An Introduction to the Philosophy of Science

In practice, much of statistical reasoning in science relies on probabilities subject to interpretation as relative frequencies. This chapter explains how probability can be understood in terms of relative frequencies and the uses scientists and philosophers have devised for frequentist probabilities. Particularly prominent in those uses are error probabilities associated with particular approaches to hypothesis testing. The approaches pioneered by Ronald Fisher and by Jerzy Neyman and Egon Pearson are outlined and explained through examples. The chapter then explores the error-statistical philosophy advocated by Deborah Mayo as a general framework for thinking about how we learn from empirical data. The error-statistical approach utilizes a frequentist framework for probabilities to articulate a view of severe testingof hypotheses as the means by which scientists increase experimental knowledge. Error statistics represents an important alternative to Bayesian approaches to scientific inquiry, and this chapter considers its prospects and challenges.