Journal Article

  • The “law of large numbers” indicates that as sample size increases, sample statistics become less
    variable and more closely estimate their corresponding population parameters. Different
    research studies investigating how people consider sample size when evaluating the reliability of
    a sample statistic have found a wide range of responses, from no consideration of sample size to
    over consideration of sample size. This paper provides a qualitative meta-analysis of studies that
    have used what we dub the “Hospital Task” for investigating peoples’ thinking about the role of
    sample size in parameter estimation. This paper aims to investigate what the Hospital Task can
    tell us about how people make decisions under uncertainty and the usefulness of the task for
    developing models of students’ statistical reasoning. To achieve these goals, we review the
    original task, synthesize results of other studies which have used some version of this task,
    provide a critique of the different versions of the task, discuss implications of the task for
    research, and provide insights and viewpoints from a small group of statisticians. The paper
    concludes with implications for further research

  • Correlated predictors in regression models are a fact of life in applied social science research.
    The extent to which they are correlated will influence the estimates and statistics associated with
    the other variables they are modeled along with. These effects, for example, may include
    enhanced regression coefficients for the other variables—a situation that may suggest the
    presence of a suppressor variable. This paper examines the history, definitions, and design
    implications and interpretations when variables are tested as suppressors versus when variables
    are found that act as suppressors. Longitudinal course evaluation data from a single study
    illustrate three different approaches to studying potential suppressors and the different results and
    interpretations they lead to.

  • Histograms are adept at revealing the distribution of data values, especially the shape of the
    distribution and any outlier values. They are included in introductory statistics texts, research
    methods texts, and in the popular press, yet students often have difficulty interpreting the
    information conveyed by a histogram. This research identifies and discusses four
    misconceptions prevalent in student understanding of histograms. In addition, it presents pre and
    post-test results on an instrument designed to measure the extent to which the
    misconceptions persist after instruction. The results presented indicate not only that the
    misconceptions are commonly held by students prior to instruction, but also that they persist
    after instruction. Future directions for teaching and research are considered.

  • In this article, I introduce a novel applet (“module”) for exploring probability distributions, their
    samples, and various related statistical concepts. The module is primarily designed to be used by
    the instructor in the introductory course, but it can be used far beyond it as well. It is a free,
    cross-platform, stand-alone interactive application based on Wolfram Research’s novel
    computable document format (CDF) technology. It features over thirty common discrete and
    continuous distributions and can be used to illustrate concepts such as random samples,
    population and sample means and medians, histograms, kernel density estimators, boxplots, and
    cumulative distribution, survival, and hazard functions all while dynamically linking samples
    and estimators to adjustable distribution parameters in real-time. Additionally, the module
    includes real-world datasets to aid in communicating the concept of fitting a distribution to data.
    It is hoped that the module will be helpful to instructors at both the high school and college
    levels for the conceptual understanding of distributions. A simplified version geared specifically
    toward out-of-class student learning in the introductory course is also made available for
    students’ use. Both are accessible from

  • The purpose of the current research was to investigate the relationship between preference for
    numerical information (PNI), math self-concept, and six types of statistics anxiety in an attempt
    to establish support for the nomological validity of the PNI. Correlations indicate that four types
    of statistics anxiety were strongly related to PNI, and two were not related. Math self-concept
    was also strongly related to PNI. Results suggest that higher PNI is associated with higher math
    self-concept and lower statistics anxiety in graduate students, and indicate support for the
    nomological validity of the PNI within the context of graduate statistics classes.

  • Although Bayesian methodology has become a powerful approach for describing uncertainty, it
    has largely been avoided in undergraduate statistics education. Here we demonstrate that one can present Bayes' Rule in the classroom through a hypothetical, yet realistic, legal scenario designed to spur the interests of students in introductory- and intermediate-level statistics classes. The teaching scenario described in this paper not only illustrates the practical application of Bayes'
    Rule to legal decision-making, but also emphasizes the cumulative nature of the Bayesian
    method in measuring the strength of the evidence. This highlights the Bayesian method as an
    alternative to the traditional inferential methods, such as p value and hypothesis tests. Within the
    context of the legal scenario, we also introduce DNA analysis, implement a modified version of
    Bayes' Rule, and utilize Bayes’ Factor in the computation process to further promote students'
    intellectual curiosities and incite lively discussion pertaining to the jury decision-making process
    about the defendant's status of guilt.

