accounting fundamentals
TRANSCRIPT
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CORRELATION TOOLS AND TECHNIQUES AFTERSCHO☺OL – DEVELOPING CHANGE MAKERS
CENTRE FOR SOCIAL ENTREPRENEURSHIP PGPSE PROGRAMME –
World’ Most Comprehensive programme in social entrepreneurship & spiritual entrepreneurship
OPEN FOR ALL FREE FOR ALL
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CORRELATION TOOLS AND TECHNIQUES
Dr. T.K. Jain.
AFTERSCHO☺OLCentre for social entrepreneurship
Bikaner M: 9414430763
www.afterschool.tk, www.afterschoool.tk
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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
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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.
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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.
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Find rank correlation among the following
Name Height Weight
Amit 180 70
Giriraj 170 58
Dushyant 190 53
Nitin 166 51
Jayant 168 90
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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
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Next step : apply formula?
• =1 – { 6∑d^2 / (n(n^2 -1))}
• =1- {(6*18) / (5(25-1))}
• =1 - .9
• =.1 answer.
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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
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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.
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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.
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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
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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.
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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
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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.
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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
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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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