Journal Article

  • This paper reports on the results of an empirical study of students' conceptions and understanding of statistics. Six qualitatively different conceptions are described, ranging from fragmented to inclusive views. Students expressing the more inclusive and holistic conceptions approach their study of statistics through a focus on 'higher-order' statistical thinking. Students expressing limited and fragmented views may not be able to understand the complexity or applications of the discipline. This paper describes the use of a qualitative methodology - phenomenography - that aims to explore the qualitatively different ways in which a group of people experience a specific phenomenon, in this case statistics. It also describes an overarching framework, the "Professional Entity," that relates students' understanding of statistics and their perceptions of working as a statistician. Investigating and describing the ways in which students learn statistics, how they understand statistics, and how they perceive their own work will enable teachers to develop curricula that focus on enhancing the student learning environment and guiding student conceptions of 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.

  • This paper describes an interactive project developed to use for teaching statistical sampling methods in an introductory undergraduate statistics course, an Advanced Placement (AP) statistics course, or, with adaptation, in a statistical sampling course or a statistical simulation course. The project allows students to compare the performance of simple random sampling, stratified random sampling, systematic random sampling, and cluster random sampling in an archaeological setting.

  • This paper begins by describing two hands-on activities developed for teaching basic statistical concepts to junior high students. Through generating, collecting, displaying, and analyzing data, students are given the opportunity to explore a variety of descriptive statistical techniques and develop an understanding of the distinction between theoretical, subjective, and empirical (or experimental) probabilities. These activities are then extended to introduce the sampling distribution of a sample proportion. The extension is appropriate for use in grades 9 through 12, in an Advanced Placement (AP) Statistics course, or in an introductory statistics course at the undergraduate level.

  • Members of the faculty of Le Moyne College made sweeping changes in the basic statistics course provided for the social and life sciences by the Department of Mathematics. The departments involved undertook an intensive collaboration. Intense scrutiny was given to the purpose and goals of the course. The result is a course that is significantly different from its predecessor. It places more emphasis on concepts and technology. A laboratory component was added to give students experience with Minitab and messy datasets. The implementation of the course had the expected problems. These are documented along with what was done to improve the course the second time it was offered.

  • I recently introduced an advanced statistical methods course into our curriculum with a two-tiered prerequisite system - students were required to have taken either an introductory statistics course or Calculus II. As a result, this course served as a first course in statistics for some quantitatively strong students and a follow-up course for others. I used a case study approach to introduce and motivate ideas to students new to statistics while engaging and challenging students for whom some ideas were review. Given constraints on resources which exist at smaller schools, a data-centered course such as this offered a good first experience in statistics for math students, one which piqued their interest and set a solid foundation for further study. In addition, the mixed audience led to an intellectually exciting class atmosphere for all students in the class. A quantitative assessment of students' understanding of important statistical concepts is described to provide insight into whether or not students with no statistical experience can comprehend and apply basic ideas as well as if they had taken an introductory statistics class.

  • This dataset contains information on life expectancies in various countries of the world and the densities of people per television set and of people per physician in those countries. The example has proven very useful for helping students to discover the fundamental principle that correlation does not imply causation. The data also give students an opportunity to explore data transformations and to consider whether a causal connection is necessary for one variable to be a useful predictor of another.

  • Classical estimators for the parameter of a uniform distribution on the interval are often discussed in mathematical statistics courses, but students are frequently left wondering how to distinguish which among the variety of classical estimators are better than the others. We show how classical estimators can be derived as Bayes estimators from a family of improper prior distributions. We believe that linking the estimation criteria in a Bayesian framework is of value to students in a mathematical statistics course, and we believe that the students benefit from the exposure to Bayesian methods. In addition, we compare classical and Bayesian interval estimators for the parameter Phi and illustrate the Bayesian analysis with an example.

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