chapter four

4 From evidence to decisions: Neyman, Pearson, and the principles of hypothesis testing

 

This chapter covers

  • Jerzy Neyman and Egon Pearson’s On the Problem of the Most Efficient Tests of Statistical Hypotheses (1933) and their stepwise hypothesis testing framework
  • How the Neyman-Pearson framework transforms statistical evidence into disciplined decisions under uncertainty
  • How significance levels and the trade-offs between Type I and Type II errors shape statistical decision-making
  • How the same framework applies across diverse problems despite differences in research questions and statistical tests
  • Why the Neyman-Pearson framework remains a timeless foundation for statistical inference and decision-making

Bayes established a framework for updating beliefs in light of new evidence. Fisher developed maximum likelihood estimation as a rigorous method for estimating unknown parameters from observed data, assuming a known probability model. Together, these contributions laid the foundations of modern statistical inference by providing a principled way to learn from data.

4.1 The stepwise framework of hypothesis testing

4.1.1 Step 1: state the hypotheses

4.1.2 Step 2: choose a significance level

4.1.3 Step 3: select the test

4.1.4 Step 4: compute the test statistic

4.1.5 Step 5: establish the decision rule

4.1.6 Step 6: make a decision

4.1.7 Step 7: draw a conclusion

4.1.8 From framework to practice

4.2 Hypothesis testing in action

4.2.1 Example 1: beverage fill volumes

4.2.2 Example 2: safety monitoring

4.2.3 Example 3: a small clinical trial

4.2.4 From examples to principles

4.3 Why it matters

4.3.1 From evidence to action

4.3.2 Making decisions reproducible

4.3.3 A framework beyond statistics

4.4 An enduring framework for decision-making

4.5 Summary