Post by Tamrin on Mar 17, 2012 7:19:29 GMT 10
Mar 17, 2012 0:51:54 GMT 10 @brandt said:
Keeping in mind that the probability of the hypothesis given the data is not the same as the probability of the data given the hypothesis. NHST was mentioned a few times and I thought it was time to throw up the caution flag on that.The Bayesian approach to testing hypotheses has two critical elements. First, a Bayesian approach stands the classical (by which I mean frequentist but I can’t bring myself to type these “ist” designations) approach on its head. In the classical approach, our questions revolve around the probability of the data, given a specific hypothesis. In the Bayesian approach, our questions revolve around the probability of various hypotheses, given the data. You can see that the derivation of Bayesian methods will involve the same assumptions and manipulations of conditional probabilities that we discussed when we covered Bayesian estimation methods.
Technically, our Bayesian questions revolve around the likelihood of various hypotheses, given the data, which is not the same as the probabilities of various hypotheses; we will not delve into this distinction here - this is a heuristic exercise, after all. The point is that the classical approach is based on calculating probabilities of the data in hand under certain conditions (which are encompassed by the null and alternative hypotheses) and the Bayesian approach looks at probabilities of competing conditions (which are the hypotheses being compared) given the data in hand.
Technically, our Bayesian questions revolve around the likelihood of various hypotheses, given the data, which is not the same as the probabilities of various hypotheses; we will not delve into this distinction here - this is a heuristic exercise, after all. The point is that the classical approach is based on calculating probabilities of the data in hand under certain conditions (which are encompassed by the null and alternative hypotheses) and the Bayesian approach looks at probabilities of competing conditions (which are the hypotheses being compared) given the data in hand.
Null Hypothesis Significance Testing (NHST):
We have three recommendations to those who are in the process of writing or revising a research or statistics text. First, consider introducing a section on the NHST controversy. This section would, at the minimum, point out that there is currently debate about whether NHST is the best method for advancing research in the fields of education and the social sciences. Second, because the fifth edition of the APA (2001) publication manual includes information on the importance of reporting effect sizes and confidence intervals, an author should provide specific examples (as might be published in a journal) of what to do following a statistically significant outcome. We also recommend reporting effect size for nonsignificant outcomes. Third, provide more help (with examples) for deciding whether a result has practical significance or importance.
Which ever approach you take, some relevant data is required to analyze.