Statistics Course Research Articles

Teaching principles in Type 1 error and reproducible research using dice

AbstractControlling Type 1 error and encouraging reproducible research are important in clinical and translational research. These concepts are frequently discussed in lectures with mathematical language, analytic examples, and probability distributions that demonstrate the issues. However, first‐time learners in biostatistics courses focusing on fundamental topics may benefit from a more interactive demonstration in which learners participate, contribute to the results, and have a personal stake in the outcomes. This article summarizes a simple activity using dice to simulate Type 1 error that requires minimal preparation and cost. The activity may be appropriate for learners enrolled in a first course in statistics, biostatistics, or probability.

Parental separation penalties among university students in Italy

AbstractThis paper addresses the long-standing question of whether parental separation shapes offspring school performance drawing on retrospective data from a group of university students in Italy, a country that has historically had very low separation rates yet has experienced an important rise in family dissolution over the last two decades. Using survey data from 1st-year enrollees in undergraduate courses in Economics and Statistics at two points in time (2000 and 2017), we explore whether the association between parental separation and children’s school performance (i) is observed both at the level of middle school (MS) and high school (HS); (ii) varies according to the age at which students experienced separation, and (iii) varies by parental socio-economic status (SES). Our results suggest that students whose parents separated before MS completion score on average 2 points less on the end-of-middle-school exam relative to students whose parents did not separate or separated after MS completion. Similarly, students whose parents separated before HS completion score 1 point less on the end-of-high-school exam relative to their counterpart. As such, we document a parental separation penalty both at the level of MS and HS, yet lower by half when separation occurs later in students’ life course. Moreover, for HS grade parental separation is associated with more negative consequences when students experience it at very young ages (0–5), while for MS grade heterogeneity by age is less clear-cut. Such penalties are concentrated among children of low-educated mothers, particularly for HS, providing support to the “compensatory advantage” hypothesis predicting smaller penalties for children of high-SES parents. Overall, findings from this study corroborate existing evidence suggesting that the consequences of parental separation vary depending on a combination of social background and the “selectivity” of the educational outcome considered.

Evidential Analysis: An Alternative to Hypothesis Testing in Normal Linear Models

Statistical hypothesis testing, as formalized by 20th century statisticians and taught in college statistics courses, has been a cornerstone of 100 years of scientific progress. Nevertheless, the methodology is increasingly questioned in many scientific disciplines. We demonstrate in this paper how many of the worrisome aspects of statistical hypothesis testing can be ameliorated with concepts and methods from evidential analysis. The model family we treat is the familiar normal linear model with fixed effects, embracing multiple regression and analysis of variance, a warhorse of everyday science in labs and field stations. Questions about study design, the applicability of the null hypothesis, the effect size, error probabilities, evidence strength, and model misspecification become more naturally housed in an evidential setting. We provide a completely worked example featuring a two-way analysis of variance.

Student knowledge gains in polar literacy and statistics after completing guided inquiry modules in an undergraduate statistics course

Climate change is a major concern to undergraduate students. Understanding climate change relies on an understanding of polar regions. However, courses on polar regions are rare at undergraduate institutions. Polar ENgagement through GUided INquiry (PENGUIN) modules were designed to give students experience with polar research in a variety of standard courses, including physics, computer science, physical chemistry, and economics, through using course-specific and computational tools to analyze polar data. Here, we present a new PENGUIN module taught in a statistics class, in which students apply statistical tools to ice core data to reconstruct past temperature records. Quantitative student responses on pre- and post-surveys were collected in a quasi-experimental context to assess student knowledge gains for a test group of 91 students and a control group of 73 students (who did not complete the module). Test-group students made statistically significant increases of 25 to 46% on all six statistics questions, with a normalized gain of 56%. By contrast, control group statistics knowledge gains ranged from −4 to 25%, with statistically significant increases for only three questions and a normalized gain of 22%. For polar research questions, the test group demonstrated increases in correct responses to polar research questions (11 to 31%), with statistically significant improvements (p < .05) of 22-31% on 3 of 6 polar research questions. These findings support the conclusion that PENGUIN modules can successfully teach course concepts while increasing polar literacy.

