Sample &Sampling Design DR.G.SINGARAVELU Associate Professor UGC-ASC BHARATHIAR UNIVERSITY COIMBATORE
DEFINITIONS Population-totality of the objects or individuals regarding inferences are made in a sampling study.Sample-smaller representation of a large whole.Sampling- is a process of selecting a subset of randomised number of the members of the population of a study
Sampling frame /Source list -complete list of all the members/ units of the population from which each sampling unitSample design / sample plan-is a definite plan for obtaining a sample from a given population.Sampling unit-is a geographical one (state,district)Sample size-number of items selected for the studySampling Error-is the difference between population value and sample value.Sampling distribution-is the relative frequency distribution of samples.
CENSUS/SAMPLING Census-collection of data from whole population.Sampling is taking any portion of a population or universe as representative of that population.Sampling method has been using in social science research since 1754 by A.L.BOWLEY
Indispensable of sampling in ResearchSaves lot of timeProvides accuracyControls unlimited dataStudies individualReduces costGives greater speed /helps to complete instipulated timeAssists to collect intensive and exhaustive dataOrganises conveniences
Steps in Sampling Process / ProceduresDefine the population (element,units,extent andtime)Specify sampling frame(Telephone directory)Specify sampling unit (retailers, ourproduct,students,unemployed)Specify sampling method/techniqueDetermine sampling sizeSpecify sampling size-(optimum sample)Specify sampling planSelect the sample
PRINCIPLES OF SAMPLINGTwo important principlesPrinciples of Statistical Regularity-random (sufficient representative of the sample),Principles of Large Numbers-(steadiness , stability and consistency)Principles are referred to as the laws of sampling
Good samplingThe sample should be true representative ofuniverse.No bias in selecting sampleQuality of the sample should be sameRegulating conditions should be same for allindividualSampling needs to be adequateEstimate the sampling errorSample study should be applicable to all items
Preparing a sampling designType of universe (set of objects)Finite/Non-finiteSampling unit (district,school,products)Sampling frameSampling sizeSampling technique
Methods of samplingBloomers and LindquistProbability Non ProbabilityRandom/simple QuotaStratified random PurposiveCluster AccidentalSystematic Incidental MultistageProportionate Snow ball
Probability Probability sampling technique is onein which every unit in the population has achance of being selected in the sample This probability can be accuratelydetermined.
Nonprobability sampling Nonprobability sampling is any sampling method where some elements of the population have no chance of selection (these are sometimes referred to as out of coverage/undercovered), or where the probability of selection cant be accurately determined. It involves the selection of elements based on assumptions regarding the population of interest, which forms the criteria for selection. The selection of elements is non random.
Simple random samplingIn a simple random sample (SRS) of a given size, allsuch subsets of the frame are given an equal probability.Method of chance selection. Lottery method,Tippet’stable, Kendall and Babington smith, Fisher and Yate’snumbers.Simple random sampling with replacement:- equalprobability selection of each unit=1/N (Monte-Carlosimulation)Simple random without replacement -varying probabilityselection of each. First unit=1/N , Second unit=1/N-1,Probality of selection of the nth unit=1/N-(n-1)(Monte-Carlo simulation
SystematicSystematic sampling involves a randomstart and then proceeds with the selectionof every kth element from then onwards.In this case, k=(population size/samplesize). It is important that the starting point is notautomatically the first in the list, but isinstead randomly chosen from within thefirst to the kth element in the listSampling interval width=I=N/n=800/40=20
Stratified or Mixed samplingWhere the population embraces a number ofdistinct categories, the frame can be organizedby these categories into separate "strata." Eachstratum is then sampled as an independent sub-population, out of which individual elements canbe randomly selected .(homogenous group)Two types-Proportionate (equal number of unitfrom each stratum proportion to size of thestrata) and Disproportionate (not equal numberof unit from each stratum proportion to size ofthe strata)
Cluster samplingCluster sampling is an example of two-stage sampling or multistage sampling/Multi phase samplingin the first stage a sample of areas ischosenin the second stage a sample ofrespondents within those areas isselected.(several stages)- State level,Distlevel,Village level,Hosehold level.
Cluster SamplingThis stepwise process is useful for those whoknow little about the population they’re studying. First, the researcher would divide the populationinto clusters (usually geographic boundaries).Then, the researcher randomly samples theclusters.Finally, the researcher must measure all unitswithin the sampled clusters. Researchers use this method when economy ofadministration is important.
Non probabilityNon probability sampling does notinvolve random selection andprobability sampling does .
Multistage samplingMultistage sampling is a complex form of clustersampling in which two or more levels of units areembedded one in the other.The first stage consists of constructing the clusters thatwill be used to sample frame.In the second stage, a sample of primary units israndomly selected from each cluster (rather than usingall units contained in all selected clusters).In following stages, in each of those selected clusters,additional samples of units are selected and so on.All ultimate units (individuals, for instance) selected atthe last step of this procedure are surveyed.
Purposive/Judgment SamplingIn purposive sampling, selecting samplewith a purpose in mindPurposive sampling can be very useful forsituations where we need to reach atargeted sample quickly and wheresampling for proportionality is not theprimary concern.It is for pilot studyQuestions / questionnaires may be tested.
Quota samplingQuota sampling, the population is firstsegmented into mutually exclusive sub-groups,just as in stratified sampling.Then judgment is used to select the subjects orunits from each segment based on a specifiedproportion. For example, an interviewer may betold to sample 200 females and 300 malesbetween the age of 45 and 60.Proportional quota samplingNonproportional quota samplingIt is very popular for market survey and opinionpoll.
Snowball Sampling Identifying someone who meets thecriteria for inclusion in the study.Snowball sampling is especially usefulwhen we are trying to reach populationsthat are inaccessible or hard to findThis method would hardly lead torepresentative samplesIntially certain members and add fewmembers latter
Convenience samplingConvenience sampling (sometimesknown as grab or opportunity sampling)is a type of nonprobability sampling whichinvolves the sample being drawn from thatpart of the population which is close tohand
Accidental SamplingThe researcher can select any sample inany place, can collect the data frompedestrian also.It can be used for exploratory studiesIt has sample error.It has less accuracy
Combination of Probability sampling and Non Probability samplingIf sampling is carried out in series ofstages, it is possible to combineprobability and non-probability sampling inone designUsers of particular product in one streetfor the particular group of people.Utility of the particular product in the town.
Sampling ErrorsThe errors which arise due to the use ofsampling surveys are known as the samplingerrors.Two types of sampling errors-Biased Errors,Unbiased ErrorsBiased Errors-Which arise due to selection ofsampling techniques.-size of the sampleUnbiased Errors / Random sampling errors-arisedue to chance differences between the membersof the population included in the sample and notincluded.
Methods of reducing Sampling ErrorsSpecific problem selectionSystematic documentation of relatedresearchEffective enumerationEffective pre testingControlling methodological biasSelection of appropriate samplingtechniques.
Non-sampling ErrorsNon-sampling errors refers to biases and mistakes in selection of sample.CAUSES FOR NON-SAMPLING ERRORS Sampling operations Inadequate of response Misunderstanding the concept Lack of knowledge Concealment of the truth. Loaded questions Processing errors Sample size
Factors related to Sample size The nature of population Complexity of tabulation Problems relating to collection of data Selection of sampling techniques Limitation of accuracyCalculating sample size=(SZ / T)2S-preliminary SD of the universeZ-number of standard errorsT-errors to be tolerated