Recurring controversies about P values and confidence intervals revisited.

Abstract

The paper focused primarily on certain charges, claims, and interpretations of the P value as they relate to CIs and the AIC. It as argued that some of these comparisons and claims are misleading because they ignore key differences in the procedures being compared, such as (1) their primary aims and objectives, (2) the nature of the question posed to the data, as well as (3) the nature of their underlying reasoning and the ensuing inferences. In the case of the P value, the crucial issue is whether Fisher's evidential interpretation of the P value as "indicating the strength of evidence against H0" is appropriate. It is argued that, despite Fisher's maligning of the Type II error, a principled way to provide an adequate evidential account, in the form of post-data severity evaluation, calls for taking into account the power of the test. The error-statistical perspective brings out a key weakness of the P value and addresses several foundational issues raised in frequentist testing, including the fallacies of acceptance and rejection as well as misinterpretations of observed CIs: see Mayo-Spanos (2011). The paper also uncovers the connection between model selection procedures and hypothesis testing, revealing the inherent unreliability of the former. Hence, the choice between different procedures should not be "stylistic" (Murtaugh 2013), but should depend on the questions of interest, the answers sought, and the reliability of the procedures.