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Stats in the news
Transcript of Stats in the news
by Steven Strogatz NYT Calculated Risks by Gerd Gigerenzer Breast Cancer Question "estimate the probability that a woman with a positive mammogram actually has breast cancer, even though she’s in a low-risk group: 40 to 50 years old, with no symptoms or family history of breast cancer."
In addition they were given the following statistics:
"The probability that one of these women has breast cancer is 0.8 percent. If a woman has breast cancer, the probability is 90 percent that she will have a positive mammogram. If a woman does not have breast cancer, the probability is 7 percent that she will still have a positive mammogram. Imagine a woman who has a positive mammogram. What is the probability that she actually has breast cancer?"
Results Out of 24 German doctos asked:
8 thought below 10%
8 thought above 90%
8 thought between 50% and 80% Correct answer: 9% Out of 100 American doctors asked, 95 estimated the woman’s probability of having breast cancer to be somewhere around 75 percent. Breakdown Eight out of every 1,000 women have breast cancer. Of these 8 women with breast cancer, 7 will have a positive mammogram. Of the remaining 992 women who don’t have breast cancer, some 70 will still have a positive mammogram. Imagine a sample of women who have positive mammograms in screening. How many of these women actually have breast cancer?
Since a total of 7 + 70 = 77 women have positive mammograms, and only 7 of them truly have breast cancer, the probability of having breast cancer given a positive mammogram is 7 out of 77, which is 1 in 11, or about 9 percent. Class Application and Critique Probability, kind of