A Characterization of Most(More) Powerful Test Statistics with Simple Nonparametric Applications

Data-driven most powerful tests are statistical hypothesis decision-making tools that deliver the greatest power against a fixed null among all corresponding data-based of given size. When underlying data distributions known, likelihood ratio principle can be applied to conduct tests. Reversing this notion, we consider following questions. (a) Assuming test statistic, say T, is given, how transform T improve test? (b) Can used generate (c) How does one compare statistics with respect an attribute desired procedure? To examine these questions, propose one-to-one mapping term” powerful” distribution properties statistic via matching characterization. This form characterization has practical applicability and aligns well general sufficiency. Findings indicate test, employ relevant ancillary do not have changes in their tested hypotheses. As example, present method illustrated by modifying usual t-test under nonparametric settings. Numerical studies based on generated real-data set confirm proposed approach useful practice.