Literature Index

Recent years have witnessed a strong movement away from what might be termed classical statistics to a more empirical, data-oriented approach to statistics, sometimes termed exploratory data analysis, or EDA. This movement has been active among professional statisticians for twenty or twenty-five years but has begun permeating the area of statistical education for non-statisticians only in the past five to ten years. At this point, there seems to be little doubt that EDA approaches to applied statistics will gain support over classical approaches in the years to come. That is not to say that classical statistics will disappear. The two approaches begin with different assumptions and have different objectives, but both are important. These differences will be outlined in this article.

In the article "The Probabilistic Abacus", by A. Engel (Educational Studies in Mathematics 6, 1975, p. 1 - 22), we have introduced the probabilistic abacus and we have applied it to absorbing Markov chains. We have explained in detail how to compute absorption probabilities and expected times to absorption, but we gave no proofs. In this paper we give more applications of the abacus and we supply proofs for most of its properties.

The author states that the reason why students have major difficulty in learning statistics and that distinguishes statistics from other disciplines is that the important fundamental concepts of statistics are quintessentially abstract. In his view, concepts that are fundamental in statistics cannot be directly demonstrated, experienced, or drawn. Other factors are listed as making the problem worse: 1) intro stats courses involve more abstract concepts which are used frequently; 2) students must deal with truly abstract concepts AND immediately relate and apply these concepts to reality; 3) problems in statistics are always open to interpretation and have several solutions, none of which are truly known as being the correct ones; 4) the difference between statistics and mathematics lies in the type of numbers that are obtained- in mathematics, the numbers are obtained from calculations whereas in statistics, numbers are obtained from experiments; and 5) statistical notation and terminology are ambiguous and confusing. Watt's solution to the above problem is for statisticians to improve the notation and terminology by making the terms more meaningful and removing ambiguities.

Measures of biologic and behavioural variables on a patient often estimate longer term latent values, with the two connected by a simple response error model. For example, a subject's measured total cholesterol is an estimate (equal to the best linear unbiased estimate (BLUE)) of a subject's latent total cholesterol. With known (or estimated) variances, an alternative estimate is the best linear unbiased predictor (BLUP). We illustrate and discuss when the BLUE or BLUP will be a better estimate of a subject's latent value given a single measure on a subject, concluding that the BLUP estimator should be routinely used for total cholesterol and per cent kcal from fat, with a modified BLUP estimator used for large observed values of leisure time activity. Data from a large longitudinal study of seasonal variation in serum cholesterol forms the backdrop for the illustrations. Simulations which mimic the empirical and response error distributions are used to guide choice of an estimator. We use the simulations to describe criteria for estimator choice, to identify parameter ranges where BLUE or BLUP estimates are superior, and discuss key ideas that underlie the results.