Introductory Statistics Course Research Articles

Impact of Experimenting Computational Statistics for Data Science in Introductory Statistics Course: A Malaysian Perspective

The conventional teaching methods for statistics, especially for introductory statistics course (precursor to data science) are not in accordance with the advancement and demand of today’s data-centric world. As the backbone of modern data science, computational statistics is deemed to revamp the learning of statistics to a large extent. As such, this study investigated the impact of experimenting computational statistics for data science in introductory statistics course from a Malaysian perspective. We employed a pre-, postand delayed post-test quasi-experimental design in this study. Our sample included 100 randomly selected students enrolled in an introductory course in a Malaysian public university. Students were equally separated into computational (followed computational statistics approach in learning statistics) and conventional (followed only conventional approach in learning statistics) groups. Students in both groups were assessed at three stages: initial, medial and final, respectively. Their performance (assessment marks) was used to measure the effectiveness of computational statistics approach in the learning process of introductory statistics. Results attested that computational group students performed significantly better than the conventional group students in both medial and final assessments. Furthermore, computational group students showed greater improvement from initial to medial assessment and sustained their performance from medial to final assessment, indicating that their knowledge acquisition was effective in the computational statistics approach. Our findings implied that computational statistics approach in introductory statistics course exerted a positive impact on students’ statistics learning and performance, leading towards effective knowledge and computing skills acquisition for data science.

Students’ Reasoning about Variability in Graphs during an Introductory Statistics Course

Variation and variability are key concepts in K-16 statistics education. Prior research has investigated students’ reasoning about variability in different contexts. However, there is a lack of research on students’ development of understanding of variability when comparing distributions in bar graphs, dot plots, and histograms as they took an introductory college-level statistics course. This exploratory case study conducted three interviews with each of the ten participants through a four-month period, at the beginning, middle, and end of the course. The Structure of Observed Learning Outcomes (SOLO) taxonomy was used to analyze participants’ responses. Results indicated that overall the group of participants demonstrated a stable understanding of variability over the semester (i.e. lack of improvement). However, when examining each student’s reasoning, four types of reasoning development paths were found: improvement, lack of change, decline, and inconsistent. This study provides implications in teaching college introductory statistics course and recommendations for future research.

Implementing Mastery-Based Grading at Scale in Introductory Statistics

We report on a large-scale implementation of mastery-based grading in a General Education Introductory Statistics course at California State University Los Angeles. In Fall 2018, the course had 80 sections of approximately 30 students each and was taught by 37 instructors who ranged from long-time, experienced instructors to brand new teaching associates. In Spring 2019, the course had 16 sections with eight instructors. We discuss the design of the course, the structure of the assignments, and how we implemented mastery-based grading given that the course instructors are, for the most part, new to mastery-based grading. We have now completed two semesters of implementation and want to share our experiences and the adjustments we made for Spring 2019 as a result.

Why is it difficult to understand statistical inference? Reflections on the opposing directions of construction and application of inference framework

AbstractDifficulties in learning (and thus teaching) statistical inference are well reported in the literature. We argue the problem emanates not only from the way in which statistical inference is taught but also from what exactly is taught as statistical inference. What makes statistical inference difficult to understand is that it contains two logics that operate in opposite directions. There is a certain logic in the construction of the inference framework, and there is another in its application. The logic of construction commences from the population, reaches the sample through some steps and then comes back to the population by building and using the sampling distribution. The logic of application, on the other hand, starts from the sample and reaches the population by making use of the sampling distribution. The main problem in teaching statistical inference in our view is that students are taught the logic of application while the fundamental steps in the direction of construction are often overlooked. In this study, we examine and compare these two logics and argue that introductory statistical courses would benefit from using the direction of construction, which ensures that students internalize the way in which inference framework makes sense, rather than that of application.