Analysis of r×c Tables containing Outliers

We examine the problem of accommodating outliers in tables of measurement data when there are no replications. The suggested strategy for the determination of the cells that contain outliers and for handling them analytically is easily understood and implemented in practice and presented in even the most elementary statistics course along with the course’s ANOVA material.

A Course-Based Undergraduate Research Experience (CURE) in Statistics: Enhancing Educational Outcomes and Promoting Access to Data-Driven Careers

Course-based undergraduate research experiences (CUREs) have been shown to help students gain research skills. Few studies, however, have evaluated the impact of CUREs on long-term educational and employment outcomes. This article examines postgraduation outcomes for students enrolling in introductory statistics delivered as a CURE compared with those taking a traditional mathematics-based introductory statistics course. Participating in the CURE was found to be associated with a higher likelihood of holding a job in which a primary responsibility was working with data, greater confidence in working with data, and a higher likelihood of earning more than $100K annually. This study suggests that CUREs may not only impart technical skills but also boost students’ self-efficacy in applying statistical methods and analyzing data.

Teaching Statistics for the Social Sciences Using Active Learning: A Case Study

US college students are typically required to take at least one mathematics or statistics course, either as part their major area of study, or as a general education requirement. College mathematics requirements are an obstacle for many college students. Active learning, a pedagogical approach that places emphasis on students’ collaborative work, has been shown to increase student learning and course success in STEM fields of study and in mathematics courses. Active learning has also been shown to be adaptable to courses involving computer software and programming, such as introductory statistics. This case study is based on the author’s experience implementing an active learning model in an introductory statistics course for students majoring in sociology and related social sciences. Results indicate that the active learning approach was adaptable to the structure and particular learning goals of the course. Students perceived greater learning relative to other courses despite doing less work outside of class, and attributed this to the active learning structure of the course. These findings align with more systematic studies on the impacts of active learning in science and mathematics courses.

Teaching Modeling in Introductory Statistics: A Comparison of Formula and Tidyverse Syntaxes

When incorporating programming into a statistics course, there are many pedagogical considerations. In R, one consideration is the particular R syntax used. This article reports on a head-to-head comparison of a pair of introductory statistics labs, one conducted in the formula syntax, the other in tidyverse. Pre- and post-surveys show minimal differences between labs, with students reporting a positive experience regardless of section. Analysis of YouTube and RStudio Cloud data shows interesting distinctions. The formula section appeared to watch a larger proportion of pre-lab videos, but spend less time computing. Conversely, the tidyverse section watched a smaller proportion of videos and spent more time computing. The tidyverse labs were slightly longer in terms of lines of code and minutes of videos. The tidyverse labs exposed students to more distinct R functions, but reused functions more frequently. Both labs relied on a relatively small vocabulary of functions, which can provide a starting point for instructors interested in teaching introductory statistics in R. The instructor experience of teaching the two syntaxes diverged when discussing relationships between categorical variables, as well as working with numeric variable summary statistics. This work provides additional evidence for instructors looking to choose between syntaxes for introductory statistics.

Integration of Ideological and Political Education into the Probability Theory and Mathematical Statistics Course: A Teaching Design Based on Estimation and Hypothesis Testing

With the rapid development of higher education in China, colleges and universities are facing new challenges and impacts in talent training. Probability Theory and Mathematical Statistics is one of the important courses in higher education for science and engineering majors and economics and management majors. Its critical role in cultivating students’ thinking skills and improving their problem-solving skills is self-evident. Course ideological and political education construction is an important link in college talent training work. Combining ideological and political education with course teaching can help students establish correct value concepts and play a certain role in improving their comprehensive ability and quality. At present, the construction of ideological and political education in the Probability Theory and Mathematical Statistics course still faces some problems, mainly manifested in the lack of attention paid by teachers to course ideological and political education, insufficient exploitation of ideological and political elements, and the simplification of ideological and political education implementation methods. In order to comprehensively deepen the construction of course ideological and political education in line with the actual needs of Probability Theory and Mathematical Statistics course teaching, we should strengthen the construction of teacher teams, improve teachers’ ability to carry out course ideological and political education, integrate educational resources, develop educational resources for ideological and political education, and innovate teaching methods to improve the overall effect of ideological and political education integration.

