I studied statistics and I read statistical methods and I wrote a dissertation that employed "subjective probability" and I taught statistics in classrooms and on statewide tv. I consider there to be three basic branches of statistical analysis of experimental data:
Traditional hypothesis testing
Process analysis and quality control
Bayesian statistics
If you took a course that involved a "null hypothesis", you experienced the sort of statistical analysis that is often taught in our country. You may have wrestled with the concept of "statistical significance". That sort of approach expects some fixed data that has already been collected and will be analyzed to show support for an hypothesis or not. If you studied Bayesian statistics, you might be an advanced student or you might have had an unusual teacher or attended an unusual school. Bayesian statistics is an ongoing investigation in which the support for an idea rises or falls as new data comes in. Process analysis has been applied most often to manufacturing or some other activity that can be thought of as somewhat repetitious and one in which zero errors are prefered and aimed for.
W.E. Deming, an American statistician and statistical theorist, is well-known in certain circles for the work he did in trying to help American and Japanese manufacturers gather and analyze data that would help eliminate mistakes and flaws. He supported a principle that I have found quite helpful over the years:
Be suspicious of numbers that are used in principles and rules.
For example, I have a fever if my body temperature is above this number and I don't otherwise.
Deming advised investigators to be suspicious of numbers. What data supports that particular figure? How old is that data? How was it collected? Opinion and tradition can raise or lower a number, especially over time or in the hands of someone well-meaning or moralistic or propagandistic. You know the idea: if an aspirin is a good idea, two aspirins will be twice as good. And of course, some parameters are pulled from the air and are somebody's idea of the right amount.
