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Abstract:
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Frequentist inference appears to require hypothetical repeated sampling to interpret probability. As evidenced by the ASA's statement on p-values, there are serious misunderstandings about what is indicated by this probability. Contributing to this misunderstanding is the fact that many outside our profession do not think of probability as a limiting relative frequency. Instead, the classical interpretation is used where probabilities are proportions. Much of frequentist inference can be described using the classical interpretation and doing so will address the confusion by non statisticians and elucidate the difference between the Fisher and Neyman interpretations of frequentist inference. Both interpretations play a role in communicating inferential results. Which interpretation is more apt depends on two factors: the scope (specific, generic) and the focus (population, model) of the probability. These factors will be used to discuss Gelman's concern regarding potential comparisons arising from the fact that analyses might be different had the data been different.
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