Modeling schizophrenic behavior and testing drug efficacy using general mixture components
A critical idea in the statistical analysis of randomized experiments is that the validity of the significance level for any test-statistic is assured by finding the randomization distribution of that statistic under the null hypothesis. Since validity under the null hypothesis is certain for any statistic, the most powerful statistic should be used to test for the equivalence of treatments, that is, the statistic that is most likely to detect true differences in the treatment conditions. We illustrate the critical points about validity and power using data from a randomized experiment comparing drugs for schizophrenic patients, where computing the scientific statistic requires extensive use of Markov chain Monte Carlo techniques to fit a model that reflects current understanding of components of schizophrenic behavior.