Journal Article

  • This paper describes three spreadsheet exercises demonstrating the nature and frequency of type I errors using random number generation. The exercises are designed specifically to address issues related to testing multiple relations using correlation (Demonstration I), t tests varying in sample size (Demonstration II) and multiple comparisons using analysis of variance (Demonstration III). These demonstrations highlight the purpose and application of hypothesis testing and teach students the dangers of data dredging and a posteriori hypothesis generation.

  • Biostatistics is traditionally a difficult subject for students to learn. While the mathematical aspects are challenging, it can also be demanding for students to learn the exact language to use to correctly interpret statistical results. In particular, correctly interpreting the parameters from linear regression is both a vital tool and a potentially taxing topic. We have developed a Calibrated Peer Review (CPR) module to aid in learning the intricacies of correct interpretation for continuous, binary, and categorical predictors. Student results in interpreting regression parameters for a continuous predictor on midterm exams were compared between students who had used CPR and historical controls from the prior course offering. The risk of mistakenly interpreting a regression parameter was 6.2 times greater before the introduction of the CPR module (p=0.04). We also assessed when learning took place for a specific item for three students of differing capabilities at the start of the assignment. All three demonstrated achievement of the goal of this assignment; that they learn to correctly evaluate their written work to identify mistakes, though one did so without understanding the concept. For each student, we were able to qualitatively identify a time during their CPR assignment in which they demonstrated this understanding.

  • For many students meeting, say, the gamma distribution for the first time, it may well turn out to be a rather fruitless encounter unless they are immediately able to see an application of this probability model to some real-life situation. With this in mind, we pose here an appealing problem that can be used as the basis for a workshop activity introducing, and subsequently encouraging the exploration of, many of the well-known continuous distributions in a meaningful way. We provide suggestions as to how the session might be run, discuss any pedagogical issues that arise and highlight particularly interesting features of the distributions.

  • Language plays a crucial role in the classroom. The use of specialized language in a domain can cause a subject to seem more difficult to students than it actually is. When words that are part of everyday English are used differently in a domain, these words are said to have lexical ambiguity. Studies in other fields, such as mathematics and chemistry education, suggest that in order to help students learn vocabulary instructors should exploit the lexical ambiguity of the words. The study presented here is the second in a sequence of studies designed to understand the effects of and develop techniques for exploiting lexical ambiguities in statistics classrooms. In particular, this paper looks at five statistical terms and the meanings of these terms most commonly expressed by students at the end of an undergraduate statistics course.

  • This paper proposes an argument framework for the teaching of null hypothesis statistical testing and its application in support of research. Elements of the Toulmin (1958) model of argument are used to illustrate the use of p values and Type I and Type II error rates in support of claims about statistical parameters and subject matter research constructs. By viewing the application of null hypothesis statistical testing within this framework, the language and intent of statistical support for research can be more precisely understood and taught.

  • On the 2009 AP© Statistics Exam, students were asked to create a statistic to measure skewness in a distribution. This paper explores several of the most popular student responses and evaluates which statistic performs best when sampling from various skewed populations

  • Inferential reasoning is a central component of statistics. Researchers have suggested that students should develop an informal understanding of the ideas that underlie inference before learning the concepts formally. This paper presents a hands-on activity that is designed to help students in an introductory statistics course draw informal inferences about a bag of bingo chips and connect these ideas to the formal T-test and confidence interval. This activity is analyzed using a framework and recommendations drawn from the research literature

  • The purpose of this study was to investigate the relationship between instructor immediacy and statistics anxiety. It was predicted that students receiving immediacy would report lower levels of statistics anxiety. Using a pretest-posttest-control group design, immediacy was measured using the Instructor Immediacy scale. Statistics anxiety was measured using the Statistics Anxiety Rating Scale (STARS).<br><br>Results indicated that instructor immediacy is significantly related to six factors of statistics anxiety, with immediacy explaining between 6% and 20% of the variance in students' anxiety levels. Instructors should attempt to increase their use of immediacy behaviors in order to decrease anxiety.

  • The amount, complexity and provenance of data have dramatically increased in the past five years. Visualization of observed and simulated data is a critical component of any social, environmental, biomedical or scientific quest. Dynamic, exploratory and interactive visualization of multivariate data, without preprocessing by dimensionality reduction, remains a nearly insurmountable challenge. The Statistics Online Computational Resource (www.SOCR.ucla.edu) provides portable online aids for probability and statistics education, technology-based instruction and statistical computing. We have developed a new Java-based infrastructure, SOCR Motion Charts, for discovery-based exploratory analysis of multivariate data. This interactive data visualization tool enables the visualization of high-dimensional longitudinal data. SOCR Motion Charts allows mapping of ordinal, nominal and quantitative variables onto time, 2D axes, size, colors, glyphs and appearance characteristics, which facilitates the interactive display of multidimensional data. We validated this new visualization paradigm using several publicly available multivariate datasets including Ice-Thickness, Housing Prices, Consumer Price Index, and California Ozone Data. SOCR Motion Charts is designed using object-oriented programming, implemented as a Java Web-applet and is available to the entire community on the web at www.socr.ucla.edu/SOCR_MotionCharts. It can be used as an instructional tool for rendering and interrogating high-dimensional data in the classroom, as well as a research tool for exploratory data analysis.

  • The need for universities to achieve excellence in the services they provide has been the subject of research for several decades. The idea of involving students and recognizing the importance of their opinions has led to the creation of various models and tools. This paper focuses on teaching, a central service from which improvement actions of an academic institution should always begin. The article reviews and updates the previously developed Teaching Experiments and Student Feedback methodology. The methodology, which is primarily addressed to statistics teachers, allows practical aspects to be organized and decisions to be made based on data that has been collected from students and scientifically analyzed.<br><br>The steps for building a student satisfaction index are also described. This index, in its most complete version, takes into account possible correlations between importance of the evaluated aspect and scores, both of which are provided by the students. The paper presents an application of the methodology to a statistics course taught by one of the authors.

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