{"id":6487,"date":"2021-10-30T07:40:34","date_gmt":"2021-10-30T07:40:34","guid":{"rendered":"https:\/\/www.goseeko.com\/blog\/?p=4617"},"modified":"2025-11-12T18:40:02","modified_gmt":"2025-11-12T13:10:02","slug":"what-is-rank-correlation","status":"publish","type":"post","link":"https:\/\/www.goseeko.com\/blog\/what-is-rank-correlation\/","title":{"rendered":"What is rank correlation?"},"content":{"rendered":"\n

Overview<\/strong>(rank correlation)<\/h2>\n\n\n\n

A group of n individuals may be arranged in order to merit with respect to some characteristics. The same group would give different orders for different characteristics. Considering the orders corresponding to two characteristics A and B, the correction between these n pairs of rank is called the rank correlation <\/a>in the characteristics A and B for that group of individuals.<\/p>\n\n\n\n

formula<\/h2>\n\n\n\n

Let be the ranks of  individuals corresponding to two characteristics.<\/p>\n\n\n\n

Assuming nor two individuals are equal in either classification, each individual takes the values 1, 2, 3,  and hence their arithmetic means are, each<\/p>\n\n\n\n

\"\"\/<\/figure>\n\n\n\n

Suppose that be the values of variable X  and those of Y.<\/p>\n\n\n\n

Then<\/p>\n\n\n\n

\"\"\/<\/figure>\n\n\n\n

Here X and Y are deviations from the mean.<\/p>\n\n\n\n

\"\"\/<\/figure>\n\n\n\n
\"\"\/<\/figure>\n\n\n\n

Which is called the rank correlation or Spearman\u2019s rank correlation coefficient and we denote it by Rho <\/p>\n\n\n\n

Solved examples<\/h2>\n\n\n\n

Example: Compute Spearman\u2019s rank correlation coefficient r for the following data:<\/strong><\/p>\n\n\n\n

Person<\/strong><\/td>A<\/strong><\/td>B<\/strong><\/td>C<\/strong><\/td>D<\/strong><\/td>E<\/strong><\/td>F<\/strong><\/td>G<\/strong><\/td>H<\/strong><\/td>I<\/strong><\/td>J<\/strong><\/td><\/tr>
Rank Statistics<\/strong><\/td>9<\/strong><\/td>10<\/strong><\/td>6<\/strong><\/td>5<\/strong><\/td>7<\/strong><\/td>2<\/strong><\/td>4<\/strong><\/td>8<\/strong><\/td>1<\/strong><\/td>3<\/strong><\/td><\/tr>
Rank in income<\/strong><\/td>1<\/strong><\/td>2<\/strong><\/td>3<\/strong><\/td>4<\/strong><\/td>5<\/strong><\/td>6<\/strong><\/td>7<\/strong><\/td>8<\/strong><\/td>9<\/strong><\/td>10<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

Solution:<\/strong><\/p>\n\n\n\n

Person<\/td>Rank Statistics<\/td>Rank in income<\/td>d= R1 – R2<\/td><\/td><\/tr>
A<\/td>9<\/td>1<\/td>8<\/td>64<\/td><\/tr>
B<\/td>10<\/td>2<\/td>8<\/td>64<\/td><\/tr>
C<\/td>6<\/td>3<\/td>3<\/td>9<\/td><\/tr>
D<\/td>5<\/td>4<\/td>1<\/td>1<\/td><\/tr>
E<\/td>7<\/td>5<\/td>2<\/td>4<\/td><\/tr>
F<\/td>2<\/td>6<\/td>-4<\/td>16<\/td><\/tr>
G<\/td>4<\/td>7<\/td>-3<\/td>9<\/td><\/tr>
H<\/td>8<\/td>8<\/td>0<\/td>0<\/td><\/tr>
I<\/td>1<\/td>9<\/td>-8<\/td>64<\/td><\/tr>
J<\/td>3<\/td>10<\/td>-7<\/td>49<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n
\n
\"\"\/<\/figure><\/div>\n\n\n

Example. Three judges A,B,C give the following ranks. Find which pair of judges has common approach<\/strong><\/p>\n\n\n\n

A 1 6 5 10 3 2 4 9 7 8<\/strong><\/p>\n\n\n\n

B 3 5 8 4 7 10 2<\/span> 1 <\/b><\/span> 6 <\/b><\/span> 9<\/b><\/span><\/strong><\/p>\n\n\n\n

C 6 4 9 8 1 2 3 10 5 7<\/strong><\/p>\n\n\n\n

Solution<\/strong><\/p>\n\n\n\n

Here n = ten, so that we get the following table,<\/p>\n\n\n\n

A (=x)<\/td>Ranks byB(=y)<\/td>C (=z)<\/td>d1 =   x-y<\/td>d2 =  y – z<\/td>  d3 = z-x<\/td><\/td><\/td><\/td><\/tr>
1<\/td>3<\/td>6<\/td>-2<\/td>-3<\/td>5<\/td>4<\/td>9<\/td>25<\/td><\/tr>
6<\/td>5<\/td>4<\/td>1<\/td>1<\/td>-2<\/td>1<\/td>1<\/td>4<\/td><\/tr>
5<\/td>8<\/td>9<\/td>-3<\/td>-1<\/td>4<\/td>9<\/td>1<\/td>16<\/td><\/tr>
10<\/td>4<\/td>8<\/td>6<\/td>-4<\/td>-2<\/td>36<\/td>16<\/td>4<\/td><\/tr>
3<\/td>7<\/td>1<\/td>-4<\/td>6<\/td>-2<\/td>16<\/td>36<\/td>4<\/td><\/tr>
2<\/td>10<\/td>2<\/td>-8<\/td>8<\/td>0<\/td>64<\/td>64<\/td>0<\/td><\/tr>
4<\/td>2<\/td>3<\/td>2<\/td>-1<\/td>-1<\/td>4<\/td>1<\/td>1<\/td><\/tr>
9<\/td>1<\/td>10<\/td>8<\/td>-9<\/td>1<\/td>64<\/td>81<\/td>1<\/td><\/tr>
7<\/td>6<\/td>5<\/td>1<\/td>1<\/td>-2<\/td>1<\/td>1<\/td>4<\/td><\/tr>
8<\/td>9<\/td>7<\/td>-1<\/td>2<\/td>-1<\/td>1<\/td>4<\/td>1<\/td><\/tr>
Total<\/td> <\/td> <\/td>0<\/td>0<\/td>0<\/td>200<\/td>214<\/td>60<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

.<\/p>\n\n\n\n

Since is maximum, so that the pair of judge A and C have the nearest common approach.<\/p>\n\n\n\n

Interested in learning about similar topics? Here are a few hand-picked blogs for you!<\/strong><\/p>\n\n\n\n