Introductory Statistics Course Research Articles

Changes in Undergraduate Students’ Self-Efficacy and Outcome Expectancy in an Introductory Statistics Course

The exploration of psychological variables that potentially impact college student performance in challenging academic courses can be useful for understanding success in introductory statistics. Although previous research has examined specific beliefs that students hold about their abilities and future outcomes, the current study is novel in its examination of changes in both self-efficacy (SE) and outcome expectancy (OE) in relation to performance over the course of an undergraduate introductory psychology statistics course. These psychological variables—relating to one’s belief about one’s ability to accomplish a task and the anticipated outcomes—may impact student motivation and performance. Students’ SE, OE, and other variables related to statistics performance were measured through a survey administered at the beginning and end of the course. Multivariate logistic regression and McNemar tests were conducted to examine factors that affected changes in SE and OE as the semester progressed. Students with lower scores on the final exam demonstrated a decrease in both high SE and positive OE. However, higher scores on exams earlier in the course were associated with increased odds for high SE but not for positive OE, suggesting that SE is less resilient to course performance. Based on these findings, the authors recommend that statistics instructors identify students at risk for decreasing SE. Instructors can help foster high SE in students struggling academically by connecting the course content to their everyday lives and suggesting strategies to enhance their confidence in their content knowledge and increase their comfort in navigating such a challenging course.

The Teaching of Introductory Statistics: Results of a National Survey

The Statistics Teaching Inventory (STI) was designed to assess the teaching practices of U.S.-based, college-level introductory statistics instructors in a variety of institutions and departments. This instrument has now been updated to reflect current trends and recommendations in statistics education. In this study, we used the STI to examine the current state of the curricular and instructional practices being used by U.S.-based, college-level introductory statistics instructors. We explore the extent to which instructors report that their introductory statistics courses are aligned with recommended practices as outlined by the 2016 GAISE College Report. Data were collected from a sample of college-level U.S.-based, college-level introductory statistics instructors. Results based on 228 usable responses indicated that instructors, by-and-large, tended to be following the GAISE recommendations, especially related to content. However, courses may not yet be aligned with newer content recommendations (e.g., provide students opportunities to work with multivariate data), and there is still a large percentage of instructors that are not embracing student-oriented pedagogies and assessment methods. Supplementary materials for this article are available online.

Diversifying Crime Datasets in Introductory Statistical Courses in Criminology

Diversifying Crime Datasets in Introductory Statistical Courses in Criminology

Using Formative Assessment and Feedback from Student Response Systems (SRS) to Revise Statistics Instruction and Promote Student Growth for All

Instructors are increasingly using interactive student response systems (SRS) to foster active learning and deepen student understanding in statistics education. Yet most studies focus on either the benefits of SRS or on how students can receive and use feedback, rather than on how instructors can use formative assessment data to inform instructional revisions for the purpose of enacting inclusive pedagogy to reach more learners. This article draws from a case study of an introductory statistics course at a community college to detail a framework for how an instructor can engage in what I call a reciprocal formative assessment and feedback cycle using SRS. This cycle is designed to address the goal of increasing equity—as defined by learning growth for all students—through a structured approach of reflecting on student misconceptions to determine who to reteach, what to reteach, when to reteach, and how to reteach course content.

Diversifying Crime Datasets in Introductory Statistical Courses in Criminology

Contemporary criminology issues are increasingly global, cross-cultural, and multilingual. Moreover, students from different cultural and national backgrounds will need to apply data analytics in their respective contexts. Crime data used in statistical courses should reflect this diversity, and in turn enhance the equality and inclusivity of the teaching curriculum. Supported by evidence-based pedagogic principles and evaluations, researchers have identified strategies to enhance the teaching and learning of quantitative skills. Promoting students’ understanding of quantitative methods and their application in criminology requires that teaching materials reflect real-world problems and the diversity of today’s student population. To facilitate this aim, the article first describes over 40 open and accessible crime data sources across political, cultural, and linguistic borders in the Global South. Moreover, to support educators in their implementation and use of these datasets, the article presents three case studies of exemplar pedagogic activities using available data sources in an undergraduate Criminology program in the UK. Exemplar activities include (1) time series analysis of homicide in Asia; (2) bivariate analysis of trust in police and victimization in Algeria; and (3) mapping kidnappings in Mexico. We end by discussing the pedagogical and research implications of diversifying datasets and some future challenges.

