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Chapter ObjectivesChapter Objectives

12/12/201012/12/2010 Biju K ThapaliaBiju K Thapalia 11

Introduction

Sampling Techniques

Sampling Design

Sample Size

Sampling Errors Sampling Distribution

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To show how estimation is done.

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Sampling is that part of statistical

practice concerned with the selection of

an unbiased or random subset of

individual observations within a

population of individuals intended to

yield some knowledge about thepopulation of concern, especially for the

purposes of making predictions based on

statistical inference.

Sampling is the act, process, or technique of

selecting a suitable sample, or arepresentative part of a population for the

purpose of determining parameters or

characteristics of the whole population.

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A census studydraws inferences from the

entire bodyofunits of interest (thepopulation)

A sample studydraws inferences from a

sample drawnfrom the population

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Basic reasons-

Cost is too highPopulation is dynamic, it may change

Time limitation

Improve qualityofdata

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Defining Population

Specifying a samplingframe, a setof items or

events possible to measure

Specifying a sampling methodfor selectingitems or events from the frame

Determiningthe sample size

Implementingthe sampling plan

Sampling anddata collecting

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ProbabilitySampling

Probability sampling is anobjective procedure

inwhich the probabilityofselection is known

in advance for each population unit

Non-probabilitySampling

Nonprobability sampling is a subjective

procedure inwhich the probabilityofselection

for each population unit is unknown

beforehand

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Non-probability

Quota

Snowball

Convenience

Purposive

y Probability

y Simple random

y

Systematicy Stratifiedrandom

y Cluster

y Multi-stage

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Each elementofthe population have equal and

independentopportunityto be selected

Entire population should be enumeratedUse ofLoterry or Random numbers table

Useful for homogeneous populationw.r.t

specific characteristics

Sampling error is more for same sample size-

so large sample size needed

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For population is large anddifficultto list all

Arrangementofelements on some pattern

w.r.t studyfeatureChoose anyfirst element andthenrepeatnext

kth element and soon

kdepends on sample size(n) and population

size (N); k=N/n

Easyto administer

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For hetrogenous population

Population is divided into strataSimple random samplingorSystematic

sampling in each strata

Proportionate ordisproportionate allocation

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When population is widely spreadortoo large

Lookfornatural Clusters

Randomly choose clustersIn each cluster select elementrandomly

Also known as multi-stage samplingtechnique

Less accurate thanfrom otherrandom

sampling

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Think and lets find it-

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Used in multi-stage sampling

Probabilityofselecting a Cluster is dependentonthe size ofthe cluster

Insures representative sample ofpopulation

elements

Used in multi-stage sampling

Probabilityofselecting a Cluster is dependentonthe size ofthe cluster

Insures representative sample ofpopulation

elements

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Atthe convenience ofresearcher

Useful for idea testingor

groundwork

Cheap and easyto administer

Biased and unrepresentative

Non-probability Sampling

Convenience sampling

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Selectionofsubjects are basedon

some judgmentor purpose

It is guided, sonotrandom

Depends onresearchers abilityto

analyze the subject matterofresearch

Easyto use

Results cannot be generalized

Non-probability Sampling

Judgment sampling

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Mix ofstratified and convenience

sampling

Less costly and easyto implement Mostly use in marketing surveys,

opinion polls, etc.

Non-probability Sampling

Quota sampling

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Subjectguides next subjectofthe

population

Easy ifall population is not known

or samplingframe is not available

Non-probability Sampling

Snowball sampling

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What should be our sample size?

Whatdetermines it?

Research Design- Descriptive or

Experimental

Precisionofmeasure-Validity and Reliability

Approaches todetermine the size-

Via Statistical Significance

Via Confidence Interval

Sample Size-A million dollar question

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What should be the sample size?What should be the sample size?

Three factors indetermining sample size

The variabilityofthe population

The level ofconfidence desired inthe estimation

The degree ofprecisiondesired in estimatingthe

population characteristics

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Sample size for estimating a MeanSample size for estimating a Mean

The sample size n is given by

n= W>/e)2

Where

W= estimationofpopulation standard

deviation

Z = the standardized z-value associated

with the level ofconfidencee =Acceptable tolerance level oferror

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Sample size for estimating a ProportionSample size for estimating a Proportion

The sample size n is given by

n= Z2 pq/e2

Where

p = estimationofexpected population

proportion holdingthe characteristic

of intereston intuitionor prior

information, q = 1-p

Z = the standardized z-value associated

with the level ofconfidence

e =Acceptable tolerance level oferror

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NumericalNumerical

A survey proposed to be conducted toknow the annual earnings of old MBAstudents of PU. How large should be

sample size be taken in order toestimate the mean annual earningswithin plus and minus Rs. 1000 at 95%confidence level? The standard deviation

of the annual earnings of the entirepopulation is known to be 15000.

Answer n =732

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NumericalNumerical

Assume you are a manger of a bank inKathmandu. When you were posted inDharan you remember that among 200customers 45 % of them availed anattractive loan scheme. Now your bosswants you to know how the same schemewill be taken in Kathmandu. He needs yourestimation to be precise of +3 % with a 99

% confidence level. So what will be yoursample size?

Answern= 1831

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Sampling ErrorsSampling Errors

Errors which are made in selecting samples

that are not representative of population dueto wrong definition of sample frame or

excluding some population Bound to present however we are

careful.

Will reduce if increase the size of thesample- but not in same proportion

Can reduce (but not eliminate) if usedrandom sampling

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Sampling DistributionSampling Distribution

Sampling distribution of a statistics is thefrequency distribution which is formed withvarious values of statistic computed fromdifferent samples of the same size drawnfrom the same population.

This distribution approaches normal shapeeven when the population is notdistributed as such.

The mean and standard deviatio n o f thesample distribution holds some relationwith true parameter value

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Sampling DistributionSampling Distribution-- Why important?Why important?

Characteristics of its helps us to

To estimate the unknown population

parameter

To setthe confidence limits ofthe

parametervalues estimated

Totest hypothesis anddraw statistical

inference from it

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Reference forSampling chapterReference forSampling chapter

y Social Science Research and ThesisWriting Wolffand Pant

y MethodologyofResearch inSocial Science Krishnaswami and Ranganatham

y Marketing Research within a ChangingInformationEnvironment

Hair, Bush and Ortinau

y Statistics (CAFoundation Course)

Arora andAroray Statistics forManagement

Levin