Assessing math attitude through the Attitude Toward Mathematics Inventory – Short form in introductory statistics course students

Math attitude refers to emotional responses, beliefs, and behaviors towards mathematics. Several studies measured the relation with math learning and related variables, but very few with statistics learning. To better investigate this relation has become increasingly relevant to have a measure that ensuring multidimensionality and shortness. The aim of the present paper was to confirm the factor structure of the Lin and Huang (2014)'s ATMI - Short Form (ATMI - SF) when administered to Italian college students attending introductory statistics course, and to test its measurement invariance applying a multigroup confirmatory analysis. We also assessed the reliability and the incremental validity of the ATMI - SF by verifying whether it predicted statistics achievement over and above the effect of math knowledge. The overall findings provide that ATMI - SF is a reliable and valid measure to assess math attitude among college students who attend introductory statistics courses in non-mathematical courses.

Helping Introductory Statistics Students Find Their Way Using Maps

ABSTRACTMaps are a primary method of displaying statistical data that comes from a geographical frame. Maps are esthetically appealing and make it easier to identify geographic patterns in a dataset. However, few introductory statistical texts and courses explicitly present maps as a way to display data. In this article, we will present examples of different types of statistical maps and illustrate how these maps can be used in the instruction of an introductory statistics course.

Simulation Methods for Teaching Sampling Distributions: Should Hands-on Activities Precede the Computer?

Sampling distributions are fundamental to an understanding of statistical inference, yet research shows that students in introductory statistics courses tend to have multiple misconceptions of this important concept. A common instructional method used to address these misconceptions is computer simulation, often preceded by hands-on simulation activities. However, the results on computer simulation activities’ effects on student understanding of sampling distributions, and if hands-on simulation activities are necessary, are mixed. In this article, we describe an empirical intervention study in which each of eight discussion sections of an introductory statistics course at a large research university was assigned to one of two in-class activity sequences on sampling distributions: one consisting of computer simulation activities preceded by hands-on simulation using dice, cards, or tickets, and the other comprised of computer simulation alone with the same time-on-task. Using a longitudinal model of changes in standardized exam scores across three exams, we found significant evidence that students who took part in a hands-on activity before computer simulation had better improvement from the first midterm to the final exam, on average, compared to those who only did computer simulations. Supplementary materials for this article are available online.

Student Perceptions of Engagement in an Introductory Statistics Course

This article presents the results of a case study from one professor’s experience teaching an introductory statistics course. The goal of this study was to better understand student perceptions of engagement in a statistics course. Voluntary, self-reported data were collected daily for students to evaluate the engagement level of the class that day, and students also identified activities that they considered engaging. A final survey was administered at the end of the semester to provide a holistic, retrospective measure of engagement in the course and to collect feedback on various questions related to perceptions of engagement. Results indicate variation in student engagement scores and variation in engagement scores across the semester indicating some influence of class activity on perceptions of engagement. Perceptions of engagement are contextualized with students’ comments from the daily surveys. Associations between engagement and final course grade were also investigated. Student perceptions of engagement were also compared to the professor’s perception of engagement for students.

Teaching Introductory Statistics with DataCamp

We designed a sequence of courses for the DataCamp online learning platform that approximates the content of a typical introductory statistics course. We discuss the design and implementation of these courses and illustrate how they can be successfully integrated into a brick-and-mortar class. We reflect on the process of creating content for online consumers, ruminate on the pedagogical considerations we faced, and describe an R package for statistical inference that became a by-product of this development process. We discuss the pros and cons of creating the course sequence and express our view that some aspects were particularly problematic. The issues raised should be relevant to nearly all statistics instructors. Supplementary materials for this article are available online.

Modelling Dependency Structures Produced by the Introduction of a Flipped Classroom

Teaching processes have been changing in the lasts few decades from a traditional lecture-example-homework format to more active strategies to engage the students in the learning process. One of the most popular methodologies is the flipped classroom, where traditional structure of the course is turned over by moving out of the classroom, most basic knowledge acquisition. However, due to the workload involved in this kind of methodology, an objective analysis of the results should be carried out to assess whether the lecturer’s workload is worth the effort or not. In this paper, we compare the results obtained from two different methodologies: traditional lecturing and flipped classroom methodology, in terms of some performance indicators and an attitudinal survey, in an introductory statistics course for engineering students. Finally, we analysed the changes in the relationships among variables of interest when the traditional teaching was moved to a flipped classroom by using Bayesian networks.