Latine Students’ Motivational and Emotional Experiences Related to Their Introductory Statistics Course: Differences by Institution Type Necessitate Tailored Interventions

The study compared concerns, anxiety, mindsets, and belonging in introductory statistics among Latine students across three higher education institutions. Students at the Predominantly White Institution voiced more concerns about R-coding and lack of prior knowledge. Students at the Hispanic-Serving Institutions voiced more concerns about math anxiety and social comparison and had more fixed mindsets, yet higher levels of belonging—pointing toward the value of exploring Latine students’ experiences across different contexts and providing tailored interventions.

RESOURCES AND TENSIONS IN STUDENT THINKING ABOUT STATISTICAL DESIGN

Reform efforts in statistics education emphasize the need for students to develop statistical thinking. Critical to this goal is a solid understanding of design in the process of collecting data, evaluating evidence, and drawing conclusions. We collected survey responses from over 700 college students at the start of an introductory statistics course to determine how they evaluated the validity of different designs. Despite preferring different designs, students offered a variety of productive arguments supporting their choices. For example, some students viewed intervention as a weakness that disrupted the ability to generalize results, whereas others viewed intervention as critical for identifying causality. Our results highlight that instruction should frame design as the balancing of different priorities: namely causality, generalizability, and power.

How to think clearly about the central limit theorem.

The central limit theorem (CLT) is one of the most important theorems in statistics, and it is often introduced to social sciences researchers in an introductory statistics course. However, the recent replication crisis in the social sciences prompts us to investigate just how common certain misconceptions of statistical concepts are. The main purposes of this article are to investigate the misconceptions of the CLT among social sciences researchers and to address these misconceptions by clarifying the definition and properties of the CLT in a manner that is approachable to social science researchers. As part of our article, we conducted a survey to examine the misconceptions of the CLT among graduate students and researchers in the social sciences. We found that the most common misconception of the CLT is that researchers think the CLT is about the convergence of sample data to the normal distribution. We also found that most researchers did not realize that the CLT applies to both sample means and sample sums, and that the CLT has implications for many common statistical concepts and techniques. Our article addresses these misconceptions of the CLT by explaining the preliminaries needed to understand the CLT, introducing the formal definition of the CLT, and elaborating on the implications of the CLT. We hope that through this article, researchers can obtain a more accurate and nuanced understanding of how the CLT operates as well as its role in a variety of statistical concepts and techniques. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

Bridging Theory and Measurement of Student Engagement

Learner engagement is well-established as critical for learning online. Professional development for online instructors emphasizes techniques for engaging students, and learning technology products tout features intended to promote engagement (e.g., adaptive content, video, gamification). But the influence of particular instructor practices and of particular learning technology features on theory-based aspects of student engagement is infrequently tested empirically, and even more rarely with Black, Latine, and low-income students, who are more likely to face barriers to learning online. This paper first provides a research-based theoretical model of affective engagement developed in conjunction with ongoing studies of blended learning implementations of courseware designed to enhance learning and engagement among historically and systemically marginalized students. Next, the paper describes development of survey-based measures of four components of affective engagement and the use of responses from over 850 students in introductory statistics courses to evaluate the reliability and factor structure of those measures. We conclude with implications for use of the engagement measures in future improvement-oriented research and practice.

USING A MIDTERM WARNING SYSTEM TO IMPROVE STUDENT PERFORMANCE AND ENGAGEMENT IN AN INTRODUCTORY STATISTICS COURSE: A RANDOMIZED CONTROLLED TRIAL

