The importance of proving the null. Export

@article{Gallistel_2009_importance, abstract = {Null hypotheses are simple, precise, and theoretically important. Conventional statistical analysis cannot support them; Bayesian analysis can. The challenge in a Bayesian analysis is to formulate a suitably vague alternative, because the vaguer the alternative is (the more it spreads out the unit mass of prior probability), the more the null is favored. A general solution is a sensitivity analysis: Compute the odds for or against the null as a function of the limit(s) on the vagueness of the alternative. If the odds on the null approach 1 from above as the hypothesized maximum size of the possible effect approaches 0, then the data favor the null over any vaguer alternative to it. The simple computations and the intuitive graphic representation of the analysis are illustrated by the analysis of diverse examples from the current literature. They pose 3 common experimental questions: (a) Are 2 means the same? (b) Is performance at chance? (c) Are factors additive?}, author = {Gallistel, C. R.}, citeulike-article-id = {5626239}, citeulike-linkout-0 = {http://dx.doi.org/10.1037/a0015251}, citeulike-linkout-1 = {http://view.ncbi.nlm.nih.gov/pubmed/19348549}, citeulike-linkout-2 = {http://www.hubmed.org/display.cgi?uids=19348549}, doi = {10.1037/a0015251}, issn = {0033-295X}, journal = {Psychological review}, keywords = {bayesian, method, statistics}, month = {April}, number = {2}, pages = {439--453}, pdf = {gallistel\_09\_importance.pdf}, posted-at = {2009-09-28 09:40:29}, priority = {2}, title = {The importance of proving the null.}, url = {http://dx.doi.org/10.1037/a0015251}, volume = {116}, year = {2009} }

TY - JOUR ID - Gallistel_2009_importance L3 - citeulike-article-id:5626239 N2 - Null hypotheses are simple, precise, and theoretically important. Conventional statistical analysis cannot support them; Bayesian analysis can. The challenge in a Bayesian analysis is to formulate a suitably vague alternative, because the vaguer the alternative is (the more it spreads out the unit mass of prior probability), the more the null is favored. A general solution is a sensitivity analysis: Compute the odds for or against the null as a function of the limit(s) on the vagueness of the alternative. If the odds on the null approach 1 from above as the hypothesized maximum size of the possible effect approaches 0, then the data favor the null over any vaguer alternative to it. The simple computations and the intuitive graphic representation of the analysis are illustrated by the analysis of diverse examples from the current literature. They pose 3 common experimental questions: (a) Are 2 means the same? (b) Is performance at chance? (c) Are factors additive? IS - 2 JF - Psychological review SN - 0033-295X EP - 453 TI - The importance of proving the null. VL - 116 SP - 439 KW - bayesian KW - method KW - statistics AU - Gallistel, CR PY - 2009/April// UR - http://dx.doi.org/10.1037/a0015251 ER -