Research Methodology 6

8/18/2019 Research Methodology 6

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ResearchMethodology 6

Presented by Dr Sarmistha Das


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Time Horizon

Cross-sectional studies› Snapshot of constructs at a single point in

time

› Use of representative sample Multiple cross-sectional studies

› Constructs measured at multiple points intime

›

Use of dierent sample Longitudinal studies

› Constructs measured at multiple points intime

› Use of same sample = a true panel


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How to calculate the extentof variation

SD of the sample mean of the samplingdistribution

STANDAD !"

The standard deviation of the distributionof a sample statistics is #no$n as theStandard !rror of the statistics%

&ndicates the accuracy $e are li#ely toget if $e use a sample statistic toestimate a population parameter%


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SD of the distributionSD of the distribution

of sample meansof sample means

S! of meanS! of mean

SD of the distributionSD of the distributionof sample medianof sample median

S! of medianS! of median

SD of the distributionSD of the distribution

of sample proportionof sample proportion

S! of proportionS! of proportion


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A lo$er value of standard error'''''

(alue of S! $hen sample si)eincreases'''

*hat $ill be the shape of the samplingdistribution of sample mean $ith

dierently shaped populationdistribution+

Central Limit Theorem


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Central Limit Theorem

• !f a population is normallydistri"uted# The mean of thesampling distri"ution of the mean

will e$ual the population mean regardless of the sample size.

• As the sample size increases# thesampling distri"ution of the meanwill approach to normality# regardless of

the shape of the population distribution%


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Standard !rror

• !n%nitepopulationsize-----

Standard !rror =,-.n

1−

−∂

N

n N

n

&initepopulationsize----'tandard(rror )


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Statistical &nference

• (stimation-'' estimation ofpopulation parameter on the basis ofsample statistic%

•Testing of hypotheses


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Estimation

Point estimate Interval estimate


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*oint (stimate

• Sample statistic that is used to estimatethe population parameter%

• Single number that is used to estimate anun#no$n population%


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!stimator/ !stimates

populatiopopulatio

nnPopulationPopulation

parameterparameterto beto beestimatedestimated

(stimator(stimator

+sample+samplestatistic we usestatistic we useto estimate ato estimate apopulationpopulation

parameterparameter))

!stimate!stimate

0 speci1c0 speci1cobservedobservedvalue of thevalue of thestatistic2statistic2

Customersatisfact

ionsurveyof thecustomers of

,odafon

Service ofService ofvodafone isvodafone isbest inbest in

3uality3uality

4ean "pinion of4ean "pinion ofevery 1fthevery 1fthcustomer of thecustomer of the

customer datacustomer databasebase

./0


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*oint (stimation

• Point estimate based on representativeness ofthe sample''''''''''''''&t is either right or $rong%

• &t is dierent for dierent samples dra$n fromthe same population%

• Necessary to estimate population parameter in a

range%• methods

– 4a5imum li#elihood

– 6east s3uare

– method of moment


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&nterval !stimate

• Mar1eting Manager says# 2Mean opinionof the customer lies "etween to 3.4

• ange of values used to estimate a populationparameter $ith some degree of con1dencethat the parameter $ill fall in that range%

• derive an interval that is e5pected to include

the true value of the parameter $ith thedesired level of con1dence


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• esearcher is interested to specify therange/ for each Parameter/ with inwhich the mean opinion of the

customers may lie% And the pro"a"ilitythat the it $ould lie in that range%

• 7889con1dent that the mean opinion of

the customers regarding the speed $ill liebet$een :%;' 7:%;' 889%• !nterval estimate of customer

satisfaction level of the ,odafone 35

customers


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Use of ? statistic for estimation• Central limit theorem> sample means for

large samples 0n@:2 are normallydistributed/ regardless of the shape ofpopulation distribution%

• ?=0B'2 - ,-.n

• = B') ,-.n'''''''''' $here B is the samplemean%

• Sample mean can be greater or less than

population mean%

n

z X ∂±= µ


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inite Population

• Con1dence interval for estimating population mean

interval.confidencetheoutsideiswhichcurvenormalunder the

areatailedonetheis 2

interval,cinfidencetheoutsideiswhich

curvenormalunder theareatheis

SD, population

size,sampleisnmean,sampletheisX

1212

α

α

α µ α

is

N

n N

n

Z X

N

n N

n

Z X

∂

−

−∂+≥≤

−

−∂−


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Con1dence interval for estimatingpopulation mean

interval.confidencetheoutsideiswhichcurvenormalunder the

areatailedonetheis 2

interval,cinfidencetheoutsideiswhich

curvenormalunder theareatheis

SD, population

size,sampleisnmean,sampletheisX

22

2

α

α

α µ

α

α µ

is

n Z X n Z X

n Z X

∂

∂

+≤≤

∂

−

∂±=


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Con%dence interval when population' is un1nown

Large sample +n7389• 'ample will follow

normal distri"ution+ Central Limit

theorem9.

• :se z statistic formulato estimate

con%dence interval.

• 'ample ' can "eused for *opulation

'.

'mall sample +n;389• 'ample will follow t

distri"ution +even ifthe population

follows normaldistri"ution9

• :se t statisticformula to estimate

con%dence interval.

• 'ample ' can "eused for *opulation'.


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Trade o bet$een sample si)e/interval $idth/ level of con1dence%

• 7Ereater the con1dence intervalmore $ill be the con1dence level%

• actors aecting the $idth of acon1dence level – con1dence interval/

– sample si)e

– Population standard deviation


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Properties for good estimation

• Unbiasedness

• Consistency/

•!Fciency/

• suFciency

Research Methodology 6

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