For generations of students schooled in the statistical theories of Fisher and Neyman-Pearson, Royall (biostatistics, Johns Hopkins U.) delivers an alternative likelihood paradigm focusing on what he deems the neglected Law of Likelihood. After weighing their assets and weaknesses, he persuasively dares question what most were taught as gospels of the scientific method: What is wrong with one-sided tests? Why not use the most powerful test? Must the significance level be predetermined? Is the strength of the evidence limited by the researcher's expectations? Includes exercises in this "new" statistics. Annotation c. by Book News, Inc., Portland, Or.