Thursday, Aug 7: 8:30 AM - 10:20 AM
4213
Contributed Papers
Music City Center
Room: CC-103A
Main Sponsor
Section on Statistics and Data Science Education
Presentations
Modern tools for reproducible research can be productively adapted to pedagogical uses. In particular, tools for adaptive documents can produce near-
limitless practice problems, potentially including in-depth solutions. With a good framework in place, even teachers with modest coding skills can build
templates for reproducible problems (and solutions). I present a new templating framework using R, Markdown, and Shiny, with tools for delivering
templates as rapid-fire practice problems or as more traditional exam packets.
Keywords
Teaching tools
Pedagogy
Typesetting software
Reproducible research
An important skill for introductory statistics students who have been introduced to several inference procedures (e.g. confidence intervals and tests for means, proportions, paired data, two sample situations, and/or correlations) is to confidently identify which procedure is appropriate for a given question and data situation. The SCORE network (https://scorenetwork.org) provides a repository of datasets and teaching modules based on sports examples and one of the modules includes materials for a general review of many of the inference topics encountered in an introductory statistics course. The goal Is to present students with a series of questions on a common theme that each require a different inference procedure to address. For example, "Is the average home field advantage in football really about 3 points?" or "How often does the favored team win a game?". As a quick in-class review students can simply be asked to identify the appropriate procedure, but we also provide the data (in this case all scores and point spreads for a full NFL season) so that students could also be asked to do the full analysis to answer some (or all) of the questions.
Keywords
inference review
sports data
football
First Author
Robin Lock, St. Lawrence University
Presenting Author
Robin Lock, St. Lawrence University
This study aims to bridge the gap between research and practice by examining the impact of voice-modded lectures on student performance within the Introductory Statistics service unit, enrolling over a thousand students each session from various predominantly non-statistical disciplines. Previous research suggests that heavily accented speech can hinder learning outcomes, particularly for non-English speaking students. This research explores whether AI-based voice-modding technology can enhance lecture clarity, engagement, and academic performance. By comparing student perceptions and performance between original and voice-modded lectures, the study aims to provide practical insights into the technology's potential to improve accessibility and equity in higher education.
Keywords
AI in Education
Large enrolment service unit Introductory Statistics
Student engagement
Voice-Modded Technology
Inclusive Learning Practices
Equity in Higher Education
Classical hypothesis tests implicitly require that an ordering be defined on the elements of a sample space. Colloquially, this ordering is used to describe the "extremity" of a sample element in the direction of the alternative hypothesis. More extreme elements provide greater evidence for the alternative hypothesis and against the null hypothesis. In many applications, especially those described in introductory statistics courses, the notion of extremity is quite natural. However, in other cases, constructing a reasonable ordering of the sample space is far less straightforward. We present such an example in the context of studying rater disagreement in evaluating nursing home patient care needs. The trinomial sample space for these data was difficult to order in a way that was both consistent with the classical statistical practice and needed modification. Ultimately, Bayesian methods were employed to construct a reasonable ordering for use with a classical test of hypotheses.
Keywords
Bayesian inference
classical inference
p-values
extremity
sample space ordering
Confidence interval estimation in undergraduate statistics textbooks is generally carried out using equations (for, e.g., normal means and binomial proportions) that, when derived, are derived using the so-called pivotal method. This approach has been motivated by the long-term use of statistical tables for evaluating interval bounds, and is thus inherently limited (and, in the age of computers, woefully inadequate). In this talk, we discuss a more modern approach to interval estimation that we follow when teaching mathematical statistics to undergraduates at Carnegie Mellon, which is based on the interval-estimation method dubbed "Pivoting the CDF" by Casella & Berger (2002; section 9.2.3). We show how, when the cumulative distribution function of the sampling distribution of the adopted statistic is known but not easily inverted, numerical estimates are easily achieved, and how, when the cdf is unknown, we can make estimates via simulation and numerical optimization. We argue that these non-analytic approaches to interval estimation make the process wholly accessible to students with minimal programming experience, including those in non-calculus-based introductory classes.
Keywords
confidence intervals
mathematical statistics
statistical inference
instructional design
undergraduate statistics curriculum
statistical practice
As (almost) everybody knows, the game of tic-tac-toe can end in any one of three outcomes: 1) Player X (who moves first) wins; 2) Player O (who moves second) wins; 3) The game is a draw. Furthermore, almost everybody knows that if both players know what they are doing, the game is guaranteed to end in a draw (often called a "cat's game").
Suppose now that both players make each of their moves at random. For such a game (called "randomized tic-tac-toe") all three of the outcomes listed above can occur. In this presentation the probabilities associated with each of the three outcomes will be determined.
These probabilities were originally determined by the presenter (with the assistance of a statistics major working on his senior project) in the spring quarter of 2004. Recently the presenter incorporated this problem into his statistics courses as a "class project". Thus, this presentation will also include a discussion of the class projects.
Keywords
randomized tic-tac-toe
class projects
This talk advocates for a conceptually grounded approach to teaching hypothesis testing in introductory statistics courses, particularly in the context of one-sided tests for mean and proportion inference. While standard instructional materials typically present the null hypothesis as an equality regardless of whether a test is one-sided or two-sided, we propose framing the null and alternative as complementary hypotheses—an approach that naturally leads to inequalities in the null for one-sided tests. This framing aligns with the Neyman-Pearson paradigm, and enhances conceptual clarity for students. Through a review of mainstream introductory textbooks, we examine how key concepts such as the null hypothesis and significance level are commonly presented, and offer refinements. We demonstrate that defining the null as an inequality allows for a more precise treatment of the Type I error. To support instruction, we present a classroom activity that guides students in discovering this property through empirical and visual means. Our approach preserves procedural simplicity while deepening students' understanding of core inferential ideas.
Keywords
Teaching hypothesis testing
mean and proportion inference
introductory statistics
Type I error
significance level,
class activity