Teaching

  • The Price is Right is a popular U.S. television game show in which contestants play product-pricing games in order to win prizes. Games involve some knowledge of prices, but many involve the element of chance as well. This paper describes a classroom activity I have designed to help teach probability concepts to students in an upper-level course. It is based on the television game show The Price is Right. This exercise is designed to help students better understand basic concepts such as probability rules, common distributions, and expectations. The exercise is intended for an upper-level statistics course, but could easily be adapted for use in an introductory statistics course as well. This paper describes The Price is Right classroom activity in detail. Student evaluations of the activity are also included.

  • This paper outlines one of a series of tutorials developed as part of an introductory statistics course for Agricultural and Natural Resource Sciences students. Here we compare two methods of sampling from an aerial photograph to obtain an estimate of the proportion of a particular type of vegetation. One method, transect sampling, is traditionally used by field ecologists, while the other is simple random sampling in a plane. Preparation details and possible extensions to the tutorial are described.

  • In the lottery game Lotto n/N, the winning n numbers are selected randomly and without replacement from {1, 2, 3, ..., N}. The selection of the winning numbers is normally done with a highly sophisticated mechanical device, and one of the appealing aspects of Lotto is that this procedure is seen to be fair and unbiased. An important perceived consequence is that no one (for a given amount of money) is seen to have a better chance of winning than anyone else. Few people would be willing to let an individual perform this task because of possible bias, but do we really know how difficult it is for an individual to be random in selecting numbers? In an experiment to observe the types and degrees of bias an individual might possess, data were collected from students who were asked to perform as 'random' number generators for the Lotto 6/42 game. Data consisting of the winning numbers from the Irish National Lottery game Lotto 6/42 were obtained from previous years, and a statistical package (in this case, S-Plus) was used to generate other simulated data. A comparison of the three sets of data using many of the basic tools in descriptive statistics together with some goodness of fit tests provides a useful exercise for students to test their intuition about randomness and to discover some of the inherent (and sometimes subtle) biases individuals possess when they attempt to be random.

  • There has been much concern about making the curriculum for engineering statistics more relevant to the needs of industry. One proposed solution is to include decision risk analysis in the curriculum. However, the current coverage of decision risk analysis in statistics textbooks is either nonexistent or very introductory. In part, this reflects the fact that decision risk analysis, as currently taught, relies on the complex notion of a utility function.<br>Recent research in decision theory suggests a way of comprehensively and rigorously discussing decision theory without using utility functions. In this new approach, the decision risk analysis course focuses on making decisions so as to maximize the probability of meeting a target. This allows decision theory to be integrated with reliability theory. This course would be more comprehensive than the conventional introductory treatment of decision theory and no more difficult to teach. In addition, integrating decision theory with reliability theory facilitates its incorporation in curricula that currently exclude decision theory.

  • Courses taught using problem-based learning methods give life sciences graduate students direct practice in the statistical reasoning skills needed to choose appropriate procedures for analyzing data from their research studies. This paper describes a graduate-level, case-based biostatistics course designed to cultivate these skills in veterinary medical science students who have had some initial preparation in statistics. The course gives students practical experience by focusing on the analysis of data from actual biomedical research studies. Student evaluations indicated that this course improved the students' ability to understand and apply statistical methods in their research.

  • A simple procedure is presented for obtaining the sample size and acceptance number for a single sample acceptance sampling plan, given the probability of lot acceptance for lots having proportion defective equal to p1, and the probability of lot rejection for lots having proportion defective equal to p2. The procedure gives a practical illustration of the use of the normal approximation to the binomial distribution that is appropriate for courses on statistical quality control as well as on introductory statistics.

  • 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.

  • A data set containing n = 210 observations and published by Lieblein and Zelen (1956) provides a useful example of multiple linear regression applied to an engineering problem. It relates percentiles of the failure time distribution for ball bearings to characteristics of the bearings (load, ball diameter, number of balls) in a theoretically derived equation that can be put into linear form. The analysis requires testing the equality of regression coefficients between manufacturers and between types of ball bearing within manufacturer to see if the same equation applies across the industry. Furthermore, there is special interest in confirming an accepted value for one of these coefficients. The original analysis employed weighted least squares, although this may have been unnecessary. In addition to the regression aspects of the problem, the example is useful for the extensive data manipulation required.

  • In a residential home, energy consumption is closely related to the outdoor temperature and size of the house. In a home of a given size, fuel consumption varies fairly predictably through the year. When homeowners add a room, other things being equal, energy consumption should increase. This dataset permits students to estimate the energy demand, make forecasts for future months, and investigate other relationships.

  • Data presented in a newspaper advertisement suggest the use of simple linear regression to relate the prices of diamond rings to the weights of their diamond stones. The intercept of the resulting regression line is negative and significantly different from zero. This finding raises questions about an assumed pricing mechanism and motivates consideration of remedial actions.

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