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I'm not sure how to express my problem in proper semantic terms, so please forgive me if I am unclear, waffling or use the wrong terminology anywhere here! I'm trying to find a ranking system that will not only take into account the relative position of the data points, but also somehow factor in where their scores lie on a normal distribution. So for example, given the following data set, which we'll say represents the KPAs of 11 of my employees:

Name        Position        Score
----        --------        -----
Alf         1               97
Bert        2               95
Charlie     2               95
Dan         4               80
Ed          5               77
Frank       6               44
Gary        7               43
Hank        8               42
Ian         9               41
John        10              5
Kevin       11              4

If I just look at the order in which everyone appears, all that I have is a set of ranks from 1-11. It doesn't tell me if they're all flying high or all in deep trouble. We could say I should be rewarding anyone over a certain KPA score, arranging training for people in a certain band, and/or firing people below a certain score, but for the purposes of this exercise, let's say we're continually tweaking the KPA formulas, so we'll only really know what a "good", "mediocre" or "bad" score is when we see how people perform relative to each other. To give you an idea of what I'm going for: in the data set here, we have 3 high-flyers, 2 doing OK, 4 under-performers and 2 guys who probably need to be fired. I don't much care that Frank is in 6th position and Ian is 9th; their respective performance levels don't have much between them, and they both need to pick up their act.

Is there some formula or ranking system that would be able to rank these people as well as group them into bands or clusters of performance levels?

Shaul Behr
  • 131

1 Answers1

2

Ranking is a common problem in statistics. There is no absolute ranking system for any particular dataset. We want to specify how the model should rank these individuals.

+---------+----------+-------+------+
| Name    | Position | Score | Rank |
+---------+----------+-------+------+
| Alf     | 1        | 97    | 3    |
+---------+----------+-------+------+
| Bert    | 2        | 95    | 3    |
+---------+----------+-------+------+
| Charlie | 2        | 95    | 3    |
+---------+----------+-------+------+
| Dan     | 4        | 80    | 3    |
+---------+----------+-------+------+
| Ed      | 5        | 77    | 3    |
+---------+----------+-------+------+
| Frank   | 6        | 44    | 2    |
+---------+----------+-------+------+
| Gary    | 7        | 43    | 2    |
+---------+----------+-------+------+
| Hank    | 8        | 42    | 2    |
+---------+----------+-------+------+
| Ian     | 9        | 41    | 2    |
+---------+----------+-------+------+
| John    | 10       | 5     | 1    |
+---------+----------+-------+------+
| Kevin   | 11       | 4     | 1    |
+---------+----------+-------+------+

A Rank variable was defined and then linear regression was used to fit the values to the rankings.

+-------------+----------------+
| Observation | Predicted Rank |
+-------------+----------------+
| 1           | 3.181470043    |
+-------------+----------------+
| 2           | 3.136442248    |
+-------------+----------------+
| 3           | 3.136442248    |
+-------------+----------------+
| 4           | 2.798733786    |
+-------------+----------------+
| 5           | 2.731192094    |
+-------------+----------------+
| 6           | 1.988233477    |
+-------------+----------------+
| 7           | 1.96571958     |
+-------------+----------------+
| 8           | 1.943205683    |
+-------------+----------------+
| 9           | 1.920691785    |
+-------------+----------------+
| 10          | 1.110191476    |
+-------------+----------------+
| 11          | 1.087677579    |
+-------------+----------------+

Round off the values from the Predicted Rank variable.

targetXING
  • 79