Accounting Fundamentals

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CORRELATION TOOLS AND TECHNIQUES AFTERSCHO☺OL – DEVELOPING CHANGE MAKERS

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CORRELATION TOOLS AND TECHNIQUES

Dr. T.K. Jain.

AFTERSCHO☺OLCentre for social entrepreneurship

Bikaner M: 9414430763

[email protected]

www.afterschool.tk, www.afterschoool.tk


Calculate correlation based on 5 year moving average based shot term

oscillators from the following data:

• CLICK THE FOLLOWING LINK TO SEE THE EXCEL FILE WITH SOLUTIONS


Correlation between Rank and Placements is .6, N = 60, find the limits of population correlation?

• Formula of standard error :

• = (1- r^2) / sqrt (n)

• =(1- .36) / (sqrt(60))

• =.082

• Upper limit = .6 + .082 = .682

• Lower limit = .6 - .082 = .518 answer.


Rank Correlation

• Developed by SPEARMAN

• Formula:

• =1 – { 6∑d^2 / (n(n^2 -1))}

• D = difference between two ranks

• N = numer of pairs.

• Very easy and simple method for calculation of correlation.


Find rank correlation among the following

Name Height Weight

Amit 180 70

Giriraj 170 58

Dushyant 190 53

Nitin 166 51

Jayant 168 90


Solution

Name Height rank Weight

rankd =

(diff) d^2

Amit 180 2 70 2 0 0

Giriraj 170 3 58 3 0 0

Dushyant 190 1 53

4 -3 9

Nitin 166 5 51 5 0 0

Jayant 168 4 90 1 3 9

18


Next step : apply formula?

• =1 – { 6∑d^2 / (n(n^2 -1))}

• =1- {(6*18) / (5(25-1))}

• =1 - .9

• =.1 answer.


Find rank correlation in the following two series…

x rank y rank D d^2

50 9 110 8.5 0.5 0.3

55 6.5 110 8.5 -2 4

65 3.5 115 7 -4 12

50 9 125 4 5 25

55 6.5 140 2 4.5 20

60 5 115 7 -2 4

50 9 130 3 6 36

65 3.5 120 5 -2 2.3

70 2 115 7 -5 25

75 1 160 1 0 0

129


Solution

• Apply the formula…

• =1 – { 6∑d^2 + 1/12(m^3 –m) / (n(n^2 -1))}

• =1 – (6*129 + 1/12 (2^3 – 2)+1/12 (2^3-2) +1/12(3^3-3) +1/(2^3 -2)+1/12 (3^3 -3)/ (10 * (99))

• =1-.78

• =.22 answer.


Solution…

• M = number of pairs

• 1/12 is always used in this format only.

• We use as many 1/12 (m^3 –m) as there are pairs.


Example of negative correlation

Name Height rank Weight

rank d d^2

Amit 180 4 70 2 2 4

Giriraj 191 2 58 3 -1 1

Dushyant

190 3 534 -1 1

Nitin 192 1 51 5 -4 16

Jayant 168 5 90 1 4 16

38


Solution

• Here we can see that correlation is -.9

• Because when we apply the formula, we get 1 -1.9 = .9

• Thus here there is a negative correlation between the two values.

• Answer.


What is the level of correlation between the judgements of 2 judges?

candidate rank1 rank2 D D^2

SHARUKH 1 2 -1 1

DIPIKA 6 7 -1 1

SALMAN 7 3 4 16

KATRINA 3 1 2 4

AKSHAY 2 5 -3 9

PRIYANKA 4 4 0 0

IMRAN 5 6 -1 1

URMILA 10 10 0 0

KARINA 8 8 0 0

SAIF 9 9 0 0

RANK CORRELATION 0.19 0.81 32


CONCURRENT DEVIATION METHOD

• In this method we look at concurrent deviations in order to find correlation.

• The formula is : • R = + - sqrt (+ - (2c-n)/n)• C = concurrent deviations (plus signs)• N = number of pairs• R = correlation• It takes into account the direction only and

not the quantity of change.


Solution…

class varshadeviatio

n amit c

8 77 65

9 64 - 50 - +

10 67 + 40 - -

11 86 + 57 + +

12 74 - 47 - +

grad. 67 - 55 + -

3 plus


Apply to the formula

• R = + - sqrt (+ - (2c-n)/n)

• N = number of pairs compared

• R = + - sqrt(+ - (2*3 – 5/5)

• =+ - sqrt (1/5)

• =.45

• Thus correlation is .45 (positive) answer.


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only


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Accounting Fundamentals

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formula r

social development ngo

sqrt n

d rank y rank x