Wednesday 4 August 2010

Reading through Reckoning with Risk...

Quoted from the blurb:
"However much we want certainty in our lives, it feels as if we live in an uncertain and dangerous world. But are we guilty of wildly exaggerating the chances of some unwanted event happening to us? Are we misled by our ignorance of the reality of risk?"

So far, the book mainly talks about innumeracy, which is the misunderstanding of mathematical concepts. The book is more about misinterpreted probabilities and uncertainty rather than the existance of random, but it is very informative and may become useful to me in the future.

"The following information is available about asymptomatic women aged 40 to 50 in such a region who participate in mammography screening:

The probability that one of these womem has breast cancer in 0.8 percent. If a woman has breast caner, 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 have a positive mammogram. Imagine a woman who has a positive mammogram. What is the probability that she actually has cancer?

Let us try to turn [...] innumeracy into insight by communicating in natural frequencies rather than probabilities:

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?

The information is the same as before (with rounding) and it leads to the same answer. But now it is much easier to see what that answer is. Only 7 of the 77 women who test positive (70+7) actually have breast cancer, which is 1 in 11."

This may be an interesting topic to use in my presentation. It shows that before we can even begin to question randomness, we must be sure that we are certain about probabilities and possible misinterpretation of them. Reading this book has shown me that there is so much more to randomness than just trying to predict what will happen. Many probabilities must be proven and understood, and numerous tests/experiments need to be carried out.

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