ABSTRACT
This chapter is concerned with an extremely important but at the same time controversial side of statistics: the notion of statistical significance and testing of statistical hypotheses. There is a formal part, where the different mathematical types of hypotheses are identified and a less formal part, where the hypotheses are classified according to their purpose in a statistical investigation. The notion of test statistic and significance are discussed, and concepts such as critical region, power, size, level of test, as well and types of error are introduced. The relation between set estimation and significance testing is described, and everything is illustrated with a range of examples, in particular a number of standard tests as they often are used in linear normal models. There is some emphasis on methods for calculating p-values, either by Monte Carlo methods or using the asymptotic results as developed in Chapter 5.