Research on the Application of PBL + SPOC Blended Teaching Model in Probability and Statistics Course

To cultivate talents with an exploratory spirit and practical skills in the era of information technology, it is imperative to reform teaching methods and approaches. In the teaching process of the Probability and Statistics course, an application-oriented blended teaching model combining problem-based learning and small private online course was explored. By organizing and implementing online and offline teaching activities based on problem-based learning, a multidimensional process-oriented learning assessment system was established. Practice has shown that this model can effectively enhance classroom teaching effectiveness, benefiting the improvement of students’ overall skills and mathematical literacy.

Exploration of the Three in One Professional Course Ideological and Political Teaching Model of Virtue, Knowledge, and Creativity -- Taking the statistics major course Probability Theory as an example

Professional courses are important carriers of ideological and political education in courses. Probability Theory, as a core course in statistics, is of great significance in cultivating students ability to think randomly and solve complex problems. The existing ideological and political research on the course of Probability Theory mainly focuses on public basic courses. In depth analysis of the characteristics and curriculum features of statistics major, propose a deep integration of morality, knowledge, and creativity in the curriculum ideological and political education model, including the formation of morality, knowledge, and creativity integrated curriculum ideological and political education goals, the improvement of morality, knowledge, and creativity integrated curriculum ideological and political teaching links, the deepening of morality, knowledge, and creativity integrated curriculum ideological and political teaching content, and the innovation of morality, knowledge, and creativity integrated curriculum ideological and political teaching methods. Practice has shown that the three in one curriculum ideological and political model of morality, knowledge, and creativity effectively stimulates students interest in learning and enhances their professional confidence.

Jerry (Jerald) Rudmann (1944-2024).

Jerry was born on September 7, 1944, to Doris and Francis Rudmann. He completed his bachelor's degree in psychology at California State University, Fullerton (1967), where a course in statistics forever changed his life. There he met his future wife, Bari. They were married 57 years ago and had three children, Darrell, Brent, and Ashley (Debbie, Kristina, and Adam), and five grandchildren, Oliver, Linus, Allison, Katie, and Lukas. Jerry worked at Irvine Valley Community College for 30 years, beginning as a founding faculty (and the only psychology professor at that time). He won many awards and recognitions. Jerry died on May 16, 2024, from pancreatic cancer. Jerry was exceptional in many ways. He was a staunch advocate for students and faculty at community colleges; he worked on multiple national projects designed to improve undergraduate education; and his thoughtful kindness touched everyone with whom he interacted. His commitment to enhancing all aspects of community college came naturally. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

Navigating the D.RA.MA.: Understanding and Overcoming Student Anxiety in Criminology Research Methods and Statistics Courses

Statistics and research methods courses are essential yet challenging components of criminology curricula. Despite their importance, students often exhibit disinterest and anxiety towards these courses, negatively impacting their academic performance. This study investigates criminology students’ perceptions, focusing on disinterest, relevance argumentation, and math anxiety. Using a convenience sample of 167 students from a Hispanic-serving institution in the Western United States, responses were analyzed using the D.RA.MA. scale. Findings revealed that students in statistics courses exhibited higher math anxiety, significantly affecting their performance. Additionally, women experienced greater math anxiety, and other demographic factors influenced perceptions of relevance and disinterest. We discuss how these results underscore the need for targeted interventions among this student population and potential applied approaches that could benefit students. Addressing these factors could enhance students’ understanding and appreciation, leading to better academic performance and career preparation in criminal justice.

