Page 186 - DCOM203_DMGT204_QUANTITATIVE_TECHNIQUES_I

Unit 8: Correlation Analysis

15. A ............................rank correlation implies that a high (low) rank of an individual according Notes
to one characteristic is accompanied by its high (low) rank according to the other.
(a) Positive (b) Negative

(c) Neutral (d) Zero

Case Study Rank Correlation

teacher ranked seven of his pupils according to their academic achievement. The
order of achievement from high to low, together with family income of each
Apupil is given as follows:
Ray ( 9,200), Bhatnagar ( 4,500), Kaul ( 6,500), Das ( 8,000), Aggarwal ( 27,000), Banerjee
( 17,500) and Kannan ( 16,700). Compute rank correlation between academic achievement
and family income.

8.3 Summary

Summary of Formulae

n X Y X i Y i
i i
r (without deviations)
2 2
2 2
n X X n Y Y
i i i i
X i X Y i Y
r
2 2 (when deviations are taken from means)
X i X Y i Y
X - A Y - B
n u v u v i i
i i i i u = and v =
r , where i i
2 2 h k
n u 2 i u i n v i 2 v i
N f u v f u f v j
ij i j
j
i i
r , where N f ij
2 2
2 2
N f u f u N f v j f v j
i i
j
i i
j
2
1- r
Standard Error of r =
n
Probable Error of r = 0.6745 × SE
r
6 d i 2
1 (when ranks are not repeated)
n n 2 1
2 1 2 1
6 2 
12 12
1 (repeated ranks)
2
1

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