Multiplicity and Unification in Frequentist ( Error ) Statistics : Learning

 Long standing controversies in the foundations of frequentist statistics stem from failure to appreciate the multiplicity of frequentist methods, and erroneous conceptions of the unifying core that links together and directs their interpretation and justification  Learning from the work of statistician D.R. Cox serves to explicate the multiplicity of frequentist methods and goals, and identify the unification of principles that direct their valid use in realistic scientific inquiries.  Moving away from the oversimplified caricatures of the standard methods (e.g., significance tests, confidence intervals) on which critics focus, the tools emerge as satisfying piecemeal learning goals within a multiplicity of methods, models, and experimental designs, and interconnected checks, and reports, of error.  Denying the assumption that the overall unified principle for these methods must be merely controlling the low-long run error probabilities of methods (behavioristic rationale), we advance an epistemological principle that renders hypothetical error probabilities relevant for learning about particular phenomena.  We contrast it with current Bayesian attempts at unifications of frequentist and Bayesian methods.