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Still quoting Niederman & Boyum:

<blockquote>The most common answer was 95 percent. The correct answer is 2 percent, and it was given by only 18 percent of the alleged medical experts.</blockquote>
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I think I understand the reasoning here, which I'll state in what I have just learned is a <I>frequentist</I> mode.

<font size=4>out of 1000 people:<font size=2>%BR%
1 person will have the disease (.1 percent)%BR%
50 will test positive, but will not have the disease (5% false positive rate%BR%

OK, here's my question:

What are we comparing when we come up with an answer of 2%? (And is 'comparing' the right word here?)

1/50%BR%
or%BR%
1/51%BR%

Both ratios give you a probability of 2%, obviously, but I want to know which ratio is correct. (And is it a ratio?! I'm finally beginning to read on [[http://math.berkeley.edu/~wu/][Hung Hsi Wu]], and I gather he says that ratios aren't fractions.)

Frankly, I have no idea what the precise relationship among 'percents,' 'rates,' and 'ratios' is. 

Both Ed and I feel that we ought to divide 1 by 51 in order to get the 'probability' that a person with a positive test has the disease--but are we confusing 'probability' with 'percent'?

I realize I don't know what the definition of probability is, apart from the standard 'probability that the outcome is not due to chance' definition I learned in psych courses in college.
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[[http://www.kitchentablemath.net/twiki/bin/view/Kitchen/FalsePositives][false positives]]%BR%
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-- Main.CatherineJohnson - 17 Aug 2005

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