Comments for Platitudes in Stained-glass Attitudes

Comment on Name that work by sainthereticus

sainthereticus — Mon, 06 Jul 2009 23:41:36 +0000

Sounds like the random Kant generator. But then again, Kant sounds like the random Kant generator, too.

Comment on This discussion cracks me up by Ignoramus

Ignoramus — Tue, 09 Jun 2009 14:20:48 +0000

This discussion depresses me. It must be the difference between your (mostly) choleric temperament and my (mostly) melancholic one.

Comment on Busy by Mike

Mike — Sun, 19 Apr 2009 03:14:24 +0000

heh. will do.

Comment on Mathematical puzzle by bunthorne

bunthorne — Fri, 27 Mar 2009 20:56:48 +0000

I deleted my first response because I was assuming 100,000 each of males and females.

The mistake is that you divided the number having the disease by the number who test positive. You need to divide the number who have the disease and test positive by the total number who test positive. This is because it is given that the result was positive, so you need to exclude the small fraction who have the disease but test negative anyway.

Comment on Mathematical puzzle by Dad

Dad — Fri, 27 Mar 2009 19:01:57 +0000

I assumed a population of 100000, equal male and female proportions. I got the probability of the person having the disease as 9/(((.98 x 5) + (.01 x 49995)) +((.98 x 4) + (.01 x 49996))) = .00892

What did I do wrong?

Comment on Mathematical puzzle by bunthorne

bunthorne — Mon, 23 Mar 2009 22:51:24 +0000

Regarding Joseph's comment, see this page for citation information for one of the original studies as well as many others.

Comment on Mathematical puzzle by Dominic

Dominic — Mon, 23 Mar 2009 21:50:44 +0000

Good question. I just reworked the problem, using the same method as before, but the result I got this time was 882 / 100873 (i.e, 1764 / 201746). I was working with a CAS so I must have mistyped a number and not noticed.

The formula I used was (1/2)*((1/10000 + 1/12500)*(98/100)) / ((1/2)*((1/10000 + 1/12500)*(98/100) + (9999/1000000 + 12499/1250000))).

Comment on Mathematical puzzle by bunthorne

bunthorne — Mon, 23 Mar 2009 16:14:45 +0000

Let’s say there are 20,000,000 people. Then there are 10,000,000 males and 10,000,000 females.

Males w/ Bayesitis (B) = 1,000
Females w/ B = 800

People w/ B = 1800

People w/ B who test positive = 1,764
People w/ B who test negative = 36

People w/o B = 19,998,200
People w/o B who test positive = 199,982
People w/o B who test negative = 19,798,218

Probability that someone who tests positive has the disease = number who have it and test positive / total number who test positive = 1764 / (199,982+1764) = 1764 / 201746 = ~0.0087436677

How did you get that ratio, Dominic?

Comment on Mathematical puzzle by Dominic

Dominic — Mon, 23 Mar 2009 05:17:02 +0000

I got the first probability as ~ .0087427…, the ratio being 1112006 / 127191909.

For the second probability I got the same result as above.

Comment on Mathematical puzzle by Louis

Louis — Sun, 22 Mar 2009 15:30:16 +0000

1) What is the probability that the person has the disease?

~.0087436

2) What is the probability that the person is male?

~.5004808

It is clear without even doing the exact calculations that the probability of the person having the disease must be rather low, since only 1 out of every 10000th person at the most has the disease, and the test showing positive can only make it about 100 times more probable; hence the probability cannot be above 1%.

You can also think about this problem by considering what the overall test results would be if everyone in the population was tested.

This also implies that the test is almost worthless if you do not have any other information to gauge whether you have the disease, since regardless of whether the result is negative or positive the probability is so small that you actually have the disease that in most cases it wouldn’t matter.