Making scores comparable

Assume that we have feedback on team members from two different project managers.

People-> U V W X Y Z
Managers |
A 70 63 82 91 56 77
B 68 60 80 80 55 60

Can we say that W performs better in team A compared to team B? It looks like yes, he works better but analyse the scores a bit deeper. Project manager B has rated all team members lower than manager A. It may be that he is using tighter scoring.

In a different situation, it may be that two teams (of different people) have gone through two different tests, and we want to compare the people against others. Or, a university might want to compare people passed out in 2001 with those passed out in 2009.

The question is, how do we compare people when the scores that we have do not use the same basis.

Bell Curve - CC Attribution License

Bell Curve - Created using HSB Grapher

The answer is: normalization. We fix the mean score, and the degree of deviation that we would like to see. For a 100 marks test, we may want 50 as the score and a 20% deviation. Now, we will compare this with the actual mean and the deviation of each of the sets, and modify the scores as needed. Please refer to the attached spreadsheet which helps you do this.

 

 

 

In the given example, A has a mean of 73, and a deviation of 13. B has a mean of 67 and a deviation of 11. Let us bring both to a mean of 70 and a deviation of 15.

People-> U V W X Y Z
Managers |
A 66.3 58.1 80.4 91 49.9 74.5
B 71.2 60 87.9 87.9 53.1 60

So we note that A is indeed better in project A, but only slightly. Also from the initial figures we might have concluded that U is better in Project A, but actually the reverse is true.

Mathematically this process is called Normalization and is useful in fitting scores to a bell curve. Read more about it here if you are interested. However the spreadsheet attached is sufficient to get you started.

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One Response to “ Making scores comparable ”

  1. [...] have written about normalization before. I believe the use of this technique would have yielded more fair results. Normalization [...]

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