In an earlier post, I described rank order centroids, and their relationship to software testing. The basic problem, for which rank order centroids provide one solution, is to transform ranks (such as 1st, 2nd, 3rd, and so forth) into a set of rating metrics which sum to 1.0. For example, in my post on rank order centroids, if there were five items ranked 1st through 5th, then the corresponding ratings for the four items are 0.5208, 0.2708, 0.1458, and 0.0625. Let me describe a less sophisticated, but valid, alternate technique to convert ranks to ratings normalized on a [0.0 to 1.0] scale. This other technique is called rank sum weights (RSW), or equi-interval weights (EIW). It is easily explained by example. Suppose we have five items, A, B, C, D, E ranked 1st, 2nd, 3rd, 4th, 5th respectively. To compute rank sum weights, you sum the ranks (1 + 2 + 3 + 4 + 5 = 15), then divide each rank complement by the sum. So, A: 5 / 15 = 0.3333 and B: 4 / 15 = 0.2667 and C: 3 / 15 = 0.2000 and D: 2 / 15 = 0.1333 and E: 1 / 15 = 0.0667. Easy! Notice that the interval between each rating is the same (0.0667) which is why the technique can be called an equi-interval weight. To summarize:

Item Rank ROC RSW

============================

A 1st 0.4567 0.3333

B 2nd 0.2567 0.2667

C 3rd 0.1567 0.2000

D 4th 0.0900 0.1333

E 5th 0.0400 0.0667

—————-

Sum 1.0000 1.0000

============================

A 1st 0.4567 0.3333

B 2nd 0.2567 0.2667

C 3rd 0.1567 0.2000

D 4th 0.0900 0.1333

E 5th 0.0400 0.0667

—————-

Sum 1.0000 1.0000

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