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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