Summary. In this chapter we introduce the ideas behind the art of testing statistical hypotheses (Section 6.1). The general concepts are described, terminology is introduced, and several elementary examples are discussed. We also examine some philosophical questions about testing and some extensions to cases in which it is difficult to build the statistical models needed for testing.

The significance level, power, bias, efficiency, and robustness of statistical tests are discussed in Section 6.2. The application of Monte Carlo simulation in problem testing is discussed in Section 6.3, and in Section 6.4 we examine how hypotheses are formulated and explore some of the limitations of statistical testing. The spatial correlation structure of the atmosphere often impacts testing problems. Strategies for copying with and using this structure are discussed in Section 6.5. A number of tests of the null hypothesis of equal means and variances are discussed in Sections 6.6 and 6.7. Tests designed to provide a global interpretation for a field of local decisions, called field significance tests, are presented in Section 6.8. Univariate and multivariate recurrence analysis are discussed in Sections 6.9 and 6.10.

The Concept of Statistical Tests

Introduction. Since we should now be somewhat comfortable with the ideas underlying hypothesis testing (see [1.2.7], [4.1.7–11], and the preamble to this part of the book), we only briefly characterize the testing paradigm here.

Statistical hypothesis testing is a formalized process that uses the information in a sample to decide whether or not to reject H0, the null hypothesis.