Friday, 30 December 2011

Calculation of Pearson's Coefficient of Correlation

Direct Method No. 1

The steps involved are as follows:

(1) Find the means of the two series (X and y1)

(2) Find the deviations of each item of a series from its mean (x and y). Here x = (X—X) and = (Y- Y)

(3) Square these deviations and total them (∑x2 and ∑y2).

(4) Multiply the respective deviations of the two series and total them (∑xy)

(5) Substitute the above values in the following formula:

r = (∑xy)/(√(n&(∑x2)/n )× √((∑y2)/n))=(∑xy)/(nσ1 σ2 )

r = (∑xy)/√(∑x2×∑y2 )

Solved Example :Calculate the coefficient of correlation from the following data by the Spearman's Rank Differences method:


Prices of

Prices of

Prices of

Prices of
Tea ($)

Coffee ($)

Tea ($)

Coffee ($)
75

120

60

110
88

134

80

140
95

150

81

142
70

115

50

100

Solution: Calculation of Coefficient of Rank Correlation

Prices of Tea
(X)



R1


Prices of
Coffee
(Y)



R2



R1 R2
(d)



d2
75

4

120

4

0

0
83

7

134

5

+2

4
95

8

150

8

0

0
70

3

115

3

0

0
60

2

110

2

0

0
80

5

140

6

—1

1
81

6

142

7

—1

1
50

1

100

1

0

0

n = 8



n = 8



0


∑d2 = 6

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