Literature Index

Students in an applied statistics course offering some nonparametric methods are often (subconsciously) restricted in modeling their research problems by what they have learned from the t-test. When moving from parametric to nonparametric models, they do not have a good idea of the variety and richness of general location models. In this paper, the simple context of the Wilcoxon-Mann-Whitney (WMW) test is used to illustrate alternatives where "one distribution is to the right of the other." For those situations, it is also argued (and demonstrated by examples) that a plausible research question about a real-world experiment needs a precise formulation, and that hypotheses about a single parameter may need additional assumptions. A full and explicit description of underlying models is not always available in standard textbooks.

The 1970 draft lottery for birthdates is reviewed as an example of a government effort at randomization whose inadequacy can be exhibited by a wide variety of statistical approaches. Several methods of analyzing these data -- which were of life-and-death importance to those concerned -- are given explicitly and numerous others are cited. In addition, the corresponding data for 1971 and for 1972 are included, as are the alphabetic lottery data, which were used to select draftees by the first letters of their names. Questions for class discussion are provided. The article ends with a survey of primary and secondary sources in print.

The Wilcoxon statistics are usually taught as nonparametric alternatives for the 1- and 2- sample Student-t statistics in situations where the data appear to arise from non-normal distributions, or where sample sizes are so small that we cannot check whether they do. In the past, critical values, based on exact tail areas, were presented in tables, often laid out in a way that saves space but makes them confusing to look up. Recently, a number of textbooks have bypassed the tables altogether, and suggested using normal approximations to these distributions, but these texts are inconsistent as to the sample size n at which the standard normal distribution becomes more accurate as an approximation. In the context of non-normal data, students can find the use of this approximation confusing. This is unfortunate given that the reasoning behind - and even the derivation of - the exact distributions can be so easy to teach but also help students understand the logic behind rank tests. This note describes a heuristic approach to the Wilcoxon statistics. Going back to first principles, we represent graphically their exact distributions. To our knowledge (and surprise) these pictorial representations have not been shown earlier. These plots illustrate very well the approximate normality of the statistics with increasing sample sizes, and importantly, their remarkably fast convergence.

Examination of the statistical literature shows that consensus on definition, terminology, and interpretation of some hypothesis testing concepts is elusive. This makes hypothesis testing a difficult topic to teach and learn. This paper reports on the results of a study of novice students' conceptual knowledge of four hypothesis testing concepts through talking aloud and interview methods. While some students seemed to have a reasonable understanding of some concepts, many students seemed to have more limited understanding. The study explores students' faulty conceptual knowledge.