This article reports on an evaluation the effectiveness of e-mailed grade “nudges” on students’ performance and engagement in an introductory statistics course for undergraduate health science students. In 2020–2021, 358 students were randomized to an e-mail (n = 178) or no e-mail (n = 180) group. The intervention e-mail contained information on each student’s predicted final grade (grade nudge). Using two-sample t-tests, the statistical analysis of final grades in the course showed a higher compatibility with a model of no mean difference for students in the e-mail (73.5%) vs. no e-mail (72.1%) group. Comparison of the distributions of final grades between the two groups, however, suggested the e-mailed nudges may be related to slight improvements in final grades. Specifically, the median final grade was higher in the e-mail group (74.6 vs. 72.4); the Q1 value in the e-mail group was also higher, and the interquartile range was similar: no e-mail group (15.8) vs. e-mail group (14.2). Students also completed the Scale of Student Engagement in Statistics (SSE-S). Total engagement, affective and cognitive subscale scores of the SSE-S were higher in the e-mail group, resulting in low compatibility with a model of no difference in engagement scores. Overall, the results showed there is potential for our midterm warning system to be used to improve outcomes, particularly given that it is simple to implement, cost-effective, and easily scalable.

A Rasch-model-based hierarchical framework for statistical literacy and learning

Statistical literacy has a large and important role in the teaching of statistics. Most mathematics and statistics courses are hierarchical, and the earlier material forms the foundation for later material. We construct a hierarchical structure for an introductory statistics course using Rasch analysis of the student scripts for the final examination. This forms the basis of a statistical literacy construct that has wider implications than just an undergraduate course. The world is overwhelmed with data from an exponentially increasing number of sources. Such data is of various types and contexts, ranging from social, commercial, scientific, survey and human. Statistical literacy has therefore assumed a larger and more important role.

Exploring Achievement Behaviors in Non-Major Statistics Course: An Expectancy-Value Perspective and Thoughts for Practice

Statistics education is increasingly important to our society with enrolment increases of 16% in introductory statistics courses and 85% in upper-level statistics courses. Research has demonstrated many factors related to students’ behaviors and outcomes in statistics courses such as past achievement, attitudes, and effort. We sought to model these factors together to better understand how introductory statistics students’ attitudes were related to students' achievement behaviors and what student characteristics mediated such relationships. Structural equation modeling with data from N=301 students in an introductory statistics course for psychology majors revealed that majors with higher GPAs had more interest, enjoyment as well as utility value for statistics, and these variables were in turn related to expectations for success or achievement behaviors. Females had lower interest in statistics, and this was related to lower expectations of success. The findings highlight the need to increase interest and enjoyment and utility value for non-majors studying statistics. Recommendations for how to adapt the statistics classroom to that end are discussed.

Empathy through Data? Student Exploration of Elements of Diversity through Projects in an Introductory Statistics Course

A project involving data related to socioeconomic indicators was administered in an introductory statistics course. As part of this project, student groups investigated a data set from the United States Department of Agriculture Food and Nutrition Service website with information on recipients of Supplemental Nutrition Assistance Program (SNAP) benefits. Pre/post data from the Miville-Guzman Universality-Diversity Scale (M-GUDS) short form were collected to measure changes in diversity awareness. The survey administered also included demographic information and open-ended questions. Based on study results (n = 48), there was moderate evidence of a change in the diversity of contact subscale of the M-GUDS short form. Written feedback indicated that students demonstrated empathy for individuals with potentially different lived experiences. The focus of this paper is to describe the study results and provide information on the importance of incorporating elements of diversity into curriculum.

Integrating Diversity into Psychology Statistics Courses: Advice, Reflections, and Special Considerations

Introduction In an increasingly diverse world, there has been a call for psychology educators to make efforts to integrate diversity into the psychology curriculum. Statement of the Problem Researchers who have surveyed psychology faculty have found the amount of time devoted to diversity content in nondiversity-focused courses is limited, with faculty citing barriers to integration such as a lack of relevance and time constraints. Literature Review Educators who have worked to incorporate diversity topics into their courses have found positive outcomes. Teaching Implications We describe our approach to integrating diversity into an introductory statistics course, highlight lessons learned, and provide special considerations for psychology educators. Conclusion Integrating diversity-related content into statistics is challenging; however, the effort is worth it, particularly if integrating diversity content into required courses may be the only exposure to diversity students get.