USE OF COMMERCIAL AND FREE SOFTWARE FOR TEACHING STATISTICS

This study investigates the effectiveness of two statistical software packages, the commercial software, SPSS, and the free software, R Version 3.5.0, in teaching statistics, by comparing grades earned by students in an introductory statistics course. Students taught using R earned slightly higher grades overall than those in the SPSS class, although the difference between the two groups of students was found to be not significantly different. The responses given by students on the end of semester survey for the use of technology indicated that students felt comfortable with both software packages, and the software R was recommended more strongly for future use in a statistics course than the software SPSS. These findings provided some insights on the use of different software packages in statistics education, which might support the use of free software in teaching statistics at college level.
 First published November 2019 at Statistics Education Research Journal Archives

Comparing Two Models of Collaborative Testing for Teaching Statistics

Research on collaborative testing has shown that it decreases test anxiety, increases learning and critical thinking skills, and allows students to practice collaboration and teamwork. However, it has most often been used as a second test following traditional individual testing. This quasi-experimental study compared two models of collaborative testing in an introductory statistics course. Students who experienced collaborative testing as a pretest ( n = 35) and as a posttest ( n = 33) were compared with a control group ( n = 61) that experienced traditional individual testing only. Grade book data and a survey administered at the end of the semester provided information on student attitudes and perceptions toward learning statistics and use of collaborative testing, and the impact of each model on student learning. The same instructor taught all students and administered the same tests. The authors found that group-first testing was favored by students and provided the greatest benefit for reducing anxiety while still supporting student learning.

Examining the Factor Structure of the Survey of Attitudes Towards Statistics among Undergraduate Health Science Students

Recent studies report that students’ attitudes toward statistics play an important role in their statistics achievement. The goal of this study was to test the psychometric properties of the Survey of Attitudes Towards Statistics (SATS-28) among undergraduate health science students enrolled in an introductory statistics course. Most students held positive attitudes towards statistics. The average SATS scores were above neutral. Confirmatory factor analysis validated the four-factor structure of the questionnaire (Affect, Cognitive Competence, Value, and Difficulty), albeit with a few modifications. The RMSEA value of 0.065 was below the suggested cutoff of 0.07. Cronbach’s alpha for the entire scale was .907, which was well above the recommended cutoff value of 0.7. The study provided evidence for the appropriate metric properties of the SATS-28 as a valid instrument for measuring the statistics attitudes of a sample of first year students at the University of Minnesota Rochester.

Incorporating Open Data Into Introductory Courses in Statistics

The 2016 Guidelines for Assessment and Instruction in Statistics Education (GAISE) College Report emphasized six recommendations to teach introductory courses in statistics. Among them: use of real data with context and purpose. Many educators have created databases consisting of multiple datasets for use in class; sometimes making hundreds of datasets available. Yet “the context and purpose” component of the data may remain elusive if just a generic database is made available. We describe the use of open data in introductory courses. Countries and cities continue to share data through open data portals. Hence, educators can find regional data that engage their students more effectively. We present excerpts from case studies that show the application of statistical methods to data on: crime, housing, rainfall, tourist travel, and others. Data wrangling and discussion of results are recognized as important case study components. Thus, the open data based case studies attend most GAISE College Report recommendations. Reproducible R code is made available for each case study. Example uses of open data in more advanced courses in statistics are also described. Supplementary materials for this article are available online.

