A conceptual issue on admissions probability

gadad
Fri, 25 May 2007 16:37:00 +0000

If you’ve taken any stats, help me think through this.

Prospective students want to know if they’ve covered their bases with an adequate assortment of targets, reaches and safeties in order to ensure that they aren’t left empty-handed at the end of the process. If they can accurately estimate their odds of acceptance to at least one of their top choices, they can avoid paying $65 a pop for unnecessary applications which amount to overkill.

The likelhood of a series of events ALL coming true is equal to each of their odds multiplied together. So the odds of flipping heads four times in a row is .50 x .50 x .50 x .50 = 6.25%. Accordingly, if you look at the acceptance rate for each of the colleges in which you’re interested, decide if you are above or below their mean, and estimate a percent likelihood of acceptance to that school, then you should be able to estimate the likelihood of acceptance to at least one of your chosen schools by multilying together the likelhoods of NON-acceptance at each. For example, if your estimated chances at your top five choices are 10%, 15%, 20%, 25%, and 30%, the odds of rejection resulting at ALL of them should be .90 x .85 x .80 x .75 x .70 = 32%, meaning that you have a 68% chance of getting into at least one of them (even though your chances at any one is no better than 30%). Unless . . .

Consider that the same individuals who apply to any one selective school also apply to several other selective schools. So the acceptance rates of your five schools above reflect numerous cases of the same individual being accepted to multiple schools. But does that really matter? After all, that individual can ultimately only attend a single institution, and since you just want a spot in an entering class, does your formula need to adjust for the schools at which that individual was admitted but didn’t choose? And are there any other conceptual shortcomings of this way of estimating odds that occur to you?