Creating simulation applets to teach statistics

The purpose of this study is whether the use of software for simulating concepts of statistics and probability theory during a semester introductory statistics course ensured greater success in the final exam of the course for students who used it, compared to students who used general statistical software. The simulation software used was created for this purpose based on the average level of understanding of the students who attended the course. The students who attended the course were divided into two groups in a way that ensured that the two groups had proportionally about the same level of statistical knowledge, mathematical background, and about the same number of students in terms of origin and gender. One group used simulation software throughout the semester, while the other used general statistical software. The simulation software used in this survey was created for this purpose based on the average level of understanding of the students who attended the course. At the end of the semester after the final exam, various factors were considered and students' final exam performance (success rates), were compared based on these factors. It appeared that success in the final exam when it comes to similar populations as the two groups of students who attended the course has a strong dependence on the factor of using simulation software.

Teaching basic statistic concepts to student classes with diverse mathematical background using specialized applets

This study examines whether the use of specialized software applications can have an effective role in understanding and clarifying concepts of the basic measures of central tendency and dispersion, so that the advantages over traditional teaching are clear. Higher education students need to have a deep understanding of the concepts of theory of probability, descriptive statistics measures and statistical conclusions in order to be able to be used in their studies and in their work. For this purpose during an introductory course in Statistics at a University of Applied Sciences, two separate groups of students consisting of randomly selected members were given the same worksheet. One of these groups was additionally given specialized application software developed to visualize these concepts in order to answer the questions on the worksheet. The investigated case is whether the appropriate use of specialized software can help to effectively understand and interpret basic descriptive statistic concepts in a realistic application. The main conclusion is that appropriate specialized software applications can lead to the deepening of statistic concepts by students and in general promote the statistical literacy to a much greater extent than traditional teaching.

Concerns and Challenges in Introductory Statistics and Correlates with Motivation and Interest

We explore how students’ course concerns at the outset of their introductory statistics course predict their later perceived course challenges and future interest in statistics via a function of achievement motivation. Data were collected from undergraduate students (N = 524; 70% female; 37.8% students from racially marginalized groups) during the COVID-19 pandemic, using both open-ended (concerns and challenges) and closed-ended (achievement motivation and future interest) questions. Overall, incoming course concerns positively predicted perceived costs during the course and challenges at the end of the course and negatively predicted success expectancy and utility value during the course and future interest in statistics at the end of the course. Patterns varied by individual concerns/challenges, gender, and race/ethnicity. Cost played an important mediating role for female students and students from racially marginalized groups (e.g., Black, Latinx, or Native American/Indigenous students) between course concerns and future interest in statistics. Our findings (a) add to the increasing body of research reporting differences in how female and male students as well as students from racially marginalized backgrounds and racial majority students experience STEM courses and help explain different levels of interest in pursuing STEM careers, and (b) suggest that increasing future interest in statistics might require different interventions.

Evaluating a University-Wide Mathematics Assessment for Use in Introductory Statistics Course Performance

Students’ prior math skills are a strong indicator of potential for success in introductory statistics courses regardless of the emphasis on mathematical ability necessary for the course. Thus, many undergraduate instructors utilize some form of math skills assessment as a review for students or for students to identify weak areas in their mathematics preparation. Such evaluations may provide instructors and students with an early indication of the student's chances for success in a course and if additional assistance is required. This study illustrated the efficacy and importance of a standardized math assessment developed and administered as a university-wide mathematics placement test in student success prediction from several modeling approaches.

Average or Outlier? Introductory Statistics Adjunct Instructors’ Beliefs, Practices, and Experiences

In recent years, the adjunct faculty phenomenon has grown steadily. This research focused on adjunct instructors teaching introductory statistics courses. The purpose of the study was to give a voice to adjunct instructors by allowing them to describe their experiences teaching statistics. We conducted a qualitative study with 15 adjunct instructors of introductory statistics through semi-structured interviews. The participants came from several fields: psychology, nursing, and business, among others. Thematic analysis was used to find themes of statistical anxiety, use of technology in the classroom, lack of curriculum flexibility, and connection to the host institution. Our findings can inform institutions and interdisciplinary departments hosting introductory statistics courses. Similarly, educational statisticians can gain knowledge on the practices and barriers of adjunct instructors.

What Should We Do Differently in STAT 101?

The introductory statistics course has gotten better over the years, but there are many content areas in STAT 101 that should be reconsidered.