### Spearman’s correlation: an example from RFP proposal evaluators and their ordered ranking of law firms

The best known type of correlation is known as Pearson’s correlation, which tells how much one series of numbers varies as another series varies (See my post of Nov. 9, 2009 #3: varieties of correlation tests for various circumstances.). For example, a general counsel could calculate the correlation between months elapsed of lawsuits and total payments to law firms.

Another situation where correlations can be useful is if two or more people rank something and you want to assess the degree of correlation. For that, the Spearman correlation can treat the ordered data. As explained in Tony Cilly’s book, 50 mathematical ideas you really need to know (Quercus 2007) at 144, if several lawyers rank order a group of law firms that have submitted proposals, Spearman’s correlation coefficient describes the level of agreement among the lawyers.

Let’s say there are six lawyers and seven proposals. Each lawyer gives a 1 to the best proposal on down to a seven for the worst. Email me if you would like the formula. Meanwhile, I will walk you through it.

Take one lawyer’s rank number for a firm and subtract the other lawyer’s rank, then square the result. The sum of those seven squares is multiplied by 6 to complete the numerator. Let’s say that sum is 30. You then divide 180 (6*30) by the denominator: 6 multiplied by (6 squared minus 1) or 6 times 35 equals 210, which is .8. As the last step, subtract that from 1. At 0.14, the Spearman correlation of those two lawyers is low. Clearly they have different criteria in mind, or different weightings, or something else pushed them apart.

You can also do this with figures in different realms, like pages of patent applications compared to translation costs. To do this, you sort pages and assign ranks and sort costs and assign ranks. Then calculate the Spearman correlation for the two rankings.