A Brief Ode to Parametric Likelihood
One of the traditional instruments used in medical experiments and drug development is the testing of statistical hypotheses based on the t-test statistic or its different modifications. Despite the fact that these tests are straightforward with respect to their applications in clinical trials, it should be noted that there has been much literature on the criticism of t-test-type statistical tools. Hence, the use of t-test-type techniques in this setting is suboptimal, and is accompanied by significant difficulties in controlling the corresponding Type I error. This chapter introduces several principles and aspects of tests based on the likelihood ratio statistic. When the forms of data distributions are assumed to be known, the likelihood principle is a central tenet for developing powerful statistical inference tools for use in clinical experiments. Although many statistical publications continue to contribute to the likelihood paradigm and are very important in the statistical discipline, several significant questions naturally arise about the maximum likelihood approach's general applicability.