Bayesian way of thinking is a very smart way to do statistics in a different matter! discover in this smart article makes this approach interesting to test hypothesis in an original way
Bayes’ theorem was the subject of a detailed article. The essay is good, but over 15,000 words long — here’s the condensed version for Bayesian newcomers like myself:
- Tests are not the event. We have a cancer test, separate from the event of actually having cancer. We have a test for spam, separate from the event of actually having a spam message.
- Tests are flawed. Tests detect things that don’t exist (false positive), and miss things that do exist (false negative).
- Tests give us test probabilities, not the real probabilities. People often consider the test results directly, without considering the errors in the tests.
- False positives skew results. Suppose you are searching for something really rare (1 in a million). Even with a good test, it’s likely that a positive result is really a false positive on somebody in the 999,999.
- People prefer natural numbers. Saying “100 in 10,000″ rather than “1%” helps people work through the numbers with fewer errors, especially with multiple percentages (“Of those 100, 80 will test positive” rather than “80% of the 1% will test positive”).
- Even science is a test. At a philosophical level, scientific experiments can be considered “potentially flawed tests” and need to be treated accordingly. There is a test for a chemical, or a phenomenon, and there is the event of the phenomenon itself. Our tests and measuring equipment have some inherent rate of error.