Interpretation of correlation is often based on rules of thumb in which some boundary values are given to help decide whether correlation is non-important, weak, strong or very strong. This article shows that such rules of thumb may do more harm than good, and instead of supporting interpretation of correlation - which is their aim - they teach a schematic approach to statistics. Therefore they should be avoided in a statistics course.
The binomial distribution is used to predict the winner of the 49th International Shooting Sport Federation World Championship in double trap shooting held in 2006 in Zagreb, Croatia. The outcome of the competition was definitely unexpected.
In this short note, the difference between improbable and unexpected outcomes is demonstrated via an example that uses the hypergeometric distribution.
In manufacturing industry, many employees need to interpret and communicate statistical information to monitor and improve production processes. Often the information is reduced to the form of numerical measures, on the logic that numbers are a convenient and understandable type of information to pass among the diverse groups of employees that make up a manufacturing operation. We investigated by means of interviews and observation how several numerical measures, 'process capability indices', were used in an automotive factory and how employees were trained to use them. We found that the typical introduction to the measures deployed statistical and algebraic symbolism as well as laborious manual calculations that did not appear to support employees' understanding of the underlying mathematical relationships. These measures therefore failed to be 'boundary objects' - artifacts that inhabit different social worlds and satisfy the informational requirements of each. The goal of our subsequent design-based research was to design a representation of the process capability indices that would be easier to engage with than the existing formal symbolism used in shop floor calculations and in training. We did this by re-presenting relevant mathematical relationships in computer tools - technology-enhanced boundary objects (TEBOs) - developed in collaboration with company trainers. To evaluate our interaction with three trainers and 37 trainees in three courses in two factories, and the impact of the computer tools on practice, we followed the computer tools' trajectory from the stage of codesign with the original car factory through to the stage at which the computer tools were used by factories beyond this research project. The evaluation points to the importance of aligning statistical and workplace norms and meanings, and gives illustrations of how the tools facilitated communication between employees.
In this paper we provide a glimpse of the iterations of design, research and theorizing of a<br>probability simulation tool, Probability Explorer, that have occurred over the past decade. We<br>provide a brief description of the key features of the technology designed to allow young students<br>opportunities to explore probabilistic situations. This is followed by details about several research<br>observations made in multiple investigations of student explorations with this probability micro-<br>world software package. We then explicate how research results suggest that a focus on a<br>bidirectional interplay between theoretical distribution and empirical data can promote reasoning<br>about probabilistic phenomena, and offer implications for instruction. The paper concludes with a<br>discussion of a next generation innovation in the software for representing a theoretical distribution<br>that we believe may promote better students reasoning about the bidirectional connection between<br>theoretical distributions and empirical data
This paper discusses the development of graphical user interfaces (GUIs) to illustrate<br>sampling from a trinomial distribution by the natural extension of Galton's Quincunx to three<br>dimensions
This paper addresses the problem of generating a large number of data sets for classes of students that exhibit certain characteristics but which are sufficiently different to minimize the possibility of plagiarism. A number of R functions are provided to perform the production of the data and the answers to the relevant data.
Despite the rapidly growing population of English language learners in U.S. colleges and schools, very little research has focused on understanding the challenges of English language learners specifically in statistics education. At a university near the United States-México border, the authors conducted an exploratory qualitative case study of issues of language in learning statistics for pre-service teachers whose first (and stronger) language is Spanish. The two strongest findings that emerged from cross-case analysis of the interviews were the importance of the role of context (the setting in which information is communicated) and the confusion among registers (subsets of language). This paper overviews and synthesizes relevant literature and offers resources and recommendations for teaching and future research.
Despite the relevance of correlational studies for most research domains, many students, teachers, and researchers alike hold misconceptions concerning the Pearson product-moment correlation coefficient. One of these, the transitivity misconception, has not yet been documented in a systematic way. This paper summarizes the first empirical study, using 279 university students, and examines the relationship between student-based and task-based factors and the appearance of this misconception. In particular, two task-based factors seemed to have a significant effect on its appearance. In addition, the respondents' level of confidence in their answer to the transitivity item was significantly lower than for most other times.
Researchers in the field of psychology studying subjects' reasoning abilities and decision-making processes have identified certain common errors that are made, particularly on probability questions standard in introductory statistics courses. In addition, they have identified modifications to problems and training that promote normative reasoning in laboratory subjects. This study attempts to replicate, in the context of a statistics classroom, the results of one particular type of probability question, a two-stage conditional probability problem. The psychology literature suggests two possible implications for teaching probability. Although no effect for format modification was found, the representations training effects were replicated. The implications of these results for teaching and directions for future research are discussed.