# Is there a name for this phenomenon in statistics?

#### bruin

##### New Member
TL;DR: If you have two normally distributed populations that are identical except that one of them has an advantage in its mean, then as you move to higher and higher scores, the population with the advantage in its mean will be more and more overrepresented the higher X gets. Is there a name for this?

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LONG VERSION:

Say you start with two populations: each normally distributed, same size, same standard deviation.

But pop2 has a higher mean than pop1 -- say, 1 SD higher.

Pick any reference score somewhere roughly around the means of the two populations. Say pop1 mean = 100 and pop2 mean = 110 so you start with X=100 as your reference score (since it's right at pop1 mean and relatively close to pop2 mean).

Using this reference score you can calculate the % of pop1 that should be above this reference score, as well as the same percentage for pop2.

Then you can calculate (% pop2 above X) / (sum(%pop2aboveX, %pop1aboveX)).

This will give you the % of scores above the reference score of X that derive from pop2.

Now, as you move your reference score, X, higher and higher, you'll see that the % of scores above the reference score of X, that derive from pop2 continually and dramatically increases.

Here's a screenshot of some quick excel calculations that demonstrate what I am talking about.

Is there a name for this phenomenon?

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