ABSTRACT
Jerzy Neyman and Egon Pearson developed a new approach that plays a major role when analyzing data. They used Laplace's notion of a sampling distribution and standard error, but they proposed an alternative framework for making inferences about the population mean based on what is called hypothesis testing. This chapter elaborates on the topic of making decisions about whether some claim about the population mean, or some other parameter of interest, is consistent with data. A critical value is the value used to determine whether the null hypothesis should be rejected. It is noted that if the null hypothesis is true and the probability of a Type I error is controlled exactly, the average p-value over many studies is 0.5. A Type II error is failing to reject a null hypothesis when it should be rejected. Bootstrap methods provide a way of testing hypotheses and computing confidence intervals without assuming normality that provide major advantages over many competing techniques.
