Innovative and Alternative Approaches to Teaching Statistical Concepts

Cathy Poliak Chair
University of Houston
 
Wednesday, Aug 6: 2:00 PM - 3:50 PM
4195 
Contributed Papers 
Music City Center 
Room: CC-104D 

Main Sponsor

Section on Statistics and Data Science Education

Presentations

A Functional Approach to Teaching Statistics

Much of statistics can be organized into four types of functions: summary functions, distributions, relational and logical functions. A summary function compresses a set of values into a single item which describes the original set. A distribution function associates a likelihood with a particular input. Relational and logical functions produce truth values defined as 0 and 1 in Iverson notation and the computer language APL.
Operators are higher-order functions which modify or combine existing functions to produce new functions, thus reducing the statistical vocabulary required of students. Confidence Intervals, hypothesis tests, probabilities and simulation can be handled by applying various operators to these four types of functions.
For example, the expression: "normal probability > 1.96" will produce the value 0.025. The operator, "probability" combines the distribution "normal" with the relation ">" to form a new function: the upper-tail cumulative normal distribution applied to the argument "1.96". 

Keywords

Statistical Education

Function

APL 

First Author

Stephen Mansour

Presenting Author

Stephen Mansour

A Mixed Model of Teaching Graduate Statistic Course for Engineering Students

Guided by ASA guidelines for statistics education and informed by literature reviews and student needs, we adapted Kern's six-step approach to redesign the "Statistics for Engineers and Scientists" course, previously taught in a theory-based manner. The redesigned course, termed the Mixed Model that was not seen in literature yet, includes both in-person and virtual students in the same class meetings and incorporates mixed active learning elements. Our evaluation revealed that most students responded positively to the redesign, particularly appreciating the integration of R into daily work and in-class active learning activities. This paper compared the learning performance of in-person and virtual students within the same class meetings, a comparison not previously documented in existing literature. We found that virtual students required more time to complete the same tasks as in-person students. Additionally, graduate students perceived the coursework as excessive, despite it being reasonable (~10 hours per week), potentially raising important questions about how to align educational goals with students' perceptions of a reasonable workload in graduate course education. 

Keywords

Graduate Statistics

Engineering

Mixed Model,
in-person,
virtual

Curriculum Redesign

Programming in R

Active Learning 

First Author

Meiqin Li

Presenting Author

Meiqin Li

Alternate Forms of the One-Way ANOVA F, Kruskal-Wallis K, and Partitional Clustering B

For ease of instruction, the one-way analysis of variance F statistic is rewritten in terms of pairwise differences in individual sample means instead of differences of individual sample means from the overall sample mean. For any pair of samples, the contribution to the F statistic is proportional to the product of the sample sizes multiplied by the square of the difference in the sample means. These comments also apply to the Kruskal-Wallis K, and the between sum of squares B statistic used in partitional clustering. 

Keywords

Teaching

Intuition 

First Author

Roger Johnson, South Dakota Mines

Presenting Author

Roger Johnson, South Dakota Mines

Exploring Replication in Statistical Modeling: A Guide to Avoiding Misleading Conclusions

Constructing effective statistical models can be challenging for researchers of all experience levels. This talk highlights the critical role of replication and the risks of analyzing dependent observations as if they were independent. Such misrepresentation can inflate sample sizes, leading to incorrect p-value calculations and unreliable confidence intervals. Without properly assessing replication, researchers risk drawing invalid conclusions. Using illustrative examples, we clarify key concepts, offer practical techniques for distinguishing between types of replication, and highlight the consequences of common missteps. Finally, we introduce What Would Fisher Do (WWFD), a model-building tool that helps researchers determine appropriate degrees of freedom and build statistically sound models by accurately addressing sources of variation. 

Keywords

replication

model-building tool 

Co-Author

Julie Garai, Incredible Health

First Author

Marina Ptukhina, Whitman College

Presenting Author

Marina Ptukhina, Whitman College

Exploring Students Connections to and Conceptual Understanding of Statistics

This case study explores how students make connections between upper-level undergraduate statistical content, their previous knowledge, and concepts from their fields of interest. The purpose of this study is to contribute to the growing field of statistics education research and find better practices for teaching statistics to undergraduate students. Students prefer to have an application and connection to material they're learning (Neumann, Hood, & Neumann 2013). The aim of this study is: do students that can make a connection with the new content strive for and achieve a deeper understanding of the content? This presentation will focus on an Exit Ticket collected in the middle of the semester involving point estimation. This artifact was coded for connections and level of understanding for analysis of the relationship between performance in the course with conceptual understanding of course content. Initial results suggest that students' articulations of connections between the course material and their interests demonstrate a rich understanding of the material.  

Keywords

Statistics Education

Statistical Reasoning

Case study

Undergraduate

Qualitative Methods 

First Author

Jackie Carlton-Wargo, Washington State University

Presenting Author

Jackie Carlton-Wargo, Washington State University

Integrating Innovative Biological Research Data into Biostatistics at Two HBCUs

A collaboration between two Historically Black Universities (HBCU) was developed to improve performance in biostatistics, interest in STEM careers, and perceptions of STEM disciplines. A novel flipped classroom approach was designed. The approach incorporated videos with demonstrations for completing analyses, authentic data analysis practice, in-person small group discussions, and course-associated projects. We examined the outcomes for two cohorts (cohort 1 n = 77; cohort 2 n = 60). Further, we examined if there were differences between cohorts on key outcomes. Pre- and post-test outcomes were collected for biostatistics knowledge, career interest in STEM fields, and perceptions of STEM disciplines. Overall, there was a non-significant difference in biostatistics knowledge, F(1, 51) = 0.47, p = .495. However, a cohort effect was observed, F(1, 50) = 11.37, p = .001, where cohort 1 had an increase in scores, p = .077, Cohen's d = 2.67, and cohort 2 had a decrease in scores, p = .049, d = -1.92. There were changes in perceived STEM career support, interest, and importance, F(3, 50) = 476.19, p < .001, Wilk's Λ = .01. Both cohorts' ratings increased for career support, 

Keywords

Flipped Classroom

Innovative Research Project

Biostatistics

SAS 

Co-Author(s)

Thomas Gross, Appalachian State University
Dafeng Hui, Tennessee State University

First Author

QINGXIA LI, Fisk university

Presenting Author

QINGXIA LI, Fisk university

Practical Guidance for Using Monte Carlo Simulations

Monte Carlo simulations have become an indispensable tool across diverse fields of research, addressing challenges such as incomplete data, small sample sizes, and ethically complex questions. Originating in the late 19th and early 20th centuries, simulations have driven groundbreaking advancements, from improving the quality of beer (arguably the first simulation by Student, 1908) to modeling nuclear warfare (von Neumann & Ulam, 1949). Today, their applications span a wide range of domains, including financial risk analysis (Benhamed & Gassouma, 2023), population genetics (Griffiths & Tavaré, 1996), and pandemic modeling (Amaro & Orce, 2022).

In this session, we will briefly explore the evolution of Monte Carlo applications and provide practical guidance on designing, conducting, and evaluating simulations. Our intent is to help attendees think through realistic considerations for their own research, such as what research questions are a good fit for this methodology, how to determine an appropriate number of replications, and how to summarize and communicate results. This presentation is based on an upcoming chapter on Monte Carlo simulations. 

Keywords

Monte Carlo

Simulations 

Co-Author

Carolin Strobl, Universität Zürich

First Author

Richard Feinberg, National Board of Medical Examiners

Presenting Author

Richard Feinberg, National Board of Medical Examiners