ABSTRACT
In practice, a shift in location is often accompanied by an increase in variability (see, e.g., Singer, 2001). According to Blair and Sawilowsky (1993), this phenomenon is common in toxicological, medical, and epidemiological studies. In a placebo-controlled clinical trial, the placebo group (a placebo is a simulated medical intervention such as an inert tablet) often has a smaller variability due to differences in the response to the therapy (Bender et al., 2007). In genetics, too, variances often increase with increasing means (Jansen, 2001, p. 571). When considering gene expression data, unequal variances between different groups usually occur at least for a part of genes (Demissie et al., 2008). Figure 3.1 shows hypothetical distributions for gene expression for normal and cancerous tissues (cf. Pepe et al., 2003, p. 134). There are differences in both location and variability regarding all three displayed distributions. This was also the case for the empirical distributions observed by Pepe et al. (2003, see their Figure 3). Differences in location are also often accompanied by heteroscedasticity, that is, a difference in variability, in social and behavioral sciences (see, e.g., Neuha¨user, 2001a). Thus, the assumption of a pure shift in location, as made in Chapter 2, might be an oversimplification that is not always appropriate.
