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QUESTION

Spearman's rank correlation coefficient

THIS IS AIMED AT ENABLING A STUDENT TO CALCULATE THE SPEARMAN'S RANK CORRELATION COEFFICIENT FROM GIVEN DATA AND TO RELATE IT TO BUSINESS AS AN AREA OF APPLICATION.

CASE 1: RANKING NON-REPEATING DATA

CASE 2: RANKING REPEATING DATA

CASE 3: LINK BETWEEN SPEARMAN RANK AND BUSINESS PROFITS

1.      (a) What do you understand by the word correlation?

(b)Explain with examples the types of correlation.

(c) State and explain the formula used to calculate spearman’s rank correlation coefficient.

(d)(i)Calculate the square of deviation between the given variables in the table below.

P

Q

12

11

32

24

14

65

25

23

16

27

09

18

(ii)  Write the rank of X and of Y of the given table

X

Y

29

24

34

44

29

24

11

24

13

35

(e) Copy and fill the comments column of the tables below that have the range of spearman’s rank correlation coefficient values.

(i)

RANK

COMMENT

0 – 0.19

0.2 – 0.39

0.4 – 0.59

0.6 – 0.79

0.8 – 0.999

(ii)

RANK

COMMENT

-0 to -0.19

-0.2 to -0.39

-0.4 to -0.59

-0.6 to -0.79

-0.8 to -0.999

(f) Below is a table showing the quantity of two commodities sold within eight days.

Use it to answer the questions that follow.

Week

1

2

3

4

5

6

7

8

Commodity1

200

150

180

60

190

210

160

75

Commodity2

300

80

110

200

70

48

90

120

Profits($)

9000

3850

4350

4900

4250

4110

4200

3525

            By calculating the spearman’s rank correlation coefficient, find and explain the relationship between.

(i)                 Commodity 1 and commodity 2

(ii)               Commodity 1 and profits

(iii)             Commodity 2 and profits

(g) Using the table in (f) above, calculate the profit made from selling a single commodity of each.

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