TABLE OF CONTENTS This chapter introduces the fundamental statistical ideas that underlie the various methods discussed later. These methods involve two closely related sets of ideas. One is concerned with deciding whether an observed outcome is consistent with some preconceived view of the way the system under study should behave; this set of ideas relates to 'statistical significance tests'. The second set is concerned with estimating the size of things and, in particular, with placing error bounds on the measured quantities - 'confidence intervals' are the relevant statistical tool for such purposes.
Recall the process of using an X-bar chart on a routine basis. For simplicity, consider only the use of the rule that a point outside the action limits is a signal of a system problem. Each time we plot a point on the chart and decide whether or not a problem exists, essentially, we test the hypothesis that the analytical system is producing results that fluctuate randomly about the centre line. This is a simple example of what is called a statistical 'significance test': the observed result (X-bar) is compared to what would be expected if the hypothesis of system stability were true. This hypothesis is rejected when the observed result is inconsistent with, i.e., very unlikely under, such an hypothesis. This is judged to be the case when the plotted point falls outside the action limits. Several different significance tests will be introduced later. All such tests are conceptually the same and the basic ideas will be...
