The Art of Statistics: Learning from Data

by David Spiegelhalter

We are still making strong assumptions, even in this simple coin-flipping example. We are assuming the coin is fair and balanced, it is flipped properly so the result is not predictable, it does not land on its edge, an asteroid does not strike after the first flip, and so on. These are serious considerations (except possibly the asteroid): they serve to emphasize that all the probabilities we use are conditional – there is no such thing as the unconditional probability of an event; there are always assumptions and other factors that could affect the probability. And, as we now see, we need to be careful about what we condition on. Conditional Probability – When Our Probabilities Depend on Other Events When screening for breast cancer, mammography is roughly 90% accurate, in the sense that 90% of women with cancer, and 90% of women without cancer, will be correctly classified. Suppose 1% of women being screened actually have cancer: what is the probability that a randomly chosen woman will have a positive mammogram, and if she does, what is the chance she really has cancer?

Conditional probablity