-1, selection of each. First unit=1/N , Second unit=1/N-1, Probality of selection of the nth unit=1/N-(n-1)(Monte-Probality of selection of the nth unit=1/N-(n-1)(Monte-Carlo simulationCarlo simulation

SystematicSystematic

Systematic samplingSystematic sampling involves a random involves a random start and then proceeds with the selection start and then proceeds with the selection of every of every kkth element from then onwards. In th element from then onwards. In this case, this case, kk=(population size/sample size).=(population size/sample size). It is important that the starting point is not It is important that the starting point is not automatically the first in the list, but is automatically the first in the list, but is instead randomly chosen from within the instead randomly chosen from within the first to the first to the kkth element in the listth element in the listSampling interval width=I=N/n=800/40=20Sampling interval width=I=N/n=800/40=20

Stratified or Mixed sampling Stratified or Mixed sampling

Where the population embraces a number of Where the population embraces a number of distinct categories, the frame can be organized distinct categories, the frame can be organized by these categories into separate "strata." Each by these categories into separate "strata." Each stratum is then sampled as an independent sub-stratum is then sampled as an independent sub-population, out of which individual elements can population, out of which individual elements can be randomly selected .(homogenous group)be randomly selected .(homogenous group)

Two types-Proportionate (equal number of unit Two types-Proportionate (equal number of unit from each stratum proportion to size of the from each stratum proportion to size of the strata) and Disproportionate (not equal number strata) and Disproportionate (not equal number of unit from each stratum proportion to size of of unit from each stratum proportion to size of the strata) the strata)

Cluster samplingCluster sampling

Cluster samplingCluster sampling is an example of 'two- is an example of 'two-stage sampling' or 'stage sampling' or 'multistage samplingmultistage sampling/ / Multi phase sampling' Multi phase sampling' in the first stage a sample of areas is in the first stage a sample of areas is chosen chosen in the second stage a sample of in the second stage a sample of respondents respondents withinwithin those areas is those areas is selected.(several stages)- State level,Dist selected.(several stages)- State level,Dist level,Village level,Hosehold level.level,Village level,Hosehold level.

Cluster SamplingCluster Sampling

This stepwise process is useful for those who This stepwise process is useful for those who know little about the population they’re studying.know little about the population they’re studying. First, the researcher would divide the population First, the researcher would divide the population into clusters (usually geographic boundaries). into clusters (usually geographic boundaries). Then, the researcher randomly samples the Then, the researcher randomly samples the clusters. clusters. Finally, the researcher must measure all units Finally, the researcher must measure all units within the sampled clusters.within the sampled clusters. Researchers use this method when economy of Researchers use this method when economy of administration is important. administration is important.

Sequential samplingSequential sampling

Single samplingSingle sampling

Double samplingDouble sampling

Multiple samplingMultiple sampling

Non probabilityNon probability

Non probability sampling does not Non probability sampling does not involve involve randomrandom selection and selection and probability sampling does probability sampling does ..

Multistage samplingMultistage sampling

Multistage sampling is a complex form of cluster Multistage sampling is a complex form of cluster sampling in which two or more levels of units are sampling in which two or more levels of units are embedded one in the other. embedded one in the other. The first stage consists of constructing the clusters that The first stage consists of constructing the clusters that will be used to sample frame. will be used to sample frame. In the second stage, a sample of primary units is In the second stage, a sample of primary units is randomly selected from each cluster (rather than using randomly selected from each cluster (rather than using all units contained in all selected clusters). all units contained in all selected clusters). In following stages, in each of those selected clusters, In following stages, in each of those selected clusters, additional samples of units are selected and so on. additional samples of units are selected and so on. All ultimate units (individuals, for instance) selected at All ultimate units (individuals, for instance) selected at the last step of this procedure are surveyed.the last step of this procedure are surveyed.

Purposive/Judgment SamplingPurposive/Judgment Sampling

In purposive sampling, selecting sample In purposive sampling, selecting sample with a with a purposepurpose in mind in mind Purposive sampling can be very useful for Purposive sampling can be very useful for situations where we need to reach a situations where we need to reach a targeted sample quickly and where targeted sample quickly and where sampling for proportionality is not the sampling for proportionality is not the primary concern. primary concern. It is for pilot studyIt is for pilot studyQuestions / questionnaires may be tested.Questions / questionnaires may be tested.

