H Coda

This chapter distinguished statistical from scientific hypotheses on practical and philosophical grounds. The statistical hypothesis is part of a mathematical testing procedure and is tested by purely mathematical methods.

We also introduced the two distinct interpretations of probability: the ob­jective (frequentist) one and the subjective (Bayesian) one. In this chapter we focused on frequentist statistics, principally NHST, and how these influence scientific reasoning. Despite its popularity, NHST has notable shortcomings. Because it is an awkward amalgamation of two distinct statistical schools of thought (Fisher's and Neyman and Pearson's) that is treated as though it is a co­herent whole, its pitfalls are seldom taught to, or appreciated by, lab scientists. The inconsistencies of NHST contribute directly to the statistical confusion that plays a role in the Reproducibility Crisis.

In accordance with Popper's recommendation to adopt conventional standards for determining if a test prediction is falsified, probabilistic prop­ositions can be falsified within the limits of the uncertainty of the test. We covered some frequentist alternatives to the usual p-valued tests that avoid some of the drawbacks of NHST, although none of them is entirely free from drawbacks.

We will continue the introduction of statistical ideas in next chapter, which covers the basics of Bayesian statistics, and we'll draw on the fundamental statis­tical concepts (largely frequentist) in later chapters, where they play supporting roles in the examination of the Reproducibility Crisis (Chapter 7) and help illu­minate the advantages of the scientific hypothesis (Chapter 8).