If one claims that a sample has been randomly selected from a population, can the merits of the claim be assessed using statistical tests? Are tests alone sufficient?
If one claims that a sample has been randomly selected from a population, can the merits of the claim be assessed using statistical tests? Are tests alone sufficient?
In 1985, the North American Group of the Group for the Psychology of Mathematics Education affirmed the notion that the constructivist perspective would provide guidelines for instructors to facilitate student learning. The constructivist view of the student as an active learner as well as the present day emphases on the automation of the calculations and the student learning of the concepts has motivated the use of multimedia in the online teaching of statistics. Here, I examined the influence of the constructivist perspective on the teaching of statistics, the influence of the constructivist perspective on the use of computer assisted calculations and on the use of automated simulations and the significance of teaching with data. Based on this examination, one may improve upon the teaching of statistics (1) by accounting for the omission of elements of sound and video that were observed for past online courses, (2) by providing instruction on how data is produced for an empirical study, (3) by providing small data sets to show the influence upon the statistic of outliers, skew and variance heterogeneity through the use of manual calculations, (4) by providing large real datasets so that students may draw substantive conclusions about the statistics, and (5) by using automated simulations to convey the statistical properties of the sampling distribution of the statistic
The purpose of the paper is to share the ten years of experience of implementing small group community-oriented projects as a learning tool in three different calculus-based statistics courses at the University of St. Thomas in Minnesota. The content of the courses, specifics of group organization, authentic data issues, and the products of project work are discussed. Four examples of student projects are considered. Two of these projects were carried out for external community partners and two for community partners found inside the university. These examples serve to illustrate community involvement and community-oriented learning experienced in the statistics classroom.
This paper explores the role magic tricks can play in the teaching of probability and statistics, especially for lectures in college courses. Demonstrations are described that illustrate a variety of probabilistic and statistical topics, including basic probability and combinatorics, probability and sampling distributions, hypothesis testing, and advanced topics such as Markov chains and Bayes' Theorem. In addition to magic tricks providing visual demonstrations to supplement traditional blackboard-based lectures and the opportunity to engage students in class-participatory activities, possible benefits include a focus on conceptual understanding, development of critical thinking, and an opportunity to reflect upon the role of assumptions and estimates of probabilities.
What is "objective statistics"? How can a statistics teacher teach it? Is it possible at all? These topics are discussed in this essay. It is shown that statistics is subjective; this is pictured with an example of a relationship between two quantitative continuous variables, for which various statistical approaches can be applied. This subjectivity should not nevertheless be thought of as a bad thing - it is the intrinsic part that makes statistics an art of dealing with data. To teach statistics well, then, means to teach thinking statistically, to teach understanding statistics, and not only to teach applying statistics.
The questionnaire survey was conducted among post-graduate and under-graduate students of two agricultural universities in Poland to study their basic knowledge of graphing. A smaller group of primary school pupils was also administered in the survey for comparison purposes. The survey consisted of only two questions concerning the choice of the best and the worst chart among three options: a piechart, a vertical barchart with three-dimensional columns, and a horizontal barchart. The charts were constructed in such a way that only one type - the horizontal barchart - could be considered a good chart. The results are worrying: among university students, both under- and postgraduate, quite often the three-dimensional barchart was chosen as the best one. Among the primary school pupils the piechart was most often chosen as the best one.
An attractive way of introducing Bayesian thinking is through a discrete model approach<br>where the parameter is assigned a discrete prior. Two generic R functions are introduced for<br>implementing posterior and predictive calculations for arbitrary choices of prior and sampling<br>densities. Several examples illustrate the usefulness of these functions in summarizing the<br>posterior distributions for one and two parameter problems and for comparing models by the use<br>of Bayes factors
The proper analysis of data is predicated on the existence of a data set containing valid responses. There are many sound techniques that should be employed to minimize data errors, and to cleanse data sets. The purpose of this article is to provide instructors and their students with an overview of the mechanics of data capture; the metadata framework; outlier detection and treatment; and contemporary solutions for missing data.
This article demonstrates that art may inspire statistical thinking in many ways, providing aesthetic pleasure, scientific enlightenment, and humorous excitement. Art can serve as a fine tool for educational purposes in statistics, presenting explicit illustrations of statistical concepts. The role of statisticians here is to find a hidden meaning of a masterpiece and to interpret it for students. This work gives some examples of such an interpretation of painting from a statistical perspective.
It is well known that meaningful knowledge of statistics involves more than simple factual or procedural knowledge of statistics. For an intelligent use of statistics, conceptual understanding of the underlying theory is essential. As conceptual understanding is usually defined as the ability to perceive links and connections between important concepts that may be hierarchically organized, researchers often speak of this type of knowledge as structural knowledge. In order to gain insight into the actual structure of a student's knowledge network, specific methods of assessment are sometimes used. In this article we discuss a newly developed, specific method for assessing structural knowledge and compare its merits with more traditional methods like concept mapping and the use of simple open questions.