Example
Suppose we rank a group of five people by height and by weight:
| Person | A | B | C | D | E |
|---|---|---|---|---|---|
| Rank by Height | 1 | 2 | 3 | 4 | 5 |
| Rank by Weight | 3 | 4 | 1 | 2 | 5 |
Here person A is tallest and third-heaviest, and so on.
In order to calculate the Kendall tau distance, pair each person with every other person and count the number of times the values in list 1 are in the opposite order of the values in list 2.
| Pair | Height | Weight | Count |
|---|---|---|---|
| (A,B) | 1 < 2 | 3 < 4 | |
| (A,C) | 1 < 3 | 3 > 1 | X |
| (A,D) | 1 < 4 | 3 > 2 | X |
| (A,E) | 1 < 5 | 3 < 5 | |
| (B,C) | 2 < 3 | 4 > 1 | X |
| (B,D) | 2 < 4 | 4 > 2 | X |
| (B,E) | 2 < 5 | 4 < 5 | |
| (C,D) | 3 < 4 | 1 < 2 | |
| (C,E) | 3 < 5 | 1 < 5 | |
| (D,E) | 4 < 5 | 2 < 5 |
Since there are 4 pairs whose values are in opposite order, the Kendall tau distance is 4. The normalized Kendall tau distance is
A value of 0.4 indicates a somewhat low agreement in the rankings.
Read more about this topic: Kendall Tau Distance
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