Assessing the association between pre-course metrics of student preparation and student performance in introductory statistics: Results from early data on simulation-based inference vs. nonsimulation based inference

The recent simulation-based inference (SBI) movement in algebra-based introductory statistics courses (Stat 101) has provided preliminary evidence of improved student conceptual understanding and retention. However, little is known about whether these positive effects are preferentially distributed across types of students entering the course. We consider how two metrics of Stat 101 student preparation (pre-course performance on concept inventory and math ACT score) may or may not be associated with end of course student performance on conceptual inventories. Students across all preparation levels tended to show improvement in Stat 101, but more improvement was observed across all student preparation levels in early versions of a SBI course. Furthermore, students' gains tended to be similar regardless of whether students entered the course with more preparation or less. Recent data on a sample of students using a current version of an SBI course showed similar results, though direct comparison with non-SBI students was not possible. Overall, our analysis provides additional evidence that SBI curricula are effective at improving students' conceptual understanding of statistical ideas post-course regardless student preparation. Further work is needed to better understand nuances of student improvement based on other student demographics, prior coursework, as well as instructor and institutional variables.Comment: 16 page

Combating anti-statistical thinking using simulation-based methods throughout the undergraduate curriculum

The use of simulation-based methods for introducing inference is growing in popularity for the Stat 101 course, due in part to increasing evidence of the methods ability to improve students' statistical thinking. This impact comes from simulation-based methods (a) clearly presenting the overarching logic of inference, (b) strengthening ties between statistics and probability or mathematical concepts, (c) encouraging a focus on the entire research process, (d) facilitating student thinking about advanced statistical concepts, (e) allowing more time to explore, do, and talk about real research and messy data, and (f) acting as a firmer foundation on which to build statistical intuition. Thus, we argue that simulation-based inference should be an entry point to an undergraduate statistics program for all students, and that simulation-based inference should be used throughout all undergraduate statistics courses. In order to achieve this goal and fully recognize the benefits of simulation-based inference on the undergraduate statistics program we will need to break free of historical forces tying undergraduate statistics curricula to mathematics, consider radical and innovative new pedagogical approaches in our courses, fully implement assessment-driven content innovations, and embrace computation throughout the curriculum.Comment: To be published in "The American Statistician

Challenging the State of the Art in Post-Introductory Statistics: Preparation, Concepts, and Pedagogy

The demands for a statistically literate society are increasing, and the introductory statistics course ( Stat 101 ) remains the primary venue for learning statistics for the majority of high school and undergraduate students. After three decades of very fruitful activity in the areas of pedagogy and assessment, but with comparatively little pressure for rethinking the content of this course, the statistics education community has recently turned its attention to use of randomization-based methods to illustrate core concepts of statistical inference. This new focus not only presents an opportunity to address documented shortcomings in the standard Stat 101 course (for example, improving students’ reasoning about inference), but provides an impetus for re-thinking the timing of the introduction of multivariable statistical methods (for example, multiple regression and general linear models). Multivariable methods dominate modern statistical practice but are rarely seen in the introductory course. Instead these methods have been, traditionally, relegated to second courses in statistics for students with a background in calculus and linear algebra. Recently, curricula have been developed to bring multivariable content to students who have only taken a Stat 101 course. However, these courses tend to focus on models and model-building as an end in itself. We have developed a preliminary version of an integrated one to two semester curriculum which introduces students to the core-logic of statistical inference through randomization-methods, and then introduces students to approaches for protecting against confounding and variability through multivariable statistical design and analysis techniques. The course has been developed by putting primary emphasis on the development of students’ conceptual understanding in an intuitive, cyclical, active-learning pedagogy, while continuing to emphasize the overall process of statistical investigations, from asking questions and collecting data through making inferences and drawing conclusions. The curriculum successfully introduces introductory statistics students to multivariable techniques in their first or second course

Broadening the Impact and Effectiveness of Simulation-Based Curricula for Introductory Statistics

The demands for a statistically literate society are increasing, and the introductory statistics course “Stat 101” remains the primary venue for learning statistics for the majority of high school and undergraduate students. After three decades of very fruitful activity in the areas of pedagogy and assessment, but with comparatively little pressure for rethinking the content of this course, the statistics education community has recently turned its attention to focusing on simulation-based methods, including bootstrapping and permutation tests, to illustrate core concepts of statistical inference within the context of the overall statistical investigative process. This new focus presents an opportunity to address documented shortcomings in the standard Stat 101 course (e.g., seeing the big picture; improving statistical thinking over mere knowledge of procedures). Our group has developed and implemented one of the first cohesive curricula that (a) emphasizes the core logic of inference using simulation-based methods in an intuitive, cyclical, active-learning pedagogy, and (b) emphasizes the overall process of statistical investigations, from asking questions and collecting data through making inferences and drawing conclusions. Improved conceptual understanding and retention of inference and study design that had been observed when using early versions of the curriculum at a single institution, are now being evaluated at dozens of institutions across the country with thousands of students using the fully integrated, stand-alone version of the curriculum. Encouraging preliminary results continue to be observed. We are now leveraging the tremendous national momentum and excitement about the approach to greatly expand implementations of simulation-based curricula by offering workshops around the country to diverse sets of faculty, offering numerous online support structures including: a blog, freely available applets, free instructor materials, earning objective-based instructional videos, free instructor-focused training videos, a listserv, and peer-reviewed publications covering both rationale and assessment results. Many hundreds of instructors have been directly impacted by our workshops and hundreds more through access to the free online materials. We are also in the midst of valuating widespread transferability of the approach across diverse institutions, students, and learning environments and deepening our understanding of how students’ attitudes and conceptual understanding develop using this approach through an assessment project involving concept and attitude inventories with over 10,000 students across 200 different instructors

