Literature Index

Introductory statistics textbooks rarely discuss the concept of variability for a categorical variable and thus, in this case, do not provide a measure of variability. The impression is thus given that there is no measurement of variability for a categorical variable. A measure of variability depends on the concept of variability. Research has shown that "unalikeability" is a more natural concept than "variation about the mean" for many students. A "coefficient of unalikeablity" can be used to measure this type of variability. Variability in categorical data is different from variability in quantitative data. This paper develops the coefficient of unalikeability as a measure of categorical variability.

Although variability is of fundamental concern and interest to statisticians, often this does not get communicated to students who are taught instead to view variability as a nuisance parameter. A brief survey of a few case studies, as well as a recounting of some history, shows that variability is worthy of study in its own right, and examination of variability leads to insights that might have been missed had we focused all of our attention on the "trend" of the data. As on of the key components of statistical thinking, variability deserves more prominence in the classroom.

In this chapter we sketch some extensions of the range of observations that are normally considered in psychological analyses of judgments under uncertainty. Two levels of responses to uncertainty are discussed.

Ubiquitously people have to address the problem of uncertainty. The main focus of this article is an investigation of how people represent their knowledge about the uncertainty of events or regularities, and how they process this knowledge in order to make decisions in order to share their knowledge. In a first experiment it is asked how people gather information about frequencies of events and how this knowledge is interfered with the response mode, numerical vs. verbal estimates, they are required to use. The least interference occurs if the subjects are allowed to give verbal answers. From this it is concluded that processing knowledge about uncertainty by means of verbal expression imposes less mental work load on the organism than does numerical processing. Possibility theory is used as a framework for modeling the individual usage of verbal categories. The 'elastic' constrains on the verbal expressions for every single subject are determined in a further experiment by means of sequential testing. The results from this experiment are used to suggest a simple mechanism underlying the "availability" heuristic. In further experiments it is shown that the superiority of the verbal processing of knowledge about uncertainty quite generally reduces persistent biases reported in the literature: conservatism and negligence of regression. In a final experiment about predictions on a real-life situation it turns out that in a numerical forecasting task subjects restricted themselves to those parts of their knowledge which are numerical. On the other hand subjects in a verbal forecasting task accessed verbally as well as numerically stated knowledge. The conjecture is made that the superiority of the verbal mode in representing and in processing knowledge about uncertainty is due to "share-ability" (Freyd, in press)constrains which have evolved in the history of humankind and might even be phylogenetically determined.