Question

Twenty operators are working in a particular department of a call centre. The longserving operators feel that they should have a promotion based on length of service built into their job structure. For assessment of their efficiency, the personnel department produces a score of efficiency based on various parameters. The efficiency scores along with their length of service are given below:

S. No. Length of Service Efficiency Scores
1 2 72
2 9 90
3 5 74
4 9 88
5 4 70
6 5 77
7 6 77
8 5 78
9 7 87
10 6 80
11 4 72
12 8 83
13 8 84
14 7 84
15 8 85
16 7 90
17 3 69
18 5 89
19 7 90
20 5 79

 Compute the Spearman’s rank correlation coefficient between the length of service and efficiency scores? Also compare this coefficient with Pearson’s correlation coefficient

06 Feb 2021
Answer :
Word Count : 1599

To compute the Spearman's rank correlation coefficient between the length of service and efficiency scores, we'll follow these steps:

1. Rank the data.
2. Calculate the differences between the ranks of length of service and efficiency scores.
3. Square the differences.
4. Sum up the squared differences.
5. Use the formula to calculate the Spearman's rank correlation coefficient.

Let's start by ranking the data:

Ranking Length of Service:

S. No.   Length of Service  Length of Service Rank
1         2                4
2         9                17
3         5                8
4         9                17
5         4                6
6         5                8
7         6                10
8         5                8
9         7                13
10        6                10
11        4                6
12        8                15
13        8                15
14        7                13
15        8                15
16        7                13
17        3                2
18        5                8
19        7                13
20        5                8

Ranking Efficiency Scores:

S. No.   Efficiency Scores  Efficiency Scores Rank
1         72                3
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Twenty operators are working in a particular department of a call centre. The longserving operators feel that they should have a promotion based on length of service built into their job structure. For assessment of their efficiency, the personnel department produces a score of efficiency based on various parameters. The efficiency scores along with their length of service are given below:

S. No. Length of Service Efficiency Scores
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