slides - correlation analysis

8/4/2019 Slides - Correlation Analysis

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Correlation Analysis


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CORRELATION

Correlation is a statistical technique that can showwhether and how strongly pairs of variables arerelated

Correlation is used to measure and describe arelationship between two variables.

Usually these two variables are simply observed asthey exist in the environment; there is no attemptto control or manipulate the variables.


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CORRELATION COEFFICIENT

The correlation coefficient measures twocharacteristics of the relationship between X and Y:

STRENGTH OF THE RELATIONSHIP IS DETERMINED

BY THE CLOSENESS OF THE POINTS TO A STRAIGHTLINE WHEN A PAIR OF VALUES ARE PLOTTED ON AGRAPH

DIRECTION IS DETERMINED BY WHETHER ONEVARIABLE GENERALLY INCREASES OR DECREASESWHEN THE OTHER VARIABLE INCREASES


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PROPERTIES OF CORRELATIONCOEFFICIENT

It is pure number and isindependent of the units of

measurement.It lies between 1 and +1


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Degree of Correlation

Perfect correlationLimited degrees of correlationAbsence of correlation


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TYPESOF CORRELATION

i. Positive and Negativeii. Simple, partial and multipleiii.Linear and non-linear


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Positive Correlation

If the higher scores on X are generally pairedwith the higher scores on Y, and the lowerscores on X are generally paired with thelower scores on Y, then the direction of thecorrelation between two variables is positive


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Negative Correlation

If the higher scores on X are generally pairedwith the lower scores on Y, and the lowerscores on X are generally paired with thehigher scores on Y, then the direction of thecorrelation between two variables is negative.


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MULTIPLE & PARTIAL CORRELATION

X1-Yield of rice X2-Amount of Rainfall X3-Amount of fertilizers

X4-Type of soil X5-Advanced technologies used.

Correlation analysis of X1,X2,X3,X4 and X5 is anexample of Multiple Correlation whereas if weonly study the the the relation between X1 andX2 it would be an example of Partial Correlation


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Linear and Non-linear

The nature of the graph gives us the ideaof the linear type of correlation between

two variables. If the graph is in a straightline, the correlation is called a "linearcorrelation" and if the graph is not in a

straight line, the correlation is non-linear or curvi-linear.


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Methods Of Determining Correlation

Scatter Plot

Karl Pearsons coefficient of

correlation Spearmans Rank -correlation

coefficient.


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Scatter Plot ( Scatter diagram or dotdiagram )

In this method the values of th e two variablesare plotted on a graph paper . One is takenalong the horizontal ( (x-axis) and the otheralong the vertical (y-axis). By plotting the data,we get points (dots) on the graph which aregenerally scattered and hence the nameScatter Plot.

The manner in which these points arescattered, suggest the degree and thedirection of correlation.
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Karl Pearsons coefficient of

correlation It gives the numerical expression for the

measure of correlation. it is noted by r . Thevalue of r gives the magnitude of correlation and sign denotes its direction.

Formula for coefficient of correlation writtenon white board


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E.G. ( CALCULATION OF KARL PEARSONSCOEFFICIENT OF CORRELATION)

CALCULATE THE KARL PEARSONSCOEFFICIENT OF CORRELATION FROM THEFOLLOWING DATA

X 100 200 300 400 500 600 700

y 30 50 60 80 100 110 130


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x dx d x y dy d y dx.d y

100 30

200 50

300 60400 80

500 100

600 110

700 130


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E.G. (KARL PEARSONS COEFFICIENT OFCORRELATION)

A COMPANY GIVES ON THE JOB TRANING TO ITSSALESMEN,FOLLOWED BY A TEST.

IT IS CONSIDERING WHETHER IT SHOULD TERMINATETHE SERVICES OF ANY SALESMAN WHO DOES NOT DO

WELL IN THE TEST. FOLLOWING DATA GIVE THE TEST SCORES AND SALES

(IN 1000 Rs ) MADE BY NINE SALES MEN DURING LASTONE YEAR.

COMPUTE COEFFICIENT OF CORRELATION BETWEENTEST SCORES & SALES.

DOES IT INDICATE TERMINATION OF SERVICES OFSALESMEN WITH LOW SCORES IS JUSTIFIED.


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TESTSCORES(X)

dx d x SALES( in 1000Rs) (Y)

dy d y dx.d y

14 3119 3624 48

21 3726 5022 45

15 3320 4119 39


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Spearmans rank Correlation This method is applied to measure the association

when only THE ORDINAL OR RANK DATA is available In other words this method is applied in a situation in

which quantitative measures of certain qualitativefactors such as judgement, TV programs, color etccannot be fixed but observations can be arranged in adefinite order.

We start with rank 1 for either in terms of quantity orquality.

Formula for coefficient of correlation WRITTEN ONWHITE BOARD


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E.G. ( SPEARMANS COEFF OFCORRELATION)

THE RANKING OF 10 STUDENTS INACCORDANCE WITH THEIR PERFORMANCE INTWO SUBJECTS A & B ARE GIVEN BELOW.CALCULATE RANK CORRELATION COEFFICIENT

A 6 5 3 10 2 4 9 7 8 1

B 3 8 4 9 1 6 10 7 5 2

RANK 1 RANK 2 d R1 R2 d


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RANK 1(R1)

RANK 2(R2)

d= R1-R2 d

6 3

5 83 4

10 9

2 14 69 10

7 78 51 2

E G ( SPEARMANS COEFFICIENT OF


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E.G. ( SPEARMANS COEFFICIENT OFCORRELATION)

CALCULATE SPEARMA NS COEFF OF CORRELATION BETWEENMARKS ASSIGNED TO TEN STUDENTS BY JUDGES X & Y IN ACERTAIN COMPETITIVE TEST

STUDENT MARKS BY JUDGEX

MARKS BY JUDGE Y

1 52 65

2 53 68

3 42 43

4 60 38

5 45 776 41 48

7 37 35

8 38 30

9 25 2510 27 50


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MARKSBYJUDGE X

RANK 1 MARKSBYJUDGE Y

RANK 2 d=R1-R2 d

52 6553 68

42 43

60 38

45 77

41 48

37 35

38 3025 25

27 50


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Thank you

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