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Topic: Milo said...
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Posts: 12
Registered: 1/30/05
Milo said...
Posted: Aug 8, 2006 9:15 AM
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Milo said:

Consider these phrases:
1. The percentage of men who are smokers
2. The percentage of men among smokers
This is the difference between P(Smoker|Man) and P(Man|Smoker)
where the vertical bar means "given that."

Consider these two statements:
3. Widows are more likely among suicides than widowers.
4. Widows are more likely to commit suicide than widowers.
The first compares P(Widow|Suicide) with P(Widower|Suicide).
The second compares P(Suicide|Widow) with P(Suicide|Widower).

Interestingly, with the exception of the use of the term "percentage",
these are not mathematical statements and can be understood, parsed,
demonstrated with diagrams, or otherwise understood with literate
skills only. In my view, having numerate skills neither adds nor
subtracts to the capability of a literate person to see the difference
between statements 1 & 2, and statements 3 & 4. If, however, the
sentences after the numbered items in both cases were the only
information provided with no hints, cues, or definition of the terms,
innumerate individuals would be unlikely to understand the difference.
In teaching math, we can assume (or not) literacy on the part of the
student, but if I state something "mathematical" and I see eyes rolling
back in the head, yawns, eruptions of discussions, 10 hands fly up in
the air, etc. then I think that I have to recast what I said in
understandable terms; I have to work to identify if it was the math or
the English (or both or just me!) that caused the lack of understanding
. later, mark

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