Recent likelihood theory produces p-values that have remarkable accuracy and wide applicability. The calculations use familiar tools such as maximum likelihood values (MLEs), observed informations, and parameter rescaling. The usual evaluation of such p-values is by simulations, and such simulations do verify that the global distribution of the p-values is uniform(0,1), to high accuracy in repeated sampling. The derivation of the p-values however asserts a stronger statement, that they have a uniform(0,1) distribution conditionally, given identified precision information provided by the data. We take a simple regression example that involves exact precision information and use large sample techniques to extract highly accurate information as to the statistical position of the data point with respect to the parameter: specifically, we examine various p-values and Bayesian posterior survivor s-values for validity. With observed data we numerically evaluate the various p-values and s-values, and we also record the related general formulas. We then assess the numerical values for accuracy using Markov chain Monte Carlo (McMC) methods. We also propose some third-order likelihood-based procedures

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La revue canadienne de statistique