Undergraduate Statistics Course Research Articles

Assessing the impact of group projects on examination performance in social statistics

College teachers in the sciences and professional studies have endorsed collaborative learning group strategies for teaching undergraduate statistics courses, but few researchers provide empirical evidence that students’ quantitative skills actually increase as a result of the collaborative experience. Assessment of the efficacy of collaborative learning group techniques is frequently subjectively based, and often relies on casual comments from students or faculty. Despite this shortcoming, instructors searching for new and effective ways of teaching quantitative courses continue to experiment with collaborative pedagogy. Consequently, an exploration of the effectiveness of collaborative teaching modalities on students’ statistical knowledge seems warranted. This study examined the relationship between performance on collaborative learning group assignments and students’ examination scores in statistics. Data were derived from 270 students enrolled in nine sections of a social statistics course, taught between 1996 and 2004. The results both challenge and support the efficacy of collaborative learning groups, and suggest that faculty modify such techniques when evidence of student learning cannot be empirically linked to the collaborative experience.

Pedagogical utilization and assessment of the statistic online computational resource in introductory probability and statistics courses

Technology-based instruction represents a new recent pedagogical paradigm that is rooted in the realization that new generations are much more comfortable with, and excited about, new technologies. The rapid technological advancement over the past decade has fueled an enormous demand for the integration of modern networking, informational and computational tools with classical pedagogical instruments. Consequently, teaching with technology typically involves utilizing a variety of IT and multimedia resources for online learning, course management, electronic course materials, and novel tools of communication, engagement, experimental, critical thinking, and assessment. The NSF-funded Statistics Online Computational Resource (SOCR) provides a number of interactive tools for enhancing instruction in various undergraduate and graduate courses in probability and statistics. These resources include online instructional materials, statistical calculators, interactive graphical user interfaces, computational and simulation applets, tools for data analysis and visualization. The tools provided as part of SOCR include conceptual simulations and statistical computing interfaces, which are designed to bridge between the introductory and the more advanced computational and applied probability and statistics courses. In this manuscript, we describe our designs for utilizing SOCR technology in instruction in a recent study. In addition, present the results of the effectiveness of using SOCR tools at two different course intensity levels on three outcome measures: exam scores, student satisfaction and choice of technology to complete assignments. Learning styles assessment was completed at baseline. We have used three very different designs for three different undergraduate classes. Each course included a treatment group, using the SOCR resources, and a control group, using classical instruction techniques. Our findings include marginal effects of the SOCR treatment per individual classes; however, pooling the results across all courses and sections, SOCR effects on the treatment groups were exceptionally robust and significant. Coupling these findings with a clear decrease in the variance of the quantitative examination measures in the treatment groups indicates that employing technology, like SOCR, in a sound pedagogical and scientific manner enhances overall the students’ understanding and suggests better long-term knowledge retention.

Dollars and Sense: Convincing Students That They Can Learn and Want to Learn Statistics

QUANTITATIVE METHODS ARE an integral part of much sociological research. For that reason, many sociology departments require a course in statistics as part of an undergraduate major in sociology, and most faculty view the undergraduate statistics course as a valuable part of an undergraduate student’s training in sociology. Unfortunately, most undergraduates do not feel the same. Instead, a majority of students fear and loathe the required statistics course. Students often postpone taking the course as long as possible and experience anger and anxiety during the class.

Applying Japanese Lesson Study Principles to an Upper-level Undergraduate Statistics Course

Japanese Lesson Study is a collaborative approach for teachers to plan, present, observe, and critique classroom lessons. Through the lesson study process, teachers systematically and thoughtfully examine both student learning and their own teaching practices. In addition, the process paves the way for a much broader approach to education research by gathering data about student learning directly in the classroom. By piloting an approach using Japanese Lesson Study principles in an upper division statistics course, we discovered some of the challenges it poses, but also some surprisingly promising results for statistics teaching. This case study should provide others considering this approach with information about the philosophy and methodology involved in the lesson study process as well as some practical ideas for its implementation.Supplemental data for this article can be accessed on the publisher's website.

