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%
You made some respectable points there. I looked on the internet for the difficulty and found most people will go together with along with your website.
You really make it seem really easy along with your presentation but I in finding this topic to be really one thing which I believe I’d never understand. It sort of feels too complicated and very huge for me. I’m looking forward in your next put up, I’ll attempt to get the cling of it!
F*ckin¦ tremendous things here. I am very satisfied to see your post. Thank you a lot and i am looking ahead to contact you. Will you kindly drop me a e-mail?
Hmm is anyone else experiencing problems with the images on this blog loading? I’m trying to find out if its a problem on my end or if it’s the blog. Any feed-back would be greatly appreciated.
you have a great blog here! would you like to make some invite posts on my blog?
When I originally commented I clicked the -Notify me when new comments are added- checkbox and now each time a comment is added I get four emails with the same comment. Is there any way you can remove me from that service? Thanks!
hey there and thank you for your information – I’ve certainly picked up something new from right here. I did however expertise a few technical issues using this site, since I experienced to reload the web site a lot of times previous to I could get it to load properly. I had been wondering if your web host is OK? Not that I’m complaining, but slow loading instances times will sometimes affect your placement in google and can damage your high quality score if ads and marketing with Adwords. Anyway I am adding this RSS to my e-mail and could look out for a lot more of your respective exciting content. Make sure you update this again soon..
It¦s actually a nice and useful piece of information. I am satisfied that you simply shared this helpful info with us. Please stay us up to date like this. Thank you for sharing.
You need to take part in a contest for among the finest blogs on the web. I will recommend this site!
I love your blog.. very nice colors & theme. Did you create this website yourself? Plz reply back as I’m looking to create my own blog and would like to know wheere u got this from. thanks
It¦s really a cool and helpful piece of info. I¦m glad that you simply shared this useful info with us. Please stay us up to date like this. Thank you for sharing.
Woh I enjoy your posts, saved to my bookmarks! .
It’s perfect time to make some plans for the longer term and it’s time to be happy. I’ve learn this post and if I may just I wish to counsel you few interesting issues or advice. Maybe you could write next articles referring to this article. I want to read more issues approximately it!
I couldn’t resist commenting
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¦ll add you back to my daily bloglist. You deserve it my friend 🙂
You are my breathing in, I possess few web logs and occasionally run out from to post : (.
I like looking through and I conceive this website got some really utilitarian stuff on it! .
I am always thought about this, thanks for posting.
Thank you for the good writeup. It in fact was a amusement account it. Look advanced to more added agreeable from you! By the way, how could we communicate?
Hi, just required you to know I he added your site to my Google bookmarks due to your layout. But seriously, I believe your internet site has 1 in the freshest theme I??ve came across. It extremely helps make reading your blog significantly easier.
I truly enjoy examining on this site, it contains superb articles.
I’m really enjoying the theme/design of your weblog. Do you ever run into any web browser compatibility problems? A number of my blog readers have complained about my site not working correctly in Explorer but looks great in Chrome. Do you have any suggestions to help fix this problem?
With havin so much content and articles do you ever run into any problems of plagorism or copyright infringement? My blog has a lot of exclusive content I’ve either created myself or outsourced but it appears a lot of it is popping it up all over the web without my authorization. Do you know any ways to help protect against content from being ripped off? I’d really appreciate it.
Youre so cool! I dont suppose Ive learn anything like this before. So nice to seek out someone with some unique thoughts on this subject. realy thank you for starting this up. this website is something that’s needed on the net, somebody with slightly originality. useful job for bringing something new to the web!
You are a very bright individual!
I truly appreciate this post. I have been looking everywhere for this! Thank goodness I found it on Bing. You’ve made my day! Thank you again
What i do not understood is in reality how you are not really a lot more well-liked than you may be now. You’re so intelligent. You realize thus significantly when it comes to this matter, made me in my opinion believe it from so many varied angles. Its like women and men are not interested except it’s one thing to do with Lady gaga! Your own stuffs great. Always take care of it up!
I like this website very much, Its a rattling nice place to read and receive information. “Never hold discussions with the monkey when the organ grinder is in the room.” by Sir Winston Churchill.
Simply desire to say your article is as surprising. The clearness on your publish is simply great and i can suppose you’re a professional on this subject. Fine together with your permission let me to seize your RSS feed to keep updated with coming near near post. Thank you 1,000,000 and please carry on the gratifying work.
I have been surfing on-line more than 3 hours these days, but I never found any fascinating article like yours. It is lovely value enough for me. In my view, if all website owners and bloggers made just right content material as you did, the internet will be much more helpful than ever before. “Wherever they burn books, they will also, in the end, burn people.” by Heinrich Heine.
Utterly pent subject material, appreciate it for information. “The bravest thing you can do when you are not brave is to profess courage and act accordingly.” by Corra Harris.
With havin so much content do you ever run into any problems of plagorism or copyright infringement? My blog has a lot of unique content I’ve either created myself or outsourced but it seems a lot of it is popping it up all over the internet without my authorization. Do you know any techniques to help protect against content from being stolen? I’d genuinely appreciate it.
Appreciate it for this post, I am a big fan of this web site would like to continue updated.
Heya i am for the primary time here. I came across this board and I to find It really helpful & it helped me out much. I hope to provide something back and aid others such as you aided me.
I’ve been absent for some time, but now I remember why I used to love this web site. Thank you, I will try and check back more frequently. How frequently you update your website?
Can I just say what a relief to find someone who actually knows what theyre talking about on the internet. You definitely know how to bring an issue to light and make it important. More people need to read this and understand this side of the story. I cant believe youre not more popular because you definitely have the gift.
You could definitely see your expertise within the paintings you write. The sector hopes for more passionate writers like you who aren’t afraid to say how they believe. Always follow your heart. “No man should marry until he has studied anatomy and dissected at least one woman.” by Honore’ de Balzac.
I really like your writing style, good information, thank you for posting :D. “In university they don’t tell you that the greater part of the law is learning to tolerate fools.” by Doris Lessing.
Excellent read, I just passed this onto a colleague who was doing some research on that. And he just bought me lunch as I found it for him smile Thus let me rephrase that: Thank you for lunch!
As a Newbie, I am continuously searching online for articles that can aid me. Thank you
A person necessarily lend a hand to make severely posts I’d state. This is the first time I frequented your website page and so far? I surprised with the research you made to create this actual post extraordinary. Great task!
What i do not realize is actually how you are no longer actually a lot more well-appreciated than you may be right now. You are very intelligent. You know thus significantly on the subject of this matter, produced me individually imagine it from so many varied angles. Its like men and women aren’t involved until it is one thing to accomplish with Lady gaga! Your individual stuffs outstanding. Always care for it up!
hi!,I love your writing so much! percentage we be in contact extra approximately your article on AOL? I need a specialist on this space to unravel my problem. May be that’s you! Looking ahead to see you.
You are my inspiration, I possess few blogs and sometimes run out from brand :). “He who controls the past commands the future. He who commands the future conquers the past.” by George Orwell.
Of course, what a splendid website and educative posts, I surely will bookmark your site.Have an awsome day!
I like this web blog so much, saved to my bookmarks. “I don’t care what is written about me so long as it isn’t true.” by Dorothy Parker.
Glad to be one of many visitors on this awe inspiring web site : D.
Hello there! I know this is somewhat off topic but I was wondering if you knew where I could get a captcha plugin for my comment form? I’m using the same blog platform as yours and I’m having difficulty finding one? Thanks a lot!
Greetings! Very helpful advice on this article! It is the little changes that make the biggest changes. Thanks a lot for sharing!
I like this website so much, saved to favorites.