The State of Statistics Education Research in Client Disciplines: Themes and Trends Across the University

The reform movement in statistics education has led to a revitalization of the undergraduate introductory statistics course. However, many students satisfy their degree requirements by taking statistics courses in “client departments” such as business, the social sciences, and the lab sciences, typically taught by non-statisticians. This article presents the findings of a metasynthesis of the existing literature on teaching statistics in these client disciplines to learn (1) what is currently being taught and how, and (2) the most important challenges for statistics teachers in other departments. Articles were reviewed using qualitative axial coding and quantitative text analysis to identify common research themes and ideas in the literature for each discipline. Research themes, attitudes toward statistics instruction, and pedagogical techniques were found to vary from discipline to discipline. Collaboration with instructors in other disciplines may be a welcome step toward improving statistics instruction across the university.

Questionable Claims for Simple Versions of the Bootstrap

Recent years have seen increasing interest in incorporating resampling methods into introductory statistics courses and the high school mathematics curriculum. While the use of permutation tests for data from experiments is a step forward, the use of simple bootstrap methods for sampling situations is more problematical. This article demonstrates via counterexamples that many of the claims made for these simple methods are simply wrong. Their use with beginners can only be justified after their true properties have been fully researched, and their many limitations explained to students. Supplementary materials for this article are available online.

Teaching Visually Impaired College Students in Introductory Statistics

Instructors of postsecondary classes in statistics rely heavily on visuals in their teaching, both within the classroom and in resources like textbooks, handouts, and software, but this information is often inaccessible to students who are blind or visually impaired (BVI). The unique challenges involved in adapting both pedagogy and course materials to accommodate a BVI student may provoke anxiety among instructors teaching a BVI student for the first time, and instructors may end up feeling unprepared or “reinventing the wheel.” We discuss a wide variety of accommodations inside and outside of the classroom grounded in the empirical literature on cognition and learning and informed by our own experience teaching a blind student in an introductory statistics course.

Introducing Data Science Techniques by Connecting Database Concepts and dplyr

Early exposure to data science skills, such as relational databases, is essential for students in statistics as well as many other disciplines in an increasingly data driven society. The goal of the presented pedagogy is to introduce undergraduate students to fundamental database concepts and to illuminate the connection between these database concepts and the functionality provided by the dplyr package for R. Specifically, students are introduced to relational database concepts using visualizations that are specifically designed for students with no data science or computing background. These educational tools, which are freely available on the Web, engage students in the learning process through a dynamic presentation that gently introduces relational databases and how to ask questions of data stored in a relational database. The visualizations are specifically designed for self-study by students, including a formative self-assessment feature. Students are then assigned a corresponding statistics lesson to utilize statistical software in R within the dplyr framework and to emphasize the need for these database skills. This article describes a pilot experience of introducing this pedagogy into a calculus-based introductory statistics course for mathematics and statistics majors, and provides a brief evaluation of the student perspective of the experience. Supplementary materials for this article are available online.

Statistical Software Output in the Classroom: A Comparison of R and SPSS

The current study examines whether R or SPSS output induces greater initial anxiety in students and whether anxiety toward one or both changes after being taught one type of software output throughout the course. The authors each taught an introductory statistics course, with the first course ( n = 43) teaching R output exclusively and the second course ( n = 39) teaching SPSS output exclusively. Students in both courses were given surveys assessing their anxiety and confidence toward R and SPSS output on the first and last days of class. Students initially reported greater anxiety and lower confidence when viewing R compared to SPSS output. However, the initial difference between R- and SPSS-related anxiety and confidence level disappeared when students were taught R and decreased substantially when students were taught SPSS. The results suggest that although R output may seem more intimidating initially, students adapt to it as well as they do to SPSS.

Teaching Data Reproducibility through Service Learning

Data reproducibility is becoming increasingly important in the social sciences, but it has yet to be incorporated into many undergraduate sociology programs. This note describes a service-learning activity that can be added to an introductory statistics course. Students partner with a nonprofit and analyze quantitative data to answer questions selected by the agency. Reproducibility is the central mechanism of communication between the nonprofit, the students, and the course instructor. An assessment of the project suggests that students achieve an understanding of how to create reproducible data. They also come to see its value as a method of communication about data decisions.