A New Definition of P-Value Involving the Maximum Likelihood Estimator

Abstract

We present here an alternative definition of the P-value for statistical hypothesis test of a real-valued parameter for a continuous random variable X . Our approach uses neither the notion of Type I error nor the assumption that null hypothesis is true. Instead, the new P-value involves the maximum likelihood estimator, which is usually available for a parameter such as the mean μ or standard deviation σ of a random variable X with a common distribution.