This from 2009:
Yudkowsky poses the following canonical problem:
1% of women at age forty who participate in routine screening have breast cancer. 80% of women with breast cancer will get positive mammographies. 9.6% of women without breast cancer will also get positive mammographies.
A woman in this age group had a positive mammography in a routine screening. What is the probability that she actually has breast cancer?
The frightening thing is that only 15% of doctors get this right. And they’re off by a lot. That is, the average answer is in the range of 80% while the correct answer is 7.8%. Apparently, there is something about the way we think about the problem that makes 7.8% hard to accept, and Yudkowsky does a great job of walking you through the logic in painfully small steps.
Let’s try something similar here…
What Do We Know & What Does It Imply?
We have three pieces of information:
1% of sample are TRUE (that is, they have cancer)
80% of sample who are TRUE will test TRUE
9.6% of sample who are FALSE will test TRUE.
On the face of it, we should guess that the percentage of women who test TRUE who actually are TRUE (test positive and actually have cancer) is pretty small based on two facts provided: the actual percentage of women from the sample who are TRUE (regardless of testing) is only 1%, and the test has a false positive for 9.6% of those tested.
So, to solve this:
1) Assume we have a sample of 1000 women (I use 1000 to reduce the amount I have to talk about fractional people, but I don’t use 10,000 as I get lost in the zeros).
2) We know that the reality is that of the 1,000 women, 10 will have cancer (1%).
990 = no cancer
10 = cancer
3) Of the 10 who have cancer, 8 will test positive
8 out 1000 women tested will test True and are True
4) Of the 990 with no cancer 9.6% will also test positive = 990 * .096 = 95.04.
95.04 women out of 1,000 will test True but are False.
5) The total number testing true is 8 + 95.04 = 103.04.
Of these, 8 actually have Cancer.
6) So the value for tests positive (103.04) versus is positive (8) is 8/103.4 or 0.773 or 7.8%
Hiya, I’m really glad I have found this info. Today bloggers publish only about gossips and internet and this is actually frustrating. A good site with interesting content, that’s what I need. Thank you for keeping this web site, I’ll be visiting it. Do you do newsletters? Can’t find it.
Some genuinely good content on this site, regards for contribution.
Hello! I just would like to give a huge thumbs up for the great info you have here on this post. I will be coming back to your blog for more soon.
It’s really a great and helpful piece of information. I’m glad that you shared this useful info with us. Please keep us informed like this. Thanks for sharing.
Hello! I’ve been reading your blog for a long time now and finally got the bravery to go ahead and give you a shout out from Kingwood Texas! Just wanted to tell you keep up the excellent work!
I believe that is one of the most important info for me. And i’m satisfied reading your article. But should observation on some common things, The site style is wonderful, the articles is really excellent : D. Excellent job, cheers
I simply could not leave your web site prior to suggesting that I really loved the usual information a person supply in your visitors? Is gonna be again often in order to check out new posts.
Hey There. I discovered your weblog the usage of msn. This is an extremely well written article. I’ll make sure to bookmark it and return to read more of your useful information. Thanks for the post. I will definitely comeback.
This is a topic close to my heart cheers, where are your contact details though?
What¦s Taking place i am new to this, I stumbled upon this I’ve found It absolutely helpful and it has aided me out loads. I hope to contribute & aid different customers like its aided me. Great job.
I rattling thankful to find this site on bing, just what I was searching for : D also saved to fav.
Great ?V I should certainly pronounce, impressed with your site. I had no trouble navigating through all tabs as well as related information ended up being truly simple to do to access. I recently found what I hoped for before you know it in the least. Reasonably unusual. Is likely to appreciate it for those who add forums or something, website theme . a tones way for your customer to communicate. Excellent task..
You could definitely see your enthusiasm in the paintings you write. The arena hopes for more passionate writers like you who are not afraid to say how they believe. Always follow your heart.
Very interesting details you have remarked, appreciate it for posting.
Very interesting details you have mentioned, thanks for posting.
Woah! I’m really digging the template/theme of this blog. It’s simple, yet effective. A lot of times it’s challenging to get that “perfect balance” between usability and appearance. I must say you’ve done a superb job with this. Additionally, the blog loads very quick for me on Firefox. Outstanding Blog!
Hey there would you mind sharing which blog platform you’re using? I’m planning to start my own blog soon but I’m having a hard time selecting between BlogEngine/Wordpress/B2evolution and Drupal. The reason I ask is because your layout seems different then most blogs and I’m looking for something unique. P.S My apologies for being off-topic but I had to ask!