A Comparison of Student Achievement and Satisfaction in an Online Versus a Traditional Face-to-Face Statistics Class

In this study we examined differences between online distance education and traditional classroom learning for an introductory undergraduate statistics course. Two outcome dimensions were measured: students’ final grades and student satisfaction with the course. Using independent samples t-tests, results indicated that there was no significant difference in grades between the online and traditional classroom contexts. However, students enrolled in the online course were significantly less satisfied with the course than the traditional classroom students on several dimensions. This finding is inconsistent with the “no significant difference phenomenon,” described in Russell’s (1999) annotated bibliography, which supports minimal outcome differences between online courses and face-to-face courses.

Multidimensional Scaling for Selecting Small Groups in College Courses

Many college courses use group work as a part of the learning and evaluation process. Class groups are often selected randomly or by allowing students to organize groups themselves. However, if it is desired to control some aspect of the group structure, such as increasing schedule compatibility within groups, multidimensional scaling can be used to form such groups. This article describes how this has been adopted in an undergraduate statistics course. Resulting groups have been more homogeneous with respect to student schedules than groups selected randomly—an example from winter quarter 2004 increased correlations between student schedules from a mean of .29 before grouping to a within-group mean of .50. Further, the exercise allows opportunities to discuss a wealth of statistical concepts in class, including surveys, association measures, multidimensional scaling, and statistical graphics.

The Effects of Peer-Controlled or Moderated Online Collaboration on Group Problem Solving and Related Attitudes

Abstract. This study investigated the relative benefits of peer-controlled and moderated online collaboration during group problem solving. Thirty-five self-selected groups of four or five students were randomly assigned to the two conditions, which used the same online collaborative tool to solve twelve problem scenarios in an undergraduate statistics course. A score for the correctness of the solutions and a reasoning score were analyzed. A survey was administered to reveal differences in students' related attitudes. Three conclusions were reached: 1. Groups assigned to moderated forums displayed significantly higher reasoning scores than those in the peer-controlled condition, but the moderation did not affect correctness of solutions. 2. Students in the moderated forums reported being more likely to choose to use an optional online forum for future collaborations. 3. Students who reported having no difficulty during collaboration reported being more likely to choose to use an optional online forum in the future.

Archaeological Sampling Strategies

This paper describes an interactive project developed to use for teaching statistical sampling methods in an introductory undergraduate statistics course, an Advanced Placement (AP) statistics course, or, with adaptation, in a statistical sampling course or a statistical simulation course. The project allows students to compare the performance of simple random sampling, stratified random sampling, systematic random sampling, and cluster random sampling in an archaeological setting.Supplemental data for this article can be accessed on the publisher's website.

Observations on the effect of the prior distribution on the predictive distribution in Bayesian inferences

Typically, in the brief discussion of Bayesian inferential methods presented at the beginning of calculus-based undergraduate or graduate mathematical statistics courses, little attention is paid to the process of choosing the parameter value(s) for the prior distribution. Even less attention is paid to the impact of these choices on the predictive distribution of the data. Reasons for this include that the posterior can be found by ignoring the predictive distribution thereby streamlining the derivation of the posterior and/or that computer software can be used to find the posterior distribution. In this paper, the binomial, negative-binomial and Poisson distributions along with their conjugate beta and gamma priors are utilized to obtain the resulting predictive distributions. It is then demonstrated that specific choices of the parameters of the priors can lead to predictive distributions with properties that might be surprising to a non-expert user of Bayesian methods.

Helping criminal justice students learn statistics: A quasi-experimental evaluation of learning assistance*

Undergraduate statistics courses in criminology and criminal justice programs tend to have high failure rates relative to other courses in the curriculum. One solution to this problem is to focus on helping the students “learn how to learn” difficult material. Drawing upon learning theory and incorporating web-based technology, the authors conducted an evaluation of several learning enhancement tools including Supplemental Instruction (SI), automated quizzes based on the reading, and required class attendance for at-risk students. The results indicate that Supplemental Instruction and quizzes substantially improve the failure rate in the class, (by 47% and 52% respectively) but required attendance by itself is not effective.

