CORRELATION ANALYSIS NOTES.pdf

STATISTICS FOR DECISION MAKING - CORRELATION ANALYSIS, MEANING, TYPES, METHODS OF CALCULATION OF CORRELATION

1. CORRELATION ANALYSIS

2. CORRELATION
DEFINITION
Thevariablesaresaidtobecorrelatedifthechangesinone
variableresultsinacorrespondingchangeintheother
variable.Thatis,whentwovariablesmovetogetherwesay
theyarecorrelated.
Boddingtonstatesthat“wheneversomedefiniteconnection
existsbetweenthetwoormoregroups,classesorseriesor
datathereissaidtobecorrelation”.
Bowelydefinescorrelationas,“whentwoquantitiesareso
relatedthatthefluctuationsinoneareinsympathywiththe
fluctuationsoftheother,thatanincreaseordecreaseofthe
oneisfoundinconnectionwiththeincreaseordecreaseofthe
otherandgreaterthemagnitudeofchangeintheother,the
quantitiesaresaidtobecorrelated”

3. TYPES OFCORRELATION
Thedifferenttypesofcorrelationare
oPositiveandNegativecorrelation
oLinearandNon-linearcorrelation
oSimple,MultipleandPartialcorrelation.
PositiveCorrelation
Whenthevaluesoftwovariablesmovesame
direction,correlationissaidtobepositive.
ie;anincreaseinthevalueofonevariableresultsintoan
increaseintheothervariablealsoorifdecreaseinthe
valueofonevariableresultsintoadecreaseintheother
variablealsocorrelationissaidtobepositive.
Eg.Temperatureandvolume

4. Negativecorrelation
Whenthevaluesoftwovariablesmoveoppositedirection,
correlationissaidtobenegative.
ie;anincreaseinthevalueofonevariableresultsintoandecreaseinthe
othervariablealsoorifdecreaseinthevalueofonevariableresultsintoa
increaseintheothervariablealsocorrelationissaidtobepositive.
Eg.Pressureandvolume
LinearCorrelation
Whentheamountofchangeinonevariableleadstoaconstantratio
ofchangeintheothervariable,correlationissaidtobelinear.
NonlinearCorrelation
Correlationissaidtobenonlinear(curvelinear)whentheamountof
changeinonevariableisnotinconstantratiotothechangeintheother
variable.

5. Simplecorrelation
Inthestudyofrelationshipbetweenthevariables,ifthereare
onlytwovariables,thecorrelationissaidtobesimple.
Whenonevariableisrelatedtoanumberofothers,thecorrelation
isnotsimple.
Multiplecorrelation
Inthestudyofmultiplecorrelationwemeasurethedegreeof
associationbetweenonevariableononesideandalltheother
variabletogetherontheotherside.
Partialcorrelation
Inpartialcorrelationwestudytherelationshipofonevariable
withoneoftheothervariablespresumingthattheothervariable
remainsconstant.

6. positivecorrelation Negativecorrelation zerocorrelation
perfect positivecorrelation perfect negativecorrelation

7. Coefficient ofCorrelation
Coefficientofcorrelationisanalgebraicmethodofmeasuringcorrelation.
Underthismethod,wemeasurecorrelationbyfindingavalueknownasthe
coefficientofcorrelationusinganappropriateformula.
Coefficientofcorrelationisanumericalvalue.Itshowsthedegreeortheextentof
correlationbetweentwovariables.
Coefficientofcorrelationisapurenumberlyingbetween-1and+1.
Whenthecorrelationisnegative,itliesbetween-1and0.
Whenthecorrelationispositive,itliesbetween0and1.
Whenthecorrelationofcoefficientiszero,itindicatesthatthereisnocorrelation
betweenthevariables.
Whenthecorrelationcoefficientis1,thereisperfectcorrelation.
Betweennocorrelationandperfectcorrelationtherearevaryingdegreeof
correlation.

8. METHODS FOR STUDYINGCORRELATION
Coefficient of correlation can be computed by applyingthe methods givenbelow:
❖Karl Pearson’sCoefficient of Correlation
❖Spearman’sRank Correlation

9. PROPERTIES OF COEFFICIENT OFCORRELATION
1.Correlation coefficient has a well definedformula
2.Correlation coefficient is a pure number and is independentof
its units ofmeasurement.
3.It lies between -1 and+1.
4.Correlation coefficient does not change with referenceto
change of origin or change ofscale.
5.Correlationof coefficient between x and y is same asthat
between y andx.

10. IMPORTANCE OFCORRELATION
➢Correlation helps to study the association betweentwo
variables.
➢Coefficient of correlation is vital for all kinds ofresearch
work.
➢It helps in establishing Validity or Reliability of anevaluation
tool.
➢It helps to ascertain the traits and capacities of pupilswhile
giving guidance orcounselling.
➢Correlation analysis helps to estimate the futurevalues.

11. What would be your interpretation if thecorrelation
coefficient equalto
1)r =0
Ans : There is no correlation between thevariables
2)r =-1
Ans: negative perfectcorrelation
3)r=0.2
Ans:low positivecorrelation
4)r =0.9
Ans: high positivecorrelation
5)r= -0.3
Ans: low negativecorrelation
6)r = -0.8
Ans: High negativecorrelation

12. KARL PEARSON’S COEFFICIENT OF CORRELATION

13. WHEN DEVIATIONS ARE TAKEN FROM AN ASSUMED MEAN

14. SPEARMAN’S RANK
CORRELATIONMETHOD

15. This was
developed by
Charles Edward
Spearman in1904
The correlation of coefficient obtained fromranks
of thevariables.
6∑D
2
Definition
(R)=

16. Qn: Find the rank correlation betweenpoverty
and overcrowding from the information given
below.
Town A BC D E F G H I J
Poverty171315 16 6 11 14 9 7 12
Overcro
wding
364635 24 12 18 27 22 2 8

17. Soln.
6∑D
2
6x44
264
990
= 1-0.2667
=0.7333
(R)=
(R)=
(R)=