The logical incoherence of modern statistical practice

The great Stuart Hurlbert came to Duke to give a talk on the logical incoherence of modern statistical practice. My immediate thought after the talk was that the title of his talk was all wrong. It should be: the logical incoherence of ecological applications of statistics. The most obvious "incoherence" in modern statistics is the violations of the likelihood principle of many concepts and practices that were not mentioned at all. In fact, he could have ended the talk in five minutes by citing the first paragraph of Berger and Wolpert (1988):

Among all prescriptions for statistical behavior, the Likelihood Principle (LP) stands out as the simplest and yet most far reaching. It essentially states that all evidence, which is obtained from an experiment, about an unknown quantity [;\theta;], is contained in the likelihood function of [;\theta;] for the given data. The implications of this are profound, since most non-Bayesian approaches to statistics and indeed most standard statistical measures of evidence (such as coverage probability, error probabilities, significance level, frequentist risk, etc.) are then contraindicated.

Here is a run-down of the "sins" of statistics discussed by Hurlbert:

1. a fixed type I error probability (alpha) --
2. the use of term "significant"
3. the concept of type II error (here he thinks that we should never accept the null hypothesis)
4. one-tailed hypothesis tests
5. multiple comparisons, and
6. repeated measures ANOVA.