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Abstract:
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We endeavor into the history of using p-values, both from a Fisherian and Neyman-Pearsonian perspective. We discuss when each perspective is meaningful, and attempt to explain what is implied by the size of the p-value, and how it relates to statistical inferences on hypothesis sets. In an example based on the Normal sampling distribution, we show how p-values behave as a function of both the space of hypotheses and sample size. We conclude by examining the rate at which p-values decrease, as a function of the null hypothesis, and show that its decay rate is exponential, but is variably faster than that of the Likelihood function.
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