Dear all,
This is in response to the link to a student stats resource on "evening
the odds" pointed out on the list yesterday.
Am I the only one who thinks that - as it stands - the car accident
analogy to the Meadows case at that link is potentially creating more
confusion?
If I understand correctly, the Meadows case might be simplified as:
- M (correctly) points out that the two deaths are extremely unlikely
to be independent chance occurrences of SIDS, and are bound to have a
shared underlying cause;
- M (wrongly) privileges the hypothetical shared cause "killer parents"
without supporting evidence and in violation of the
innocent-until-proven principle over the hypothetical shared cause
"genetic disposition", which some medical evidence pointed to.
Of course in reality the debate was formulated in terms of the
probability of the second death being natural given the first death
etc. but I think the above is one reasonable way of distilling what it
boils down to. Moreover, it corresponds to the "thinking in underlying
causes" emphasis later on in the student resource.
Now what I find confusing in the traffic accident example as given is
the following:
- It is not made clear why the police think the clustering of accidents
imply they were caused by drunkenness. In other words, it is not
explained why four *other* drivers having an accident had any bearing
on the police questioning of the journalist.
An appeal to an underlying shared cause on the part of the police might
be something like "They must have all come from the same party.", but
none is provided.
Alternatively, without assuming dependence, if the reasoning is
supposed to have been: drunken accidents are more likely than no-fault
accidents, so if several accidents happen we have to assume some are of
the more likely (drunken) kind, then this is not made clear. In
particular, no appeal is made anywhere to different levels of
probability of various types of accidents. In any case the rest of the
discussion is in terms of the events being dependent.
- If it boils down to the police having acted as if they assumed the
"they're all party guests" cause, rather than the shared cause of
weather conditions, their mistake was *not* the multiplication of odds,
anymore than that was Meadows' mistake. His mistake as I see it was to
deny the hypothesis of "dependent cases of SIDS", not his rejection of
the hypothesis of "independent cases of SIDS". Likewise, the police
didn't make a mistake in multiplying the probabilities to conclude that
"something" had to be going on, but in concluding that "something" had
to be alcohol-related, rather than looking out the window.
Apologies if the confusion is mine rather than in the text!
Looking forward to hearing other people's thoughts on this.
Best,
Bilal.
******************************************************
Please note that if you press the 'Reply' button your
message will go only to the sender of this message.
If you want to reply to the whole list, use your mailer's
'Reply-to-All' button to send your message automatically
to [log in to unmask]
*******************************************************
|