ABSTRACT
There are many experimental designs or studies where the subjects are not a random sample from some well-defined population. For example, subjects recruited for a clinical trial are hardly ever a random sample from the set of all people suffering from a certain disease but are a selection of patients showing up for examination in a hospital participating in the trial. Usually, the subjects are randomly assigned to certain groups, for example a control and a treatment group, and the analysis needs to take this randomization into account. In this chapter, we discuss such test procedures usually known as (re)- randomization or permutation tests. With such tests the distribution of the test statistic under the null hypothesis is determined conditionally on the data at hand. Such conditional test procedures will be the subject of this chapter. The first data set considered will be that from the room width estimation experiment reported in Chapter 3. In this experiment 40 of the estimated widths (in feet) of 69 students and 26 of the estimated widths (in meters) of 44 students are tied. In fact, this violates one assumption of the unconditional test procedures applied in Chapter 3, namely that the measurements are drawn from a continuous distribution. In this chapter, the data will be reanalyzed using an appropriate conditional test procedure. The second example is taken from Mann (1981) who reports a study carried
out to investigate the causes of jeering or baiting behavior by a crowd when a person is threatening to commit suicide by jumping from a high building. A hypothesis is that baiting is more likely to occur in warm weather. Mann (1981) classified 21 accounts of threatened suicide by two factors, the time of year and whether or not baiting occurred. The data are given in Table 4.1 and the question is whether they give any evidence to support the hypothesis? The data come from the northern hemisphere, so June-September are the warm months.