  • This meta-analytic study focused on the quantitative integration and synthesis of the accumulated
    pedagogical research in undergraduate statistics education literature. These accumulated research studies compared the academic achievement of students who had been instructed using one of the various forms of small-group learning methods to those who had been instructed using
    lecture-based instruction. The meta-analytic results showed that cooperative, collaborative, and
    inquiry-based learning methods were used in college-level statistics courses. The results also
    showed that cooperative and collaborative learning methods supported the effectiveness of the
    small-group learning methods in improving students’ academic achievement with an overall
    average effect-size of 0.60. In contrast, the effectiveness of inquiry-based learning was close to
    zero. This significant positive average effect-size indicated that using small-group learning
    methods in statistics classrooms could increase the achievement of college students, increasing
    the scores on a statistics exam from the 50th to the 73rd percentile. In addition, the multilevel
    analysis revealed that the effect sizes were influenced significantly by the publication-year of the
    studies, with the most recently published studies having lower effect sizes. The major
    implication of this study is that evidence-based research supports the effectiveness of active
    small-group learning methods in promoting students’ achievement in statistics.

  • In this paper, we describe an in-class experiment that is easy to implement with large groups of
    students. The experiment takes approximately 15-20 minutes to run and involves each student
    completing one of four types of Sudoku puzzles and recording the time it takes to completion.
    The resulting data set can be used as a teaching tool at an introductory level right through to an
    advanced level of statistics. Basic methods for describing and displaying data as well as the
    intricacies that arise with real data may be discussed in an introductory course. The range of
    more sophisticated analyses that can be taught with the data set include chi-squared tests for
    independence, ANOVA, t- and F-tests, logistic regression and survival analysis. We describe and
    provide the tools to implement the experiment and illustrate several potential teaching topics
    using a collected data set.

  • Most research into prospective secondary mathematics teachers’ attitudes towards statistics
    indicates generally positive attitudes but a perception that statistics is difficult to learn. These
    perceptions of statistics as a difficult subject to learn may impact the approaches of prospective
    teachers to teaching statistics and in turn their students’ perceptions of statistics. This study is the
    qualitative component of a larger quantitative study. The quantitative study (Hannigan, Gill and
    Leavy 2013) investigated the conceptual knowledge of and attitudes towards statistics of a larger
    group of prospective secondary mathematics teachers (n=134). For the purposes of the present
    study, nine prospective secondary teachers, eight of whom were part of the larger study, were
    interviewed regarding their perceptions of learning and teaching statistics. This study extends our
    understandings garnered from the quantitative study by exploring the factors that contribute to
    the perception of statistics as being difficult to learn. The analysis makes explicit the tensions in
    learning statistics by highlighting the nature of thinking and reasoning unique to statistics and the
    somewhat ambiguous influence of language and context on perceptions of difficulty. It also
    provides insights into prospective teachers’ experiences and perceptions of teaching statistics
    and reveals that prospective teachers who perceive statistics as difficult to learn avoided teaching
    statistics as part of their teaching practice field placement.

  • We developed an introductory statistics course for pre-service elementary teachers. In this paper,
    we describe the goals and structure of the course, as well as the assessments we implemented.
    Additionally, we use example course work to demonstrate pre-service teachers’ progress both in
    learning statistics and as novice teachers. Overall, the course aims to help pre-service teachers
    recognize the importance of statistics in the elementary curriculum, as well as the integral role
    they, as teachers, can play in a student’s entire statistical education. Our course serves as a
    model/resource for others interested in pre-service teacher development.