Archaeological Sampling Strategies

This paper describes an interactive project developed to use for teaching statistical sampling methods in an introductory undergraduate statistics course, an AP statistics course, or, with adaptation, in a statistical sampling course or a statistical simulation course. The project allows students to compare the performance of simple random sampling, stratified random sampling, systematic random sampling, and cluster random sampling in an archaeological setting.

A Computer-Based Lab Supplement to Courses in Introductory Statistics

The computer continues to assume a role of increased importance in university education, and professors must determine appropriate means for its integration into the curriculum. This article describes the incorporation of a studio lab component into undergraduate courses in introductory statistics. We detail the objectives of these courses and describe the motivations, general structure, and main features of our approach. The labs typically involve a two-step frequentist approach where a simple hands-on experiment is performed that is subsequently replicated using the computer. We describe in detail two labs that typify the main features of our approach, and discuss the exibility of the labs with regard to the target audience. A discussion of our perception of their impact on student learning is given, along with some comments on alternative modes of delivery.

Computers, Statistics, and the Culture of University Mathematics Education

Summary Most students dread taking a course in statistics. Negative attitudes toward statistics have many different causes. Education majors are not usually required to take an undergraduate statistics course, and practicing teachers thus do not appreciate the utility of theory in general or research in particular. Other causes are more related to the way statistics and mathematics courses are taught at the university level. Professors who believe that mathematically intense courses should serve primarily as a weeding-out process sometimes intentionally make their courses more difficult than they need to be, or institute high-handed, unjust policies designed to encourage dropouts. Undue emphases on rote memorization and calculation also contribute to the problem. Because of recent developments in distance education, such high-handed policies are doomed. As students have access to a variety of higher-education courses and programs, they will refuse to patronize traditional universities with policies such as those described above. Universities will be forced to adopt more rational policies. Computers can be used to relieve students from tedious, repetitive tasks and to create more and better opportunities to teach mathematics concepts and application.

A “Jigsaw Classroom” Technique for Undergraduate Statistics Courses

Undergraduate statistics students vary widely in performance, and many are passive learners. Worksheets (problem sets) help students to be more active and to learn by doing. Working individually, however, students may require too much time to complete worksheets in class, when the instructor is available to help. In the “jigsaw classroom” technique described, a worksheet is divided into 2 to 4 complementary steps that are distributed to different groups of students. Students with the same step complete it together and then collaborate with other classmates to finish the entire worksheet in class. Students reported that this jigsaw technique helped them understand a statistical procedure, used class time efficiently, and increased the variety of learning experiences available in this challenging course.

Some Class-Participation Demonstrations for Introductory Probability and Statistics

We present several classroom demonstrations, based on well-known statistical ideas, that have sparked student involvement in our introductory undergraduate courses in probability and statistics.

Undergraduate statistics in psychology: A survey of Canadian institutions.

