Page 184 - DCOM203_DMGT204_QUANTITATIVE_TECHNIQUES_I

Unit 8: Correlation Analysis

Solution: Notes
Calculation Table

2
From the above table, we have d i 16.
2
6 d i 6 16
Rank Correlation 1 2 1 0.903
n n 1 10 99

Example: Calculate the Spearman's rank correlation coefficient between the series A and
B given below:
Series A : 57 59 62 63 64 65 55 58 57
Series B : 113 117 126 126 130 129 111 116 112

Solution:
Calculation Table
( ) Rank of ( ) Rank of
X
Y
Series A Series B d i X i Y i d i 2
Series A Series B
57 113 2.5 3 0.5 0.25
59 117 5 5 0 0
62 126 6 6.5 0.5 0.25
63 126 7 6.5 0.5 0.25
64 130 8 9 1 1.00
65 129 9 8 1 1.00
55 111 1 1 0 0
58 116 4 4 0 0
57 112 2.5 2 0.5 0.25

d 2 3.00
From the above table, we get i
Since there are two ties and two observations are tied in each case, therefore, the correction
2 2 2
m m 1 m m 1 m m 1 2 4 1
factor will be 1
12 12 6 6
2
Thus, corrected d i 3.00 1 4.00

2
6 d i 6 4
Now, 1 2 1 0.967
n n 1 9 80

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