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null hypotheses simple precise theoretically important conventional statistical analysis cannot support bayesian analysis challenge bayesian analysis formulate suitably vague alternative vaguer alternative spreads unit mass prior probability null favored general solution sensitivity analysis compute odds null function limits vagueness alternative odds null approach 1 hypothesized maximum size possible effect approaches 0 data favor null vaguer alternative simple computations intuitive graphic representation analysis illustrated analysis diverse examples current literature pose 3 common experimental questions 2 means b performance chance c factors additive