Quantitative Evidence for the Use of Simulation and Randomization in the Introductory Statistics Course

The use of simulation and randomization in the introductory statistics course is gaining popularity, but what evidence is there that these approaches are improving students’ conceptual understanding and attitudes as we hope? In this talk I will discuss evidence from early full-length versions of such a curriculum, covering issues such as (a) items and scales showing improved conceptual performance compared to traditional curriculum, (b) transferability of findings to different institutions, (c) retention of conceptual understanding post-course and (d) student attitudes. Along the way I will discuss a few areas in which students in both simulation/randomization courses and the traditional course still perform poorly on standardized assessments

21 RETENTION OF STATISTICAL CONCEPTS IN A PRELIMINARY RANDOMIZATION-BASED INTRODUCTORY STATISTICS CURRICULUM 3

Previous research suggests that a randomization-based introductory statistics course may improve student learning compared to the consensus curriculum. However, it is unclear whether these gains are retained by students post-course. We compared the conceptual understanding of a cohort of students who took a randomization-based curriculum (n = 76) to a cohort of students who used the consensus curriculum (n = 79). Overall, students taking the randomization-based curriculum showed higher conceptual retention in areas emphasized in the curriculum, with no significant decrease in conceptual retention in other areas. This study provides additional support for the use of randomization-methods in teaching introductory statistics courses

Assessing the Association Between Precourse Metrics of Student Preparation and Student Performance in Introductory Statistics: Results from Early Data on Simulation-Based Inference vs. Nonsimulation-Based Inference

The recent simulation-based inference (SBI) movement in algebra-based introductory statistics courses (Stat 101) has provided preliminary evidence of improved student conceptual understanding and retention. However, little is known about whether these positive effects are preferentially distributed across types of students entering the course. We consider how two metrics of Stat 101 student preparation (precourse performance on concept inventory and math ACT score) may or may not be associated with end of course student performance on conceptual inventories. Students across all preparation levels tended to show improvement in Stat 101, but more improvement was observed across all student preparation levels in early versions of a SBI course. Furthermore, students' gains tended to be similar regardless of whether students entered the course with more preparation or less. Recent data on a sample of students using a current version of an SBI course showed similar results, though direct comparison with non-SBI students was not possible. Overall, our analysis provides additional evidence that SBI curricula are effective at improving students' conceptual understanding of statistical ideas postcourse regardless student preparation. Further work is needed to better understand nuances of student improvement based on other student demographics, prior coursework as well as instructor and institutional variables

Introduction to Statistical Investigations

This book leads students to learn about the process of conducting statistical investigations from data collection, to exploring data, to statistical inference, to drawing appropriate conclusions. The text is designed for a one-semester introductory statistics course. It focuses on genuine research studies, active learning, and effective use of technology. Simulations and randomization tests introduce statistical inference, yielding a strong conceptual foundation that bridges students to theory-based inference approaches. Repetition allows students to see the logic and scope of inference. This implementation follows the GAISE recommendations endorsed by the American Statistical Association. This is an unbound, binder-ready version.https://digitalcollections.dordt.edu/books/1047/thumbnail.jp

A Radiation Hybrid Map of the BRCA1 Region of Chromosome 17q12-q21

The chromosomal region 17q12-q21 contains a gene (BRCA1) conferring susceptibility to early-onset familial breast and ovarian cancer. An 8000-rad radiation-reduced hybrid (RH) panel was constructed to provide a resource for long-range mapping of this region. A large fraction of the hybrids (~90%) retained detectable human chromosome 17 sequences. The complete panel of 76 hybrids was scored for the presence or absence of 22 markers from this chromosomal region, including 14 cloned genes, seven microsatellite repeats, and one anonymous DNA segment. Statistical analysis of the marker retention data employing multipoint methods provided both comprehensive and framework maps of this chromosomal region, including distance estimates between adjacent markers. The comprehensive RH map includes 17 loci and spans 179 cRays(8000). Likelihood rations of at least 1000:1 support the 10-locus framework order: cen-D17S250-ERBB2-(THRIA1, TOP2A)-D17S855-PPY-DI7S190-MTBT1-GP3A-BTR-D17S588-tel. The order obtained from RH mapping, when used in conjunction with other methods, will be useful in linkage analysis of breast cancer families and will facilitate the development of a physical map of this region.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/30614/1/0000254.pd