Probability/Chance up if applying more Ivies schools?

[siserune]

<p><a href=“mazewanderer:”>quote</a></p>

<p>2) Even with this the multiplicative approach is the correct statistical approach. Statistically the confidence interval (in laypersons terms though not really correct, the margin of error) will be very wide. Generally one would expect that multiplicative approach will lead to over stating of the results, and you will not have confidence in the results due to the introduced bias and the wide margin of error.

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<p>Given that non-multiplicative approaches invoke supernatural forces, (a) I don’t think there is any alternative method of modelling, and (b) the more stable, more reliably estimated and strategically informative quantity is the expected number of acceptances. This is just the sum of the acceptance probabilities, whether those are assumed, estimated, modelled, guessed or prayed for. It is also completely oblivious to the presence or absence of correlations, in case one prefers the ghosts and goblins.</p>

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3. There is so much of subjectivity and unknowns in the admission process that one would never be able to estimate the probability itself i.e. the probability of admission itself is an estimate, which compounds the error.

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<p>Wouldn’t a quick calculation based on best-, middle- and worst-case sets of acceptance probabilities (even just a single probability when dealing with similar schools, such as Ivy League) tell you most of what you need to know? Probabilities are also available from online chances calculators based on databases of hundreds of self-reported applicants (at each school) who give their SAT and GPA and other data together with the outcomes. Crude but far from uninformative.</p>

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At the low level, probabilities are still multiplicative but appear to be close enough to considered additive. At 1% level applying to 3 schools increases your probability to 2.97% (close enough to 3)

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<p>By “probabilities are additive at the low end” I meant that the expected value (sum of probabilities) is almost the same as the probability of one or more acceptances, which was the thing we are supposedly most interested in. This is because multiple acceptances (which account for the difference between the two calculations) are rare enough to ignore, and that rarity is due to independence. I’m sure you knew this but it doesn’t hurt to say it in more detail.</p>

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Generally one would expect that multiplicative approach will lead to over stating of the results, and you will not have confidence in the results due to the introduced bias and the wide margin of error.

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<p>Mult approach compared to what other approach? If you really care about bias you can simulate the presumed distributions, and relatively simple R code for this can be posted to CC if anyone cares to code something up.</p>