Correlation in Statistical Analysis .pdf

Correlation
Types of Correlation
Correlation Coefficient
Limitations of Correlation
Examples

1. CORRELATION
Dr. Balamurugan M
Associate Professor
Acharya Institute of Graduate Studies
Bangalore

2. Correlation
•Correlationisastatisticaltechniqueusedforanalyzing
thebehavioroftwoormorevariables.Correlationisalso
describedasco-variationintwoormorevariables.
•Correlationdoesnotnecessarilyindicateacauseand
effectrelationship,itonlyprovidesaquantitative
measure.

3. Degree&NatureofRelationship
Correlationisameasureofdegreeofrelationship
betweenX&Y.
Withthehelpofcorrelationanalysiswecanmeasurethe
degreeofrelationshipexistingbetweenthevariables.
Forexample,thereistherelationshipbetweenpriceand
supply.

4. Correlationdoesnothelpinmakingpredictions.
Correlationcoefficientsaresymmetrical.
TypesofCorrelations
PositiveCorrelation
NegativeCorrelation
NoCorrelation

5. PositiveCorrelation
Apositivecorrelationmeansthatthislinearrelationshipis
positive,andthetwovariablesincreaseordecreaseinthe
samedirection.
NegativeCorrelation(InverseCorrelation)
Anegativecorrelationisjusttheopposite.Therelationship
linehasanegativeslope,andthevariableschangein
oppositedirections.
NoCorrelation
Thevariablesbehaveverydifferentlyandthus,haveno
linearrelationship.

6. Types of Correlations

7. Correlation Coefficient
•Correlationcoefficientsgiveyouthemeasureofthe
strengthofthelinearrelationshipbetweentwovariables.
•Theletterrdenotesthevalue,anditrangesbetween-1
and+1
•Ifr<0,itimpliesnegativecorrelation
•Ifr>0,itimpliespositivecorrelation
•Ifr=0,itimpliesnocorrelation

8. Types of Correlation coefficient
Therearemainlytwotypesofcorrelationcoefficients.
1.KarlPearsonCorrelationCoefficient
•Formula
•r = Coefficient of correlation
•x bar = Mean of x-variable
•y bar = Mean of y-variable.
•xi & yi = Samples of variable x, y

9. 2.Spearman’sRankCorrelationCoefficient
•Formula
•ρ=Spearmanrankcorrelation
•di=Differencebetweentheranksofcorresponding
variables
•n=NumberofObservations

10. Limitations of Correlation
•Correlationdoesnotindicatecausalityandcannot
beusedtodoso.
•Wecannotinferthatonevariableisthecauseof
anothereventhoughthereisaveryhighrelationship
betweenthem.

11. •Wearelimitedbycorrelationtotheinformationthatis
provided.Forinstance,supposeresearchrevealedalink
betweentheamountoftimestudentsspendontheir
homework(fromhalfanhourtothreehours)andthe
numberofG.C.S.E.passes(1to6).Itwouldbeincorrectto
concludefromthisthatputtingin6hoursofhomework
wouldprobablyresultin12G.C.S.E.passes.

12. Examples
•Let’sseesomereal-lifeexamplesandseewhatdoes
negativecorrelationmeanandwhatdoespositive
correlationmean.
Body Fat and Running Time
•Anindividual'sbodyfattendstobelowerthemoretime
theyspendjogging.Inotherwords,thereisanegative
correlationbetweenthevariablebodyfatandthevariable
runningtime.Bodyfatdecreasesasrunningtime
increases.

13. Examples
Exam Results and TV Viewing Time
•Examresultstypicallysufferwhenastudentwatches
moretelevision.Inotherwords,thereisanegative
correlationbetweenthevariableamountoftimespent
watchingTVandthevariableexamgrade.Examresults
declineasTVviewingtimeincreases.