Probing Probabilities

Abstract:According to Bayes' theorem, the probability of an event is affected by how probable the event is and how accurate (or sloppy) the instrument to measure it is. In testing for something rare with an imperfect instrument, a positive result is more likely to be a mistake rather than a true positive. The formula challenges the status quo. It tells you that before you make a decision based on test results, you should look at the probability of the alternative hypothesis and the accuracy of the instrumentation. If the alternative is rare and the instrument is weak, you may want to seek another opinion. The article includes several anecdotal …

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P(B given not A) does not equal to (1 - P(B given A)), as implied in the article. There are 2 factors affecting the test accuracy: P(B given A) and P(not B given not A). The question in the article only provides one of the them and that is not sufficient. In the New England article: (1) the question to the doctors states the false positive rate = 5% and (2) P(B given A) is assumed to be 100%.
--Aldous Wong, 04-18-2014

That article and video cleared up a fuzzy topic that was taught badly in early stat classes I took, apparently, as it all makes sense now...but of course I am also much older. William Hooper is great teacher and this lesson could be added to senior year of high school math class as "extra credit" topic in new Common Core standards. It should also be mandatory in Pre-Med and Nursing training.
--Michael Clayton, 04-03-2014

Great article. One of the best I've read in QP for quite some time!
--Andrew, 03-26-2014

So if you are dealing with something rare, such as a server crash or a natural disaster, and you are guessing at what effects it will have, you can't expect to put any numbers around it at all!
--Chris Hilder, 03-10-2014

--Mike Looney, 03-07-2014

--Joseph Grzegorski, 03-07-2014

Thanks! Fascinating simplification for us all quality practitioners. This is really needed in healthcare diagnostics procedures, where heart, colesterol and blood pressure medication is given straight ahead based on 1 single lab measurement!! Finally a good application for the conditional probabilities given in technical universities 45 years ago. Still they missed all the Juran and Deming wise teachings. Our Myron Tribus book reprint on Baysean Statistics is still available here for all interested "Baysean believers": Rational Descriptions, Decisions, and Designs. M Tribus (in English). Reprint in 2000, 490 pp. First Ed 1969.
--Hakan Sodersved, 03-07-2014

--Kathleen Yanakis, 03-06-2014

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