Am I an anomaly in the MBA Matrix?

This started out as a comment to Brit-Chick’s excellent post. Her discussion is on whether non-profit applicants have an easier time getting a B-school admit. Here is a statistical viewpoint: I think the only true test for this theory is the empirical results, i.e. by comparing the acceptance rates for each of the applicant pools. In practice, assuming deliberately engineered demographics, the probability for the typical applicant to be accepted would be the same as the acceptance rate for her pool (because she would not be competing outside her pool). In order for the admit probability of a non-profit applicant to be the same as that of a consultant, the acceptance rates for both categories should be the same. I am afraid that may not be the case since this throws the door wide open for manipulation (e.g. representative candidates in a pool egging on several under-qualified candidates to jump in to the fray – who knows, I might right now be a muppet, a drone, someone’s MBA cannon-fodder :-)). The acceptance rates across pools would therefore vary and thereby the probability for acceptance should follow suit. So what am I trying to prove (besides trying to sound like I know what I’m talking about)? Just that the degree of difficulty in getting an admission from one category versus another cannot be the same.

Taking this one step further (and no more I promise), let us look within the pool itself. When talking about the probability for a category, I assumed that this is uniformly distributed across all applicants in that category. In practice, this is not the case since there is variance within the pool itself. My ‘aha’ moment: so this is the ‘differentiation’ that we’ve been hearing about! So effectively the applicant has to jump two hurdles: acceptance probability within her pool and the variance hurdle again within her own pool.

Hey did I just state the obvious – very likely, it is 2 AM in this neck of the woods. But going back to BC’s discussion, I am using my variance argument and going out on a limb by stating that certain categories, yes non-profit for instance, have better ‘tangible’ variance intrinsically than say, bankers with the uniform perception of being crunching numbers. So while the acceptance probability hurdle may not be steep for the non-profit applicants, the variance one might be. Would this even things out for all applicants? I guess we would never know.