Enhancing the Introductory Statistics Course: Comparing Student Learning and Performance in Traditional and Web-Enhanced Traditional Courses

A redesign of a traditional introductory statistics course was performed with the intent of increasing student success in the course without the extreme burden of implementing a flipped course. A study was then conducted to compare the new format (web-enhanced traditional) to the traditional format taught by the same professor with the same assignments, quizzes, and exams during the same semester. Students selected their own sections of the course to take but were not aware of the different class formats when they enrolled. Students in both course formats were similar demographically, with similar math ACT scores. It was found that students who participated in the web-enhanced traditional course were more successful in completing the course and performed better on course assessments than those students who participated in the traditional introductory statistics course. Supplementary materials for this article are available online.

Attitudes towards statistics and statistical performance: A mediation model of statistics anxiety and academic procrastination.

Students often harbour negative attitudes towards research methods and statistics courses, and such attitudes may be associated with harmful cognitive and behavioural responses. Research on these effects has been restricted to the investigation of direct links between attitudes towards statistics, statistics anxiety, academic procrastination, and course performance. This study sought to examine the interconnected impact of attitudes towards statistics, statistics anxiety, and procrastination, on course performance in a cohesive model. It was predicted that attitudes towards statistics would indirectly affect statistical performance via statistics anxiety and procrastination in a sequential manner. The sample comprised 171 undergraduate psychology students from Australian universities. An online questionnaire collected information on participant demographics, attitudes towards statistics, statistics anxiety, procrastinatory behaviours, and performance in participants most recently completed statistics course. Data were collected cross-sectionally. All responses were anonymous. A sequential mediation analysis revealed a significant indirect effect of statistics anxiety and procrastination, controlling for age and gender. The results showed that more negative attitudes towards statistics are associated with greater statistics anxiety, which is in turn associated with greater procrastination, and finally with lower statistical performance. It was concluded that students who view their statistics courses as a threatening experience may fail to see value in their statistical education, which is associated with heightened statistics anxiety, increased avoidance of course-related activities, and in turn poorer course performance. Practical implications of the findings are also discussed.

Examining the Evidence on the Statistics Prerequisite for Admission to Doctor of Nursing Practice Programs: Retrospective Cohort Study.

Doctor of Nursing Practice (DNP) programs in the United States confer the highest practice degree in nursing. The proportion of racial and ethnic minority DNP students, including those of Asian descent, keeps increasing in the United States. Statistics is commonly required for DNP programs. However, there is insufficient evidence regarding the number of years within which statistics should be taken and the minimum grade required for admission to the program. This study aimed to examine the associations of statistics prerequisite durations and grades for admission with the course performances within the DNP program. We also explored whether a postadmission statistics overview course can prepare students for a DNP statistics course as well as a required statistics prerequisite course. A retrospective cohort study was conducted with a sample of 31 DNP students at a large university in the Mid-Atlantic region. Statistical analysis of data collected over 5 years, between 2018 and 2022, was performed to examine the associations, using Spearman rank correlation analysis and Mann-Whitney U test (U). The performance of students in a DNP statistics course was not associated with prerequisite duration. There was no significant association between the duration and the DNP statistics course letter grades (ρ=0.12; P=.66), neither with exam 1 (ρ=0.03; P=.91) nor with exam 2 scores (ρ=0.01; P=.97). Prerequisite grades were positively associated with exam 1 grades (ρ=0.59; P=.02), but not exam 2 (ρ=0.35; P=.19) or course grades (ρ=0.40; P=.12). In addition, no difference was found in the performance of students whether meeting the prerequisite requirements or taking a 1-month, self-paced overview course (exam 1: U=159, P=.13; exam 2: U=102, P=.50; course letter grade: U=117, P=.92). No evidence was found to support the need for limits on when prerequisites are completed or grade requirements. Opting for a statistics overview course after admission can serve as a viable alternative to the statistics prerequisite, effectively preparing students for advanced quantitative data analysis in a DNP program.