The Pink Salt Trick is a minimalist but effective morning routine: Just drink a glass of lukewarm water mixed with a pinch of Himalayan pink salt as soon as you wake up.
Absolutely pent subject matter, Really enjoyed examining.
he blog was how do i say it… relevant, finally something that helped me. Thanks
I haven’t checked in here for a while as I thought it was getting boring, but the last few posts are good quality so I guess I’ll add you back to my everyday bloglist. You deserve it my friend 🙂
I¦ve recently started a website, the info you provide on this website has helped me tremendously. Thanks for all of your time & work.
Thanks for the sensible critique. Me and my neighbor were just preparing to do a little research about this. We got a grab a book from our local library but I think I learned more clear from this post. I’m very glad to see such fantastic information being shared freely out there.
Wow that was odd. I just wrote an incredibly long comment but after I clicked submit my comment didn’t show up. Grrrr… well I’m not writing all that over again. Regardless, just wanted to say superb blog!
F*ckin¦ tremendous issues here. I am very satisfied to peer your article. Thanks so much and i am looking ahead to contact you. Will you kindly drop me a e-mail?
Enjoyed reading through this, very good stuff, thankyou. “Curiosity killed the cat, but for a while I was a suspect.” by Steven Wright.
I have been absent for a while, but now I remember why I used to love this website. Thanks, I will try and check back more frequently. How frequently you update your website?
excellent post.Never knew this, thanks for letting me know.
I have read a few excellent stuff here. Definitely price bookmarking for revisiting. I wonder how much attempt you place to create this type of excellent informative site.
I couldn’t resist commenting
F*ckin’ remarkable issues here. I am very glad to look your post. Thank you a lot and i am taking a look forward to contact you. Will you kindly drop me a e-mail?
I was wondering if you ever thought of changing the layout of your site? Its very well written; I love what youve got to say. But maybe you could a little more in the way of content so people could connect with it better. Youve got an awful lot of text for only having one or two pictures. Maybe you could space it out better?
Sleep Lean is a natural supplement designed to improve sleep quality and aid weight loss while you sleep.
Wonderful post but I was wanting to know if you could write a litte more on this subject? I’d be very thankful if you could elaborate a little bit more. Thank you!
Lipovive acts on the metabolism, burning fat, reducing appetite, and providing more energy.
This is the right blog for anyone who wants to find out about this topic. You realize so much its almost hard to argue with you (not that I actually would want…HaHa). You definitely put a new spin on a topic thats been written about for years. Great stuff, just great!
Hi there, i read your blog from time to time and i own a similar one and i was just curious if you get a lot of spam remarks? If so how do you prevent it, any plugin or anything you can suggest? I get so much lately it’s driving me mad so any assistance is very much appreciated.
I think that is one of the most important information for me. And i’m happy reading your article. However should commentary on some normal things, The website taste is ideal, the articles is truly nice : D. Excellent process, cheers
The Pink Salt Trick is a minimalist but effective morning routine: Just drink a glass of lukewarm water mixed with a pinch of Himalayan pink salt as soon as you wake up.
Utterly written written content, Really enjoyed studying.
Spot on with this write-up, I truly assume this web site wants far more consideration. I’ll in all probability be once more to read rather more, thanks for that info.
The Pink Salt Trick is a minimalist but effective morning routine: Just drink a glass of lukewarm water mixed with a pinch of Himalayan pink salt as soon as you wake up.
I¦ll immediately snatch your rss feed as I can not in finding your e-mail subscription link or e-newsletter service. Do you’ve any? Kindly allow me know so that I may just subscribe. Thanks.
Hey There. I found your blog using msn. This is an extremely well written article. I’ll be sure to bookmark it and come back to read more of your useful info. Thanks for the post. I will certainly comeback.
You actually make it appear so easy with your presentation but I find this matter to be really one thing that I believe I would by no means understand. It kind of feels too complex and very large for me. I am taking a look forward in your subsequent publish, I’ll try to get the hold of it!
Keep working ,impressive job!
The Pink Salt Trick is a minimalist but effective morning routine: Just drink a glass of lukewarm water mixed with a pinch of Himalayan pink salt as soon as you wake up.
I’ve recently started a website, the info you provide on this website has helped me tremendously. Thanks for all of your time & work.
You could definitely see your enthusiasm within the work you write. The sector hopes for more passionate writers like you who aren’t afraid to mention how they believe. Always go after your heart. “Experience is a good school, but the fees are high.” by Heinrich Heine.
The Pink Salt Trick is a minimalist but effective morning routine: Just drink a glass of lukewarm water mixed with a pinch of Himalayan pink salt as soon as you wake up.