Quota samplingQuota sampling

Quota samplingQuota sampling, the population is first , the population is first segmented into segmented into mutually exclusivemutually exclusive sub-groups, sub-groups, just as in just as in stratified samplingstratified sampling. . Then judgment is used to select the subjects or Then judgment is used to select the subjects or units from each segment based on a specified units from each segment based on a specified proportion. For example, an interviewer may be proportion. For example, an interviewer may be told to sample 200 females and 300 males told to sample 200 females and 300 males between the age of 45 and 60.between the age of 45 and 60.Proportional quota samplingProportional quota sampling Nonproportional quota samplingNonproportional quota sampling It is very popular for market survey and opinion It is very popular for market survey and opinion poll.poll.

Snowball SamplingSnowball Sampling

Identifying someone who meets the Identifying someone who meets the criteria for inclusion in the study. criteria for inclusion in the study. Snowball sampling is especially useful Snowball sampling is especially useful when we are trying to reach populations when we are trying to reach populations that are inaccessible or hard to find that are inaccessible or hard to find This method would hardly lead to This method would hardly lead to representative samples representative samples Intially certain members and add few Intially certain members and add few members latter members latter

Convenience sampling Convenience sampling

Convenience samplingConvenience sampling (sometimes (sometimes known as known as grabgrab or or opportunity samplingopportunity sampling) ) is a type of nonprobability sampling which is a type of nonprobability sampling which involves the sample being drawn from that involves the sample being drawn from that part of the population which is close to part of the population which is close to hand hand

Accidental SamplingAccidental Sampling

The researcher can select any sample in The researcher can select any sample in any place, can collect the data from any place, can collect the data from pedestrian also.pedestrian also.

It can be used for exploratory studiesIt can be used for exploratory studies

It has sample error.It has sample error.

It has less accuracyIt has less accuracy

Combination of Probability sampling Combination of Probability sampling and Non Probability samplingand Non Probability sampling

If sampling is carried out in series of If sampling is carried out in series of stages, it is possible to combine probability stages, it is possible to combine probability and non-probability sampling in one and non-probability sampling in one designdesign

Users of particular product in one street for Users of particular product in one street for the particular group of people.the particular group of people.

Utility of the particular product in the town.Utility of the particular product in the town.

Sampling ErrorsSampling Errors

The errors which arise due to the use of The errors which arise due to the use of sampling surveys are known as the sampling sampling surveys are known as the sampling errors.errors.Two types of sampling errors-Biased Errors, Two types of sampling errors-Biased Errors, Unbiased ErrorsUnbiased ErrorsBiased Errors-Which arise due to selection of Biased Errors-Which arise due to selection of sampling techniques.-size of the samplesampling techniques.-size of the sampleUnbiased Errors / Random sampling errors-arise Unbiased Errors / Random sampling errors-arise due to chance differences between the members due to chance differences between the members of the population included in the sample and not of the population included in the sample and not included.included.

Methods of reducing Sampling Methods of reducing Sampling ErrorsErrors

Specific problem selectionSpecific problem selection

Systematic documentation of related Systematic documentation of related researchresearch

Effective enumerationEffective enumeration

Effective pre testingEffective pre testing

Controlling methodological biasControlling methodological bias

Selection of appropriate sampling Selection of appropriate sampling techniques.techniques.

Non-sampling ErrorsNon-sampling Errors

Non-sampling errors refers to biases and mistakes in Non-sampling errors refers to biases and mistakes in selection of sample.selection of sample.

CAUSES FOR NON-SAMPLING ERRORSCAUSES FOR NON-SAMPLING ERRORSSampling operationsSampling operationsInadequate of responseInadequate of responseMisunderstanding the conceptMisunderstanding the conceptLack of knowledgeLack of knowledgeConcealment of the truth.Concealment of the truth.Loaded questionsLoaded questionsProcessing errorsProcessing errorsSample sizeSample size

Factors related to Sample sizeFactors related to Sample size

The nature of populationThe nature of populationComplexity of tabulationComplexity of tabulationProblems relating to collection of dataProblems relating to collection of dataSelection of sampling techniquesSelection of sampling techniquesLimitation of accuracyLimitation of accuracy

Calculating sample size=(SZ / T)2Calculating sample size=(SZ / T)2S-preliminary SD of the universeS-preliminary SD of the universeZ-number of standard errorsZ-number of standard errorsT-errors to be toleratedT-errors to be tolerated