## Volume 7, Number 3 (November 1999)## Juliet Popper Shaffer and Yung-Pin Chen, "A Novel Method of Proof With an Application to Regression" (66K)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. --JPS
## Christine M. Anderson-Cook, "An In-Class Demonstration to Help Students Understand Confidence Intervals" (39K)This article discusses an active learning technique that can be easily incorporated into a variety of introductory statistics classes to demonstrate purely subjective and statistical confidence intervals. The concepts of confidence intervals, confidence levels, and the fixed, but unknown, population parameter are frequently misunderstood by a significant proportion of students. This class activity demonstrates these concepts by stressing the objective nature of statistical confidence intervals. It also emphasizes that the precision of the interval depends on the quality of the data used in its construction. The proposed exercise takes less than 50 minutes of lecture time and helps to solidify these essential statistical concepts in a visual and memorable way. Student reaction to the exercise has been positive as measured anecdotally by both improved student understanding of the concepts and increased interest in the activity. --CMA-C
## Philip J. Boland and Yudi Pawitan, "Trying To Be Random in Selecting Numbers for Lotto" (65K)In the lottery game Lotto
## Robert C. delMas, Joan Garfield, and Beth L. Chance, "A Model of Classroom Research in Action: Developing Simulation Activities to Improve Students' Statistical Reasoning" (80K)Researchers and educators have found that statistical
ideas are often misunderstood by students and
professionals. In order to develop better statistical
reasoning, students need to first construct a deeper
understanding of fundamental concepts. The
## "Teaching Bits: A Resource for Teachers of Statistics" (43K)This column features "bits" of information sampled from a variety of sources that may be of interest to teachers of statistics. Bob delMas abstracts information from the literature on teaching and learning statistics, while Bill Peterson summarizes articles from the news and other media that may be used with students to provoke discussions or serve as a basis for classroom activities or student projects. --JG ## Peter K. Dunn, "A Simple Dataset for Demonstrating Common Distributions" (19K)The baby boom dataset contains the time of birth, sex, and birth weight for 44 babies born in one 24-hour period at a hospital in Brisbane, Australia. The data can be used to demonstrate that some common distributions -- the normal, binomial, geometric, Poisson, and exponential -- can be used to model real situations. Because the dataset is small and easily understood, it provides a useful classroom example for discussing these distributions. --PKD
## Christopher H. Morrell, "Simpson's Paradox: An Example From a Longitudinal Study in South Africa" (11K)Real world examples of the reversal of the direction of an association when an additional explanatory variable is taken into account are unusual and hard to find. This article presents an example of Simpson's paradox from a South African longitudinal study of growth of children. The example demonstrates the importance race plays in every aspect of South African life. --CHM
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