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# portefeuille (98.93)

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April 24, 2009 – Comments (13)

Assume you conduct breast cancer screening using mammography in a certain region. You know the following information about the women in this region:

* The probability that a woman has breast cancer is 1% (prevalence)
* If a woman has breast cancer, the probability that she tests positive is 90% (sensitivity)
* If a woman does not have breast cancer, the probability that she nevertheless tests positive is 9% (false-positive rate)

A woman tests positive. She wants to know from you whether that means that she has breast cancer for sure, or what the chances are. What is the best answer?

A. The probability that she has breast cancer is about 81%.
B. Out of 10 women with a positive mammogram, about 9
have breast cancer.
C. Out of 10 women with a positive mammogram, about 1 has
breast cancer.
D. The probability that she has breast cancer is about 1%.

answer: see p.55 here

The paper is about "Statistical Illiteracy" ...

#### 13 Comments – Post Your Own

#1) On April 26, 2009 at 3:57 PM, SurvivalInfo (< 20) wrote:

Why don't you give your blogs titles?  People might actually read them then.

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#2) On April 27, 2009 at 12:22 PM, madcowmonkey (< 20) wrote:

port- just saw your comment on Deej's blog. That was really the best comment on caps so far?

Anyway, task on hand says that .....C. Out of 10 women with a positive mammogram, about 1 has breast cancer. Probability isn't one of my favorite subjects though and I have been known to be wrong. I will check out the paper later, now it is time for Lunch.....actually it was time 22 minutes ago, but I got stuck haggling over a firewall and its set up.

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#3) On April 27, 2009 at 12:25 PM, portefeuille (98.93) wrote:

yes - C it is

maybe just the funniest ...

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#4) On April 27, 2009 at 2:12 PM, Tastylunch (28.53) wrote:

Ah Statisical Illiteracy goes right in hand with financial illiteracy 82.3% of the time ;-)

thanks for the link to the paper, looks interesting.

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#5) On April 27, 2009 at 2:25 PM, madcowmonkey (< 20) wrote:

So I checked out a little bit of the paper and the sentiment is true about doctors and stats (numbers). My wife and I ran into this when we were having our first child. The doctor explained to her that the hormone level that was indicated in one of the tests shows evidence of the baby possibly having downs. It sent fear into my wifes mind and she was immediately signing up for the next test to find the results. I had to call the doctor while she stepped out and ran to the bathroom to cry (she was at work). I found out that the probability was in the range of .002%. So, in my mind it should have never been brought up or it should have been explained correctly to my wife by somebody knowledgeable about women and their hormones during pregnancy. Regardless, we did another ultrasound for them to measure the kids features. It was nothing, but I think this type of misconception is prevelant in the medical industry. It seems almost likely that they want to break it to you the wrong way so that you go running for the next treatment or test.....more \$ in the doctors pocketbooks.

So, it doesn't surprise me when the study shows that the doctors results were given at 80% or more for the positive result. Gloom and doom rules again.

OT- the funniest comment? Odd very odd:)

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#6) On April 27, 2009 at 4:10 PM, madcowmonkey (< 20) wrote:

Great pics of the throat. I think I am finding the humor in the pig comment. It has nothing to do with actual pigs.......that is kind of funny:)

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#7) On April 27, 2009 at 4:17 PM, madcowmonkey (< 20) wrote:

since you are throwing links out like crazy.

...

Comment 11....are these all things that you won on ebay:)

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#8) On April 27, 2009 at 4:38 PM, portefeuille (98.93) wrote:

should have come with a warning the throat - sorry for that!

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#9) On April 27, 2009 at 4:57 PM, portefeuille (98.93) wrote:

just my favourite portfeuilles from here

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#10) On June 12, 2009 at 8:42 PM, ChrisGraley (28.49) wrote:

4) On April 27, 2009 at 2:12 PM, Tastylunch (99.75) wrote:

Ah Statisical Illiteracy goes right in hand with financial illiteracy 82.3% of the time ;-)

thanks for the link to the paper, looks interesting.

87.425% of all statistics are just made up.

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#11) On June 13, 2009 at 10:59 AM, portefeuille (98.93) wrote:

Well, the answer is in the pdf-document and can be figured out in a few seconds with the right "mindset".

Here for those who care and who do not want to open the pdf-document.

the 30 second answer:

Out of 1000 women (always a good idea to start with a 1000, hehe ...).

ca. 10 have cancer (p = 0.01) , ca. 9 show positive result (90% sensitivity)

ca. 990 don't have cancer but ca. 0.09 * 990 of those show a positive result (9% false positive). 0.09 * 990 = ca. 89 (raw estimate).

so ca. 9 + 89 = 98 have a positive result, but just ca. 9 of those have cancer.

So the answer is p = ca. 9 / 98 = ca. 9% = ca. 10% (i.e. one in ten) -> answer C.

The 3 second answer:

tweak the numbers first (90% -> 100%, 9% -> 10%)

for every women with cancer (and she test positive (100%)) you have 100 without cancer and 10 of those test positive (10%).

1 in 11 is close to 1 in 10, so C.

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and here is why it "matters":

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...

This study illustrates a fundamental problem in health care:
Many physicians do not know the probabilities that a person has
a disease given a positive screening test—that is, the positive
predictive value. Nor are they able to estimate it from the relevant
health statistics when those are framed in terms of conditional
probabilities, even when this test is in their own area of specialty
(Hoffrage & Gigerenzer, 1998). If you want to find out yourself if
this is the case, ask your doctor. The result also shows that there
is a fast and efficient cure. Yet doctors’ and patients’ collective
innumeracy is a largely unknown problem in health care that
continues to cause undue fear in the public.

...

------------------

(from said pdf-document)

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#12) On June 13, 2009 at 11:11 AM, portefeuille (98.93) wrote:

she test

she tests

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#13) On July 18, 2009 at 10:57 AM, portefeuille (98.93) wrote:

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a guide to my blog posts can be found in the comment section to this post
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