Teaching

  • Multiple-choice randomized (MCR) examinations in which the order of the items or questions as well as the order of the possible responses is randomized independently for every student are discussed. This type of design greatly reduces the possibility of cheating and has no serious drawbacks. We briefly describe how these exams can be conveniently produced and marked. We report on an experiment we conducted to examine the possible effect of such MCR randomization on student performance and conclude that no adverse effect was detected even in a rather large sample.

  • 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.

  • Both teaching and learning are increasingly becoming technology-oriented processes, and teachers are struggling to keep up with rapid technological advances. The Internet, one of the most popular media of communication, provides fast access to vast amounts of information. There are many web sites that contain information useful for Advanced Placement Statistics teachers. This paper provides information about Internet resources available for project ideas, datasets, conferences, technical support, class notes, and much more.

  • Scores of 1997 Big Ten Conference men's basketball games involving the University of Iowa Hawkeyes are analyzed with a series of scatterplots accompanied by formal bivariate statistical inference. The analyses reveal that the Hawkeyes' defensive performance is largely unaffected by the site of the game, while offensive performance dips significantly in games played on opposing teams' courts.

  • In this article, a very simple and yet useful feature of Excel called the SPIN BUTTON is used to illustrate two concepts associated with attribute acceptance sampling plans. The first concept is calculating the probability of lot acceptance based on which the operating characteristic (OC) curve of an attribute sampling plan is drawn. The SPIN BUTTON can show, visually, that the exact probability of lot acceptance calculated using the Hypergeometric distribution can be approximated by the Binomial distribution. The second concept is how the probability of lot acceptance changes when either one of the three parameters N, n, c of a sampling plan changes. The SPIN BUTTON can also visually show us how the shape of the OC curve of a sampling plan changes when the parameters vary.

  • There is a potential misuse of the power function under the logical extreme when the null hypothesis is true. The power function is defined to measure the probability of rejecting the null given any value of the parameter being tested. It can be used to obtain the power and the beta values only under the alternative hypothesis. When the null is true, the power function can be used to obtain the size of the test. The power and the probability of committing a Type II error are, however, undefined and, hence, the power function should not be used to obtain these values.

  • Teaching prediction intervals to introductory audiences presents unique opportunities. In this article I present a strategy for involving students in the development of a nonparametric prediction interval. Properties of the resulting procedure, as well as related concepts and similar procedures that appear throughout statistics, may be illustrated and investigated within the concrete context of the data. I suggest a generalization of the usual normal theory prediction interval. This generalization, in tandem with the nonparametric method, results in an approach to prediction that may be systematically deployed throughout a course in introductory statistics.

  • Many elementary statistics textbooks recommend the sign test as an alternative to the t-test when the normality assumption is violated. This recommendation is not always warranted, as we demonstrate by extending previous studies of the effects of skewness, kurtosis, and shifting of the location parameter on the size and power of the t- and sign tests for the one-sample case. For skewed populations our simulations reveal that the power of the t-test can actually be higher than that of the t-test for a normal parent population when the location parameter is shifted in the opposite direction of the skewness of population. In that same instance, the power of the t-test is also significantly greater than that of the sign test. Furthermore, our simulations reveal that for low-kurtosis populations the power of the t-test is again greater than that of the sign test.

  • In statistics courses, students often find it difficult to understand the concept of a statistical test. An aggravating aspect of this problem is the seeming arbitrariness in the selection of the level of significance. In most hypothesis-testing exercises with a fixed level of significance, the students are just asked to choose the 5% level, and no explanation for this particular choice is given. This article tries to make this arbitrary choice more appealing by providing a nice geometric interpretation of approximate 5% hypothesis tests for means.<br>Usually, we want to know not only whether an observed deviation from the null hypothesis is statistically significant, but also whether it is of practical relevance. We can use the same geometrical approach that we use to illustrate hypothesis tests to distinguish qualitatively between small and large deviations.

  • In this article we investigate the large-sample/small-sample approach to the one-sample test for a mean when the variance is unknown, using the probability of a Type I error as the criterion of interest. We show that in most cases using a t-test (t critical value) provides a more robust test than does using the z-test (standard normal critical value). The only case in which z has some advantage is when using a small sample from a parent population with extremely high kurtosis or with skewness in the direction of the rejection region tail. The implications for teaching the large-sample/small-sample approach in introductory statistics classes are discussed in light of these findings.

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