III An Error in the Argument from Conditionality and Sufficiency to the Likelihood Principle

It is not uncommon to see statistics texts argue that in frequentist theory one is faced with the following dilemma, either to deny the appropriateness of conditioning on the precision of the tool chosen by the toss of a coin, or else to embrace the strong likelihood principle which entails that frequentist sampling distributions are irrelevant to inference once the data are obtained. This is a false dilemma: Conditioning is warranted in achieving objective frequentist goals, and the conditionality principle coupled with sufficiency does not entail the strong likelihood principle. The “dilemma” argument is therefore an illusion.