SI
SI
discoversearch

We've detected that you're using an ad content blocking browser plug-in or feature. Ads provide a critical source of revenue to the continued operation of Silicon Investor.  We ask that you disable ad blocking while on Silicon Investor in the best interests of our community.  If you are not using an ad blocker but are still receiving this message, make sure your browser's tracking protection is set to the 'standard' level.
Strategies & Market Trends : ahhaha's ahs -- Ignore unavailable to you. Want to Upgrade?


To: M. Frank Greiffenstein who wrote (569)12/11/2000 5:06:05 PM
From: BilowRead Replies (1) | Respond to of 24758
 
Hi M. Frank Greiffenstein; Re: "Well, ahhaha is correct that an odds ratio is different than a probability."

I agree completely that an "odds ratio" is different than a probability. The guy who computed an odds ratio and used it as a probability is ahhaha, not I. What I've stated is that odds are ratios of probabilities, and this is something that you clearly agree with.

As an example, consider the odds of throwing a "1" with a die before getting any "even" roll. We will all (hopefully) agree that the odds of this are 3 to 1 against, as there are three "even" faces, and only one "1" face. Compare this to the ratio of the probabilities.

The probability of rolling a "1" is 1/6. The probability of rolling an "even" is 3/6 = 1/2. The ratio of the probabilities is 1/2 to 1/6, or 3 to 1. As we both agree, the odds are the ratio of the probabilities. By the way, this example also illustrates your point about "not necessarily exhaustive" occurrences.

In fact, ahhaha made exactly the error that you are describing. What Clarke wrote was that the "odds are 263 to 1", and ahhaha took this to mean that the probability was 1/263, for instance, this post: "The fraction 1/263 is the probability that Clark mentions." #reply-14981236 . In fact, Clarke never mentioned any "probability" what he mentioned were odds, and he gave these as 263 to 1: "odds against it are 263 to 1."
mitpress.mit.edu

The dictionary agrees with your (and my) understanding of odds, not ahhaha's:

Definition of Odds:
2. a.The ratio of the probability of an event's occurring to the probability of its not occurring.
dictionary.com

I also agree with your further comments on computation of odds ratios with conditional events. With conditional events, (such as the more likely to get cancer examples), again it does follow that the "odds" are the ratios of the probabilities. Again, I refer you to this (erroneous) post of ahhaha's: "Odds aren't ratios of probabilities." #reply-14981168. Instead of this statement, you and I will agree that "probabilities aren't ratios of odds."

-- Carl

Edit: Oops, sorry, it appears that ahhaha has sort of lefthandedly admitted that he had the wrong fraction...