<p><a href=“QM:”>quote</a> in response to your question whether the multiplicative approach is the only viable one for an individual applicant who is working with pH, pY and pP (as opposed to rH, rY, and rP): yes. I think so.
[/quote]
</p>
<p>I’m glad we agree on that much. However, the extent to which this is the “only viable option” is much, much stronger than you indicate. What is really true is that any mathematical model of the selection (whether deterministic, probabilistic, or some combination of the two) that lacks independence has to explicitly involve spooky actions at a distance.</p>
<p>
</p>
<p>It isn’t necessary to assume that probability plays any role. Independence must still hold: revealing Harvard’s (random or deterministic) decision about Joe’s application provides no information about Stanford’s (random or deterministic) decision. Any model of the selection process that lacks this feature forces Stanford’s decision algorithm to depend on variables that are specific to Harvard’s processing of Joe’s application, such as whether his application reader had a headache. </p>
<p>The obvious routes for information sharing — collusion, leaks, espionage, ED, athletic recruitment — were ruled out by assumption. Alternative channels are supernatural, and I assume you would agree that models involving telepathy can be deemed “not viable”.</p>
<p>
</p>
<p>Please note that tokenadult’s AP Stat teacher source was originally quoted in the form of an equation, i.e., “Prob[H and S] is not equal to Prob[H] Prob[S] because those aren’t independent events”, when clearly discussing single-applicant outcomes.</p>
<p>Please also note that as soon as the non-independence claims were posted in the first thread where this came up — see link above — the guy arguing with tokenadult (bob9775) called it out as nonsense and said that he “questioned the teacher’s expertise”. It is a professionally disqualifying level of nonsense for someone whose job is to teach statistics, as it indicates a serious confusion about basics, such as the difference between probability and statistical inference. </p>
<p>We have had this nonsense served up for several years now as authoritative, FAQ-ed, statistically certified truth. There has been no retraction of any specific nonsensical, incorrect or misleading statement out of all those that were pointed out (and in this particular case, analyzed well past the point where the error is made manifest). To the extent that reliability of information in this forum is important, it is important to make very clear which factual or mathematical claims here are correct, and which are not, with no room for equivocation that leaves the answers in doubt. </p>
<p>
</p>
<p>“Have you taken statistics?” and “my source is a stats teacher” are not what I would call interesting ideas at the math-to-English interface. As for your discussion of cross-admits and non-independence, I will post about it later.</p>