Experimental results often support a null hypothesis, as shown by three illustrative examples from the recent literature. Conventional statistical analysis cannot support a null hypothesis, whereas Bayesian analysis can. The challenge in a Bayesian analysis is to formulate a suitably vague alternative to the null. The null is a precise hypothesis, while the alternatives to it are usually vague. Bayesian analysis penalizes vagueness: the vaguer the alternative, the more the null is favored when the observed effect is small. The question is: how vague should the alternative be? A general solution is to compute the odds for or against the null as a function of the upper limit on the vagueness of the alternative. If the odds favoring the null approach 1 from above as the hypothesized size of the effect approaches 0, then the data favor the null over any alternative to it. The simple computation and the highly intuitive graphic representation of the analysis are illustrated by the analysis of the three examples, for each of which the null is the theoretically consequential hypothesis. (click here to learn more)
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This page is maintained by Dr Charles Gallistel, Co-Director, Rutgers Center for Cognitive Science