Rank correlation

Rank correlation

1. Rank Correlation NADEEM UDDIN ASSOCIATE PROFESSOR OF STATISTICS

2. Rank Correlation:- There are many situations where numerical values are not available , but data have been a ssembled in a relative order, the best being in the first rank, the second best next and so on . OR Some time it is not possible to measure certain variable, but it is possible to arrange them in order.

3. For Example If two coffee flavor experts were asked to place 5 coffee flavor in order of preference, they would rank the five coffee flavor in order, using the number 1,2,3,4,5 . The flavor they liked best would be ranked 1. The flavor they liked least would be ranked 5.

4. The formula for correlation between ranking of two sets of data is called Rank Correlation or Spearman’s Coefficient of Rank Correlation. It is denoted by r s .   Where ‘d’ is the difference in ranking between the two sets of observations and ‘n’ is the number of data pairs.  

5. Example-1: The following table shows ten students were ranked according to their performance in their class work and their final examinations. We want to find out whether there is a relationship between the accomplishment of the students during the whole year and their performance in their exams.

6. Solution : Students Ranking based on class work (x) Ranking based on exam marks (y) Difference d d 2 A 2 1 1 1 B 5 6 -1 1 C 6 4 2 4 D 1 2 -1 1 E 4 3 1 1 F 10 7 3 9 G 7 8 -1 1 H 9 10 -1 1 I 3 5 -2 4 J 8 9 -1 1 SUM       ∑ d 2 =24

7. The rank correlation coefficient is: 1  

8. Comments : The high value of the rank correlation coefficient indicates that there is a close relationship between class work and exam performance.

9. Example-2: The marks of eight candidates in Accounting and Statistics are : Candidate 1 2 3 4 5 6 7 8 Accounting 50 58 35 86 76 43 40 60 Statistics 65 72 54 82 32 74 40 53

10. Solution: In this question ranking is not given. So we take highest mark as rank 1 and next highest mark as rank 2 and so on. Candi -dates Accoun-ting Statistics Rank Accounting (R1) Rank Statistics (R2) Difference d =R1-R2   1 50 65 5 4 1 1 2 58 72 4 3 1 1 3 35 54 8 5 3 9 4 86 82 1 1 5 76 32 2 8 -6 36 6 43 74 6 2 4 16 7 40 40 7 7 8 60 53 3 6 -3 9 SUM           ∑d 2 =72 Candi -dates Accoun-ting Statistics Rank Accounting (R1) Rank Statistics (R2) Difference d =R1-R2 1 50 65 5 4 1 1 2 58 72 4 3 1 1 3 35 54 8 5 3 9 4 86 82 1 1 5 76 32 2 8 -6 36 6 43 74 6 2 4 16 7 40 40 7 7 8 60 53 3 6 -3 9 SUM           ∑d 2 =72

11.   Very low degree of positive correlation .