Correlation Ch.-7 (Ver 8)

1 As the summer heat rises, hillstations, are crowded with more andmore visitors. Ice-cream sales becomemore brisk. Thus, the temperature isrelated to number of visitors and saleof ice-creams. Similarly, as the supplyof tomatoes increases in your localmandi, its price drops. When the localharvest starts reaching the market,the price of tomatoes drops from aprincely Rs 40 per kg to Rs 4 per kg oreven less. Thus supply is related toprice. Correlation analysis is a meansfor examining such relationshipssystematically.

2 It deals with questionssuch as: Is there any relationship betweentwo variables?Correlation71. INTRODUCTIONIn previous chapters you have learnthow to construct summary measuresout of a mass of data and changesamong similar variables. Now you willlearn how to examine the relationshipbetween two this chapter shouldenable you to: understand the meaning of theterm Correlation ; understand the nature ofrelationship between twovariables; calculate the different measuresof Correlation ; analyse the degree and directionof the FOR ECONOMICS If the value of one variablechanges, does the value of theother also change?

3 Do both the variables move in thesame direction? How strong is the relationship?2. TYPES OF RELATIONSHIPLet us look at various types ofrelationship. The relation betweenmovements in quantity demandedand the price of a commodity is anintegral part of the theory of demand,which you will study in Class XII. Lowagricultural productivity is related tolow rainfall. Such examples ofrelationship may be given a cause andeffect interpretation. Others may be justcoincidence. The relation between thearrival of migratory birds in asanctuary and the birth rates in thelocality cannot be given any cause andeffect interpretation.

4 The relationshipsare simple coincidence. Therelationship between size of theshoes and money in your pocket isanother such example. Even ifrelationship exist, they are difficultto explain another instance a thirdvariable s impact on two variablesmay give rise to a relation between thetwo variables. Brisk sale of ice-creamsmay be related to higher number ofdeaths due to drowning. The victimsare not drowned due to eating of ice-creams. Rising temperature leads tobrisk sale of ice-creams. Moreover, largenumber of people start going toswimming pools to beat the heat.

5 Thismight have raised the number of deathsby drowning. Thus temperature isbehind the high Correlation betweenthe sale of ice-creams and deaths dueto Does Correlation Measure? Correlation studies and measuresthe direction and intensity ofrelationship among measures covariation, notcausation. Correlation should never be2015-16 CORRELATION93interpreted as implying cause andeffect relation. The presence ofcorrelation between two variables Xand Y simply means that when thevalue of one variable is found to changein one direction, the value of the othervariable is found to change either in thesame direction ( positive change) orin the opposite direction ( negativechange), but in a definite way.

6 Forsimplicity we assume here that thecorrelation, if it exists, is linear, therelative movement of the two variablescan be represented by drawing astraight line on graph of CorrelationCorrelation is commonly classifiedinto negative and positivecorrelation. The Correlation is said tobe positive when the variables movetogether in the same direction. Whenthe income rises, consumption alsorises. When income falls,consumption also falls. Sale of ice-cream and temperature move in thesame direction.

7 The Correlation isnegative when they move in oppositedirections. When the price of applesfalls its demand increases. When theprices rise its demand you spend more time instudying, chances of your failingdecline. When you spend less hoursin your studies, chances of scoringlow marks/grades increase. Theseare instances of negative variables move in FOR MEASURINGCORRELATIONT hree important statistical tools usedto measure Correlation are scatterdiagrams, Karl Pearson s coefficient ofcorrelation and spearman s scatter diagram visuallypresents the nature of associationwithout giving any specificnumerical value.

8 A numericalmeasure of linear relationshipbetween two variables is given byKarl Pearson s coefficient ofcorrelation. A relationship is said tobe linear if it can be representedby a straight line. spearman scoefficient of Correlation measuresthe linear association between ranksassigned to indiviual items accordingto their attributes. Attributes arethose variables which cannot benumerically measured such asintelligence of people, physicalappearance, honesty, DiagramA scatter diagram is a usefultechnique for visually examining theform of relationship, withoutcalculating any numerical value.

9 Inthis technique, the values of the twovariables are plotted as points on agraph paper. From a scatter diagram,one can get a fairly good idea of thenature of relationship. In a scatterdiagram the degree of closeness of thescatter points and their overall directionenable us to examine the relation-2015-1694 STATISTICS FOR ECONOMICS ship. If all the points lie on a line, thecorrelation is perfect and is said to beunity. If the scatter points are widelydispersed around the line, thecorrelation is low. The Correlation issaid to be linear if the scatter points lienear a line or on a diagrams spanning overFig.

10 To Fig. give us an idea ofthe relationship between twovariables. Fig. shows a scatteraround an upward rising lineindicating the movement of thevariables in the same direction. WhenX rises Y will also rise. This is positivecorrelation. In Fig. the points arefound to be scattered around adownward sloping line. This time thevariables move in opposite X rises Y falls and vice is negative Correlation . In is no upward rising or downwardsloping line around which the pointsare scattered.