Abstract Questionnaires examining the content of undergraduate statistics courses were sent to Canadian post-secondary institutes offering major degrees in psychology. Responses received from 59% of the institutions suggest that several basic statistical procedures constitute a small core content covered in almost all undergraduate statistics courses and that the incorporation of computer applications is relatively common. Most undergraduate students with a major in psychology have had at least one or two courses in basic statistics. A course in statistics is the single most preferred course in terms of admittance into graduate school (Norcross, Hanych, & Terranova, 1996; Purdy, Reinehr, & Swartz, 1989; Smith, 1985). Thus, most psychology undergraduates are expected to have been exposed to certain core statistical concepts. This expectation can influence the content of graduate statistics courses and the expectations that supervisors have about the statistical sophistication of new graduate students. Aiken, West, Sechrest, and Reno (1990) recently assessed the statistical training of psychology graduate students; however, no similar in-depth investigation has been undertaken for undergraduates. Giesbrecht, Yell, Scialfa, Sandals, and Ehlers (1997) surveyed 17 instructors of statistics and research methods courses from a variety of disciplines. Their results indicated considerable agreement across disciplines about the relative importance of statistical topics in a hypothetical introductory statistics course. However, these results have limited applicability for the present study since they were based on a cross-disciplinary sample obtained from a single post-secondary institution and they dealt with the relative importance of topics in a hypothetical course. The focus of the present study is on the actual curriculum in the statistics courses required by undergraduate psychology departments in Canada. In April 1999, questionnaires' were mailed out to the chairs of the 51 Canadian post-secondary institutions that offered undergraduate degrees with a major in psychology.2 A cover letter requested that the survey be completed by the person (s) responsible for instructing the statistic courses offered by the department. Respondents had the option of completing and submitting the actual questionnaire they had been mailed, or they could respond to an online version of the same questionnaire. Within three months, 30 (59%) of the surveys had been returned with only a small percentage of these (viz., 20%) being submitted online. Survey Findings Ninety-seven percent of the responding departments offered undergraduate courses in statistics. The single department that did not offer statistics courses did, however, require undergraduate students majoring in psychology to take two statistics courses offered by the mathematics department. Departments required varying amounts of mandatory statistical instruction to obtain a major degree in psychology. Thirty percent of the institutes required a one-- semester course, 60% required two semesters of statistics courses, and 7% required three semesters of statistics instruction. Class sizes varied dramatically across institutions, ranging from 18 to 178 students per class with a median of 60 students per class. Incidental responses indicated that in the larger classes there was typically some kind of additional instructional support (e.g., teaching assistants); however, this question was not included in the questionnaire. There was also a fair degree of variation across departments in terms of the text book used in the mandatory statistics courses. The only texts that were used at more than two institutions were editions of David Howell's two texts (e.g., Howell, 1998, 1999) which, combined, were used in 20% of the institutions. Ninety percent of respondents included questions that involved calculations in their in-class exams, whereas just 53% of respondents used multiple-choice questions in their in-class exams. …

STAZ: interactive software for undergraduate statistics.

STAZ is an interactive computer program that demonstrates statistical concepts, many of which cannot be readily demonstrated using conventional methods. Use of dynamic graphics encourages active engagement with challenging statistical concepts. The program consists of 13 graphical demonstrations, most of which allow for interactive participation by students. A detailed Help file with guided explanations accompanies each demonstration. STAZ is a multiple document interface program that makes full use of Windows features, such as tiling, links, and multitasking. Designed to be used as a supplement for any undergraduate statistics course, STAZ may be used by either instructors in class-room settings or students working independently.

Correlation, Regression Lines, and Moments of Inertia

A student of engineering or physics discussing a random variable X with mean μ and variance σ2 might refer to μ as the center of gravity of the (probability) mass distribution of X, and to σ2 as the moment of inertia of X about μ. Is there a similar “physical” interpretation of ρ, Pearson's product-moment correlation coefficient for pairs of random variables? We answer this question affirmatively by showing that ρ is equal to the ratio of a difference and sum of two moments of inertia about certain lines in the plane. From this observation it is easy to derive familiar important properties of ρ. Similar results hold for the population version of the nonparametric correlation coefficient Spearman's rho. These ideas are readily accessible by students in an undergraduate mathematical statistics course.

Teaching Analysis of Interaction in the 2 × 2 Factorial Design

We review an approach, presented by Schaefer (1976), for teaching the analysis and interpretation of interaction in an undergraduate psychological statistics course. We present learning objectives based on this approach. Finally, we describe a Windows computer program used both for in-class lecture presentation of material and for student guided practice on each objective.

A One-Seraester, Laboratory-Based, Quality-Oriented Statistics Curriculum for Engineering Students

This article describes a new laboratory-based undergraduate engineering statistics course being offered by the Department of Industrial and Manufacturing Engineering at Penn State. The course is intended as a service course for engineering students outside of industrial engineering. We describe the topics covered in each of the eight modules of the course and how the laboratories are linked to the lecture material. We describe how the course is implemented, including facilities used, the course text, grading, student enrollment, and the implementation of continuous quality improvement in the classroom. We conclude with some remarks on the benefits of the laboratories, the effects of CQI in the classroom, and dissemination of course materials.