Page 178 - DECO504_STATISTICAL_METHODS_IN_ECONOMICS_ENGLISH

Statistical Methods in Economics

Notes Example 5: (a) Calculate the coefficient of rank correlation from the following data:

X : 48 33 40 9 16 16 65 24 16 57

Y : 13 13 24 6 15 4 20 9 6 19

Solution: Calculation of Rank Correlation Coefficient

X R Y R (R – R ) D 2
2
1 2 1 2
48 8 13 5.5 6.25
33 6 13 5.5 0.25
40 7 24 10 9.00
9 1 6 2.5 2.25
16 3 15 7 16.00
16 3 4 1 4.00
65 10 20 9 1.00
24 5 9 4 1.00
16 3 6 2.5 0.25
57 9 19 8 1.00
∑D = 41
2

∑ 6 2 +D 1 ( { 3 −m ) + 1 ( m 3 −m ) + 1 ( m 3 −m m ) }
R= − 12 12 12
1
N 3 − N
Since item 6 is repeated 3 times in series X, m = 3. Since items 13 is repeated twice and
6 is repeated twice in case of series Y, m shall be 2 in each case. Hence:

1 ( { 1 1 }
+ 641 3 − 3 ) ( +3 3 − 2 ) ( +2 3 − 2 ) 2
1
R= − 12 12 12
10 3 − 10
( ++ + ) 6 412 0.50.5 264
= −1 = −1 = 1 – 0.267 = 0.733.
990 990
Example 6: (b) Calculate the rank coefficient of correlation of the following data:
X : 80 78 75 75 68 67 60 59

Y : 12 13 14 14 14 16 15 17

Solution:
Calculation of Rank Correlation
X R Y R (R – R ) D 2
2
x y x y
80 8 12 1 49.00
78 7 13 2 25.00
75 5.5 14 4 2.25

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