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%
Way cool, some valid points! I appreciate you making this article available, the rest of the site is also high quality. Have a fun.
Lovely website! I am loving it!! Will come back again. I am bookmarking your feeds also
I think this site holds some rattling good info for everyone. “In this world second thoughts, it seems, are best.” by Euripides.
That is the fitting blog for anybody who needs to seek out out about this topic. You understand so much its almost laborious to argue with you (not that I really would need…HaHa). You definitely put a new spin on a topic thats been written about for years. Great stuff, just nice!
What¦s Going down i am new to this, I stumbled upon this I have discovered It positively useful and it has helped me out loads. I am hoping to give a contribution & assist other customers like its helped me. Good job.
Hey very cool website!! Man .. Beautiful .. Amazing .. I’ll bookmark your website and take the feeds also…I’m happy to find so many useful info here in the post, we need work out more strategies in this regard, thanks for sharing. . . . . .
Hi, Neat post. There is a problem with your website in internet explorer, would check this… IE still is the market leader and a good portion of people will miss your fantastic writing due to this problem.
Super-Duper site! I am loving it!! Will come back again. I am bookmarking your feeds also.
Hi there! This post couldn’t be written any better! Reading through this post reminds me of my previous room mate! He always kept talking about this. I will forward this article to him. Pretty sure he will have a good read. Thank you for sharing!
Hi! I’ve been reading your site for a long time now and finally got the courage to go ahead and give you a shout out from New Caney Texas! Just wanted to tell you keep up the excellent job!
Great wordpress blog here.. It’s hard to find quality writing like yours these days. I really appreciate people like you! take care
Keep working ,fantastic job!
You are my inhalation, I own few web logs and very sporadically run out from brand :). “Yet do I fear thy nature It is too full o’ the milk of human kindness.” by William Shakespeare.
I have been reading out many of your stories and i can claim pretty nice stuff. I will surely bookmark your website.
I saw a lot of website but I think this one has got something special in it in it
Hello. remarkable job. I did not anticipate this. This is a excellent story. Thanks!
I like this post, enjoyed this one appreciate it for posting. “The difference between stupidity and genius is that genius has its limits.” by Albert Einstein.
Great post and straight to the point. I am not sure if this is really the best place to ask but do you folks have any thoughts on where to employ some professional writers? Thx 🙂
Glad to be one of many visitors on this awe inspiring site : D.
I’m curious to find out what blog platform you have been working with? I’m having some small security issues with my latest website and I’d like to find something more risk-free. Do you have any recommendations?
It’s a pity you don’t have a donate button! I’d certainly donate to this outstanding blog! I guess for now i’ll settle for book-marking and adding your RSS feed to my Google account. I look forward to brand new updates and will share this website with my Facebook group. Talk soon!
Wohh exactly what I was searching for, regards for putting up.
Spot on with this write-up, I actually assume this web site wants rather more consideration. I’ll in all probability be once more to learn much more, thanks for that info.
hi!,I really like your writing very a lot! proportion we be in contact extra approximately your article on AOL? I need a specialist on this house to resolve my problem. Maybe that is you! Having a look ahead to peer you.
Hello there, simply was alert to your blog through Google, and located that it is really informative. I’m going to be careful for brussels. I’ll appreciate when you continue this in future. Lots of other folks will probably be benefited from your writing. Cheers!
You must take part in a contest for the most effective blogs on the web. I’ll recommend this site!
I dugg some of you post as I cerebrated they were extremely helpful very useful
Undeniably believe that which you stated. Your favorite reason seemed to be on the web the easiest thing to be aware of. I say to you, I certainly get annoyed while people think about worries that they plainly don’t know about. You managed to hit the nail upon the top as well as defined out the whole thing without having side effect , people can take a signal. Will probably be back to get more. Thanks
I do not even know how I ended up here, but I thought this post was good. I do not know who you are but certainly you’re going to a famous blogger if you aren’t already 😉 Cheers!
I was just seeking this information for a while. After six hours of continuous Googleing, finally I got it in your web site. I wonder what’s the lack of Google strategy that don’t rank this type of informative sites in top of the list. Generally the top web sites are full of garbage.
I am perpetually thought about this, thanks for posting.
I have not checked in here for a while since I thought it was getting boring, but the last several posts are good quality so I guess I will add you back to my daily bloglist. You deserve it my friend 🙂
Excellent blog here! Also your website loads up fast! What host are you using? Can I get your affiliate link to your host? I wish my web site loaded up as fast as yours lol
Hmm is anyone else encountering problems with the pictures on this blog loading? I’m trying to figure out if its a problem on my end or if it’s the blog. Any responses would be greatly appreciated.
I like reading through and I think this website got some truly utilitarian stuff on it! .
Great post. I am facing a couple of these problems.
What i don’t understood is in truth how you are no longer actually much more smartly-appreciated than you might be now. You’re very intelligent. You recognize therefore significantly in terms of this subject, produced me personally believe it from so many various angles. Its like men and women don’t seem to be involved until it’s one thing to accomplish with Woman gaga! Your own stuffs great. All the time deal with it up!
I’ve been surfing online greater than three hours lately, yet I never found any fascinating article like yours. It’s pretty price sufficient for me. In my opinion, if all webmasters and bloggers made just right content material as you probably did, the web will likely be much more useful than ever before.
Deference to article author, some superb information .
Thanx for the effort, keep up the good work Great work, I am going to start a small Blog Engine course work using your site I hope you enjoy blogging with the popular BlogEngine.net.Thethoughts you express are really awesome. Hope you will right some more posts.
I’m truly enjoying the design and layout of your blog. It’s a very easy on the eyes which makes it much more enjoyable for me to come here and visit more often. Did you hire out a developer to create your theme? Outstanding work!
What i do not realize is actually how you’re not actually much more well-liked than you might be right now. You’re very intelligent. You realize thus significantly relating to this subject, produced me personally consider it from a lot of varied angles. Its like women and men aren’t fascinated unless it’s one thing to accomplish with Lady gaga! Your own stuffs outstanding. Always maintain it up!
hello there and thanks on your information – I’ve definitely picked up something new from proper here. I did alternatively experience several technical points the use of this website, as I skilled to reload the website a lot of times previous to I could get it to load properly. I had been brooding about in case your web host is OK? No longer that I’m complaining, but slow loading circumstances instances will often have an effect on your placement in google and could damage your high quality ranking if ads and ***********|advertising|advertising|advertising and *********** with Adwords. Anyway I’m including this RSS to my email and can look out for much extra of your respective fascinating content. Ensure that you replace this once more very soon..
Wonderful blog! I found it while browsing on Yahoo News. Do you have any tips on how to get listed in Yahoo News? I’ve been trying for a while but I never seem to get there! Thanks
Hello my friend! I wish to say that this article is amazing, nice written and include almost all vital infos. I’d like to see more posts like this.
There is perceptibly a bundle to realize about this. I consider you made certain nice points in features also.
Keep working ,terrific job!
Merely a smiling visitant here to share the love (:, btw outstanding design.
Thank you for the good writeup. It in fact was a amusement account it. Look advanced to more added agreeable from you! However, how could we communicate?
Hello there, I discovered your website by means of Google even as searching for a similar subject, your web site got here up, it seems great. I’ve bookmarked it in my google bookmarks.