Re: [Paddlewise] swim for it?

Thank you Brad for illuminating one of my pet peeves of popularly applied
probability.

DuCharme's paper mentioned in the article is available at:
http://article.pubs.nrc-cnrc.gc.ca/ppv/RPViewDoc?_handler_=HandleInitialGet&journal=apnm&volume=32&calyLang=eng&articleFile=h07-042.pdf
(search for 60%)

My first hope was that the journalist misinterpreted something written in
the paper. But no, the article is true to DuCharme's exposition. My next
hope was that DuCharme blindly copied someone else's analysis, but this
turns out not to be so. His source is also available:

http://www.redcross.ca/cmslib/general/ws_final_m2_english2006_04_19.pdf
(Search for "VICTIM & SURVIVOR RESPONSES TO IMMERSION")

As it turns out, the 2006 Drowning Report lists, for victims and surivors
who had the choice, how many swam immediately, swam after a delay, and
stayed with the boat. Using the raw totals, here are the relevant results:
P{survive} = 0.53  (81 survivors, 72 victims)
P{survive | swim immediately} = 0.51
P{survive | swim after a delay} = 0.53
P{survive | stay with the boat} = 0.55

I haven't done the statistics, but I'm guessing that the small variation in
these numbers with a relatively small sample is not statistically
significant, so no claim can be made as to which course of action gives the
best chance of survival. (Of course, the real answer is that this is
situation dependent and must include information like, proximity to shore,
swimming ability, PFD, clothing, etc.)

While the drowning report does not report the numbers exactly as Brad
suggested, it also does not report them as DuCharme did - so he must be held
accountable for twisting his Bayesian inference all by himself.

As for whether you should swim or stay, you'll have to decide that based on
the conditions.

-Mark

PS - The good news is that of all types of boating victims, only 3% were
kayakers, making kayaks safer than rowboats, canoes or even large powerboats
(22%) (and yes, I'm kidding)

On Nov 8, 2007 6:59 PM, Bradford R. Crain <crainb_at_pdx.edu> wrote:

>   I would assume we are interested in the conditional probability of
> survival, given that the individual swam. We would also be interested
> in the conditional probability of survival, given the individual stayed
> with the boat.
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