A totally empirical basis of science

Abstract: Statistical hypothesis testing is the central method to demarcate scientific theories in both exploratory and inferential analyses. However, whether this method befits such purpose remains a matter of debate. Established approaches to hypothesis testing make several assumptions on the data generation process beyond the scientific theory. Most of these assumptions not only remain unmet in realistic datasets, but often introduce unwarranted bias in the analysis. Here, we depart from such restrictive assumptions to propose an alternative framework of total empiricism. We derive the Information-test ($I$-test) which allows for testing versatile hypotheses including non-null effects. To exemplify the adaptability of the $I$-test to application and study design, we revisit the hypothesis of interspecific metabolic scaling in mammals, ultimately rejecting both competing theories of pure allometry.