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Unit 11: Rank Correlation Method


            Example 2:  Ten competitors in a beauty contest are ranked by three judges in the following  Notes
                        order:
                1  Judge          1     6     5     10    3     2     4    9     7     8
                 st
                2  Judge          3     5     8     4     7    10     9    1     6     9
                 nd
                3 Judge           6     4     9     8     1     6     3    10    5     7
                 rd
                        Use the rank correlation coefficient to determine which pair of judges has the nearest
                        approach to common tastes in beauty.
            Solution:   In order to find out which pair of judges has the nearest approach to common tastes
                        in beauty we compare Rank Correlation between the judgments of:
                        (i) 1  Judge and 2  Judge; (ii) 2  Judge and 3  Judge; (iii) 1  Judge and 3  Judge.
                                                                       st
                                                            rd
                                                nd
                           st
                                      nd
                                                                                  rd
                                COMPUTATION OF RANK CORRELATION
                  Rank by     Rank by    Rank by      (R  – R ) 2  (R  – R ) 2  (R  – R ) 2
                                                        1  2         2  3       1   3
                  1  Judge   2  Judge    3  Judge       D  2         D 2         D 2
                              nd
                                          rd
                   st
                    R           R           R
                      1          2           3
                     1           3          6            4            9          25
                     6           5          4            1            1          4
                     5           8          9            9            1          16
                    10           4          8            36          16          4
                     3           7          1            16          36          4
                     2          10          2            64          64          0
                     4           2          3            4            1          1
                     9           1          10           64          81          1
                     7           6          5            1            1          4
                     8           9          7            1            4          1

                   N = 10     N = 10      N = 10     ∑D 2   = 200  ∑D 2   = 214  ∑D 2   = 60

                        Rank correlation between the judgments of 1  and 2  Judge:
                                                                 nd
                                                           st
                                               6D  2
                                                ∑
                                        R=  −1
                                              N 3  − N
                                     ∑D 2  = 200, N = 10
                        Here we have directly calculated D  because D’s are not required in applying formula.
                                                   2
                                               6 × 200
                        ∴               R=   1 −
                                              10 3  − 10
                        (I and II)
                                              1200
                                          =  −1    = 1 – 1.212 = – 0.212
                                               990
                        Rank correlation between the judgments of 2  and 3  Judge:
                                                           nd
                                                                  rd
                                                ∑
                                               6D  2
                                        R=  −1
                                              N 3  − N

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