The common development of the hypergeometric probability formula is typically confusing to students in introductory statistics courses. Two alternative developments that appear to be more intuitive and conceptually consistent are presented.
The common development of the hypergeometric probability formula is typically confusing to students in introductory statistics courses. Two alternative developments that appear to be more intuitive and conceptually consistent are presented.
A useful way of approaching a statistical problem is to consider whether the addition of some missing information would transform the problem into a standard form with a known solution. The EM algorithm (Dempster, Laird, and Rubin 1977), for example, makes use of this approach to simplify computation. Occasionally it turns out that knowledge of the missing values is not necessary to apply the standard approach. In such cases the following simple logical argument shows that any optimality properties of the standard approach in the full-information situation generalize immediately to the approach in the original limited-information situation: If any better estimate were available in the limited-information situation, it would also be available in the full-information situation, which would contradict the optimality of the original estimator. This approach then provides a simple proof of optimality, and often leads directly to a simple derivation of other properties of the solution. The approach can be taught to graduate students and theoretically-inclined undergraduates. Its application to the elementary proof of a result in linear regression, and some extensions, are described in this paper. The resulting derivations provide more insight into some equivalences among models as well as proofs simpler than the standard ones.
This article takes data from a paper in the Journal of the American Medical Association that examined whether the true mean body temperature is 98.6 degrees Fahrenheit. Because the dataset suggests that the true mean is approximately 98.2, it helps students to grasp concepts about true means, confidence intervals, and t-statistics. Students can use a t-test to test for sex differences in body temperature and regression to investigate the relationship between temperature and heart rate.
Dawson (1995) described a dataset giving population at risk and fatalities for an unusual mortality episode (the sinking of the ocean liner Titanic), and discussed experiences in using the dataset in an introductory statistics course. In this paper the same dataset is analyzed from the point of view of the second statistics course. A combination of exploratory analysis using tables of observed survival percentages, model building using logistic regression, and careful thought allows the statistician (and student) to get to the essence of the random process described by the data. The well-known nature of the episode gives the students a chance at determining its character, and the data are complex enough to require sophisticated modeling methods to get at the truth.
The race between Mark McGwire and Sammy Sosa to break the major league season home run record captured the attention of sports fans (and even non-sports fans) during the summer of 1998. In this article the game-by-game home run performance of each of these players is provided, along with some team statistics for each game. This dataset provides a rich set of possibilities of analyses in both introductory and advanced statistics courses, including graphical exploratory displays, categorical data analysis, analysis of variance, logistic regression, and smoothing methods for Poisson and binomial data.
The use of tangible examples can make the concepts of statistical sampling and survey design more meaningful for college students. These concepts are especially relevant with the advent of the 2000 Census and the debate over its use of statistical sampling.<br>In this paper, basic ideas from survey design are introduced using the 2000 Census as an example, in order to capitalize on the recent media attention. Then, these same concepts are applied to the National Health Interview Survey (NHIS). Data for the 1993 NHIS can be accessed through the National Center for Health Statistics web site and simple analyses can be performed over the web to demonstrate the use of sampling weights. In addition, subsets of the data can be downloaded and analyzed using statistical software packages.<br>The methods of statistical sampling and the structure of a national survey have a variety of applications in the classroom, depending on the level of the course being taught. This paper discusses some of these applications and how to access and use these data as an effective teaching tool.
An overriding goal of teaching is to stimulate learning that lasts. A way to achieve this is, surely, to make teaching memorable. By asking "what makes teaching memorable?", this paper identifies a number of fundamental characteristics of statistics teaching that will assist students in long-term retention of ideas. It structures these attributes of memorable statistics teaching and then shows, with examples, how they can be realised. The author's reflection on his extensive teaching experience underpins this paper.
A body of research on enhancing the teaching of statistics has been accumulating now for more than fifty years since the pioneering contributions of Wishart (1939) and Hotelling (1940). Yet undergraduates continue to find courses in statistics unappealing. Perhaps this is because their teachers -- even those clear and conscientious in explaining subject-matter detail, and thoughtful in their reading of the statistics education literature -- too commonly fail to open statistical vistas, and thus fail to convey a rich understanding of the purpose and structure of the subject. A vista is inherently a perspective view. This paper shows, with examples, how perspective views can illuminate both purpose and structure. A well-devised perspective on purpose, offered early, can make each topic in the course immediately meaningful. And perspectives on structure, unveiled strategically, can highlight the coherence of statistics. The author's experience over twenty-five years shows that teaching with perspectives can help to produce that ideal -- long-term retention of learning.
Long-term learning should, surely, be an outcome of higher education. What is less obvious is how to teach so that this goal is achieved. In this paper, one constructive contribution to such a goal is described in the context of statistical education: the introduction of striking demonstrations. A striking demonstration is any proposition, exposition, proof, analogy, illustration, or application that (a) is sufficiently clear and self-contained to be immediately grasped, (b) is immediately enlightening, though it may be surprising, (c) arouses curiosity and/or provokes reflection, and (d) is so presented as to enhance the impact of the foregoing three characteristics. Some 30 striking demonstrations are described and classified by statistical subfield. The intent is to display the variety of devices that can serve effectively for the purpose, as a stimulus to the reader's own enlargement of the list for his or her own pedagogical use.
This article discusses a capstone course for undergraduate statistics majors at the University of South Carolina. The course synthesizes lessons learned throughout the curriculum and develops students' nonstatistical skills to the level expected of professional statisticians. Student teams participate in a series of inexpensive laboratory experiments that emphasize ideas and techniques of applied and mathematical statistics, mathematics, and computing. They also study modules on important nonstatistical skills. Students prepare written and oral reports. If a report is not of professional quality, the student receives feedback and repeats the report. All students leave the course with a better understanding of how the pieces of their education fit together and with a firm understanding of the communication skills required of a professional statistician.