From urn models to box models: Making Neyman's (1923) insights accessible

Abstract Neyman’s 1923 paper introduced the potential outcomes framework and the foundations of randomization-based inference. We discuss the influence of Neyman’s paper on four introductory to intermediate-level textbooks by Berkeley faculty members (Scheffé; Hodges and Lehmann; Freedman, Pisani, and Purves; and Dunning). These examples illustrate that Neyman’s key insights can be explained in intuitive and interesting ways to audiences at all levels, including undergraduates in introductory statistics courses. We have found Freedman, Pisani, and Purves’s box-of-tickets model to be a valuable expository tool, and we also find their intuitive explanation of Neyman’s variance result helpful: It is a “minor miracle” that in randomized experiments, the two-sample z z -test is conservative because of “two mistakes that cancel.” All four books take a more positive view of Neyman’s results than Neyman himself did. We encourage educators and researchers to explore ways to communicate Neyman’s ideas that are helpful for their own audiences.

Expensive but Worth It: Live Projects in Statistics, Data Science, and Analytics Courses

Students in statistics, data science, analytics, and related fields study the theory and methodology of data-related topics. Some, but not all, are exposed to experiential learning courses that cover essential parts of the life cycle of practical problem-solving. Experiential learning enables students to convert real-world issues into solvable technical questions and effectively communicate their findings to clients. We describe several experiential learning course designs in statistics, data science, and analytics curricula. We present findings from interviews with faculty from the U.S., Europe, and the Middle East and surveys of former students. We observe that courses featuring live projects and coaching by experienced faculty have a high career impact, as reported by former participants. However, such courses are labor-intensive for both instructors and students. We give estimates of the required effort to deliver courses with live projects and the perceived benefits and tradeoffs of such courses. Overall, we conclude that courses offering live-project experiences, despite being more time-consuming than traditional courses, offer significant benefits for students regarding career impact and skill development, making them worthwhile investments. Supplementary materials for this article are available online.

Online assessment in the age of artificial intelligence

Online education, while not a new phenomenon, underwent a monumental shift during the COVID-19 pandemic, pushing educators and students alike into the uncharted waters of full-time digital learning. With this shift came renewed concerns about the integrity of online assessments. Amidst a landscape rapidly being reshaped by online exam/homework assistance platforms, which witnessed soaring stocks as students availed its questionable exam assistance, and the emergence of sophisticated artificial intelligence tools like ChatGPT, the traditional methods of assessment faced unprecedented challenges. This paper presents the results of an observational study, using data from an introductory statistics course taught every semester by the author, and delves into the proliferation of cheating methods. Analyzing exam score results from the pre and post introduction of ChatGPT periods, the research unpacks the extent of cheating and provides strategies to counteract this trend. The findings starkly illustrate significant increases in exam scores from when exams of similar difficulty were administered in person (pre-Covid) versus online. The format, difficulty, and grading of the exams was the same throughout. Although randomized controlled experiments are generally more effective than observational studies, we will indicate when we present the data why experiments would not be feasible for this research. In addition to presenting experimental findings, the paper offers some insights, based on the author's extensive experience, to guide educators in crafting more secure online assessments in this new era, both for courses at the introductory level and more advances courses The results and findings are relevant to introductory courses that can use multiple choice exams in any subject but the recommendations for upper-level courses will be relevant primarily to STEM subjects. The research underscores the pressing need for reinventing assessment techniques to uphold the sanctity of online education.

CAUSAL LANGUAGE AND STATISTICS INSTRUCTION: EVIDENCE FROM A RANDOMIZED EXPERIMENT

Most current statistics courses include some instruction relevant to causal inference. Whether this instruction is incorporated as material on randomized experiments or as an interpretation of associations measured by correlation or regression coefficients, the way in which this material is presented may have important implications for understanding causal inference fundamentals. Although the connection between study design and the ability to infer causality is often described well, the link between the language used to describe study results and causal attribution typically is not well defined. The current study investigates this relationship experimentally using a sample of students in a statistics course at a large western university in the United States. It also provides (non-experimental) evidence about the association between statistics instruction and the ability to understand appropriate causal attribution. The results from our experimental vignette study suggest that the wording of study findings impacts causal attribution by the reader, and, perhaps more surprisingly, that this variation in level of causal attribution across different wording conditions seems to pale in comparison to the variation across study contexts. More research, however, is needed to better understand how to tailor statistics instruction to make students sufficiently wary of unwarranted causal interpretation.