Let me be specific :)
I have built a psychometric testing system. Let's say I have a test that measures only one trait, Extroversion, for example. (tests usually measure several traits at the same time, but I'll try to keep this to the essentials). Now, let's say that I measure a big group of people; men, women, lawyers, sales people, technologists, various education levels, etc. And I am, over time, able to come up with some 'norms' for the various groups. The mean and standard deviation of 'Extroversion' for the group 'Lawyers' is different than the mean and standard deviation of 'Extroversion' for the group 'technologists'. (Again, this is massive oversimplification, most of psychometric test validation is in the searching for which groups differ significantly from each other)

NOW, a group of people inside ABC Corp take this test and I'm able to derive a mean and standard deviation of 'Extroversion' scores for this new group. The goal of the excercise here is to find out which of MY norms most closely matches the ABC Corp group.

This all leads to the purpose of my matching script. I have two groups, represented by a mean and standard deviation, and I have to find out HOW alike they are. Preferably, I want to end up with an easy to understand representation of that match, a percentage, for example.

In the case of find out how a particular individual's scores match up, that is trivial, I actually use stanine representations of the scores. (the 1.75 sigma boundaries aren't arbitrary, they are the upper limit of a score of 8 and the lower limit of a score of 2 in the stanine scale)

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