Introduction

The inherent difficulties in mastering hypothesis testing

Hypothesis testing is one of the most important but also one of the most confusing parts of statistical inference for several reasons, including the following:

1. (i) the need to introduce numerous new concepts before one is able to define the problem adequately,

2. (ii) the fact that the current textbook discussion of the problem constitutes an inept hybrid of two fundamentally different approaches to testing (what Gigerenzer (1987) called the “hybrid theory”), and

3. (iii) the fact that there is no single method for constructing “good” tests under most circumstances, comparable to the method of maximum likelihood in estimation.

An attempt is made to alleviate these problems by utilizing a number of teaching techniques, the most important of which is the historical development of testing since the late 19th century. It must be said that this is used as a teaching device and no attempt is made to provide a complete account of the historical development of testing; a major task which is yet to be undertaken. The historical dimension of testing is used primarily to ease the problem of introducing too many concepts too quickly and to bring out the differences between the Fisher and the Neyman–Pearson approaches to testing.