Statistics and Probability Commons^™

Mentoring Undergraduate Research In Statistics: Reaping The Benefits And Overcoming The Barriers, Joseph R. Nolan, Kelly S. Mcconville, Vittorio Addona, Nathan L. Tintle, Dennis K. Pearl

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Undergraduate research experiences (UREs), whether within the context of a mentor-mentee experience or a classroom framework, represent an excellent opportunity to expose students to the independent scholarship model. The high impact of undergraduate research has received recent attention in the context of STEM disciplines. Reflecting a 2017 survey of statistics faculty, this article examines the perceived benefits of UREs, as well as barriers to the incorporation of UREs, specifically within the field of statistics. Viewpoints of students, faculty mentors, and institutions are investigated. Further, the article offers several strategies for leveraging characteristics unique to the field of statistics to overcome …

Fixing Metric Fixation: A Review Of The Tyranny Of Metrics, Donald Roth

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"We should heed the author’s warning that transparent metrics and scorecards are rarely going to be effective substitutes for institutional trust."

Posting about the book The Tyranny of Metrics from In All Things - an online journal for critical reflection on faith, culture, art, and every ordinary-yet-graced square inch of God’s creation.

https://inallthings.org/fixing-metric-fixation-a-review-of-the-tyranny-of-metrics/

Data And Metrics: Do We Need Them? What Can They Tell Us? What Can't They?, Nathan L. Tintle

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"In our increasingly data-centric world, how do we think about data? How should we think about data?"

Posting about ­­­­­­­­using data to make informed decisions from In All Things - an online journal for critical reflection on faith, culture, art, and every ordinary-yet-graced square inch of God’s creation.

https://inallthings.org/data-and-metrics-do-we-need-them-what-can-they-tell-us-what-cant-they/

Genetics Analysis Workshop 20: Methods And Strategies For The New Frontiers Of Epigenetics And Pharmacogenomics, Nathan L. Tintle, David W. Fardo, Mariza De Andrade, Stella Aslibekyan, Julia N. Bailey, Justo Lorenzo Bermejo, Rita M. Cantor, Saurabh Ghosh, Philip Melton, Xuexia Wang, Jean W. Maccluer, Laura Almasy

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GAW20 provided a platform for developing and evaluating statistical methods to analyze human lipid-related phenotypes, DNA methylation, and single-nucleotide markers in a study involving a pharmaceutical intervention. In this article, we present an overview of the data sets and the contributions analyzing these data. The data, donated by the Genetics of Lipid Lowering Drugs and Diet Network (GOLDN) investigators, included data from 188 families (N = 1105) which included genome-wide DNA methylation data before and after a 3-week treatment with fenofibrate, single-nucleotide polymorphisms, metabolic syndrome components before and after treatment, and a variety of covariates. The contributions from individual …

Student Gains In Conceptual Understanding In Introductory Statistics With And Without A Curriculum Focused On Simulation-Based Inference, Beth Chance, Stephanie Mendoza, Nathan L. Tintle

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Using “simulation-based inference” (SBI) such as randomization tests as the primary vehicle for introducing students to the logic and scope of statistical inference has been advocated with the potential of improving student understanding of statistical inference, as well as the statistical investigative process as a whole. Moving beyond the individual class activity, entirely revised introductory statistics curricula centering on these ideas have been developed and tested. In this presentation we will discuss three years of cross-institutional tertiary-level data in the United States comparing SBI-focused curricula and non-SBI curricula (roughly 15,000 students). We examine several pre/post measures of conceptual understanding in …

Development Of A Tool To Assess Students’ Conceptual Understanding In Introductory Statistics, Nathan L. Tintle, Jill Vander Stoep

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Few tools exist to assess students’ conceptual understanding in post-secondary, introductory statistics courses. The CAOS test is widely considered to be the gold standard, but was first published in 2007 and does not necessarily reflect some of the changes in student learning at the secondary level. Furthermore, it may not be sensitive enough to measure student conceptual understanding in modern post-secondary statistics courses (e.g., simulation-based inference). In this paper we will describe the process of developing a new instrument which uses some CAOS items, as well as additional new items to improve validity and reliability. We will share the validity …

Lies, Statistics, Mathematics And The Truth, Nathan L. Tintle

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"Recognizing a key distinction between mathematics and statistics is helpful in understanding how we know if a statement is true."

Posting about deductive and inductive reasoning­­­­­­­­ from In All Things - an online hub committed to the claim that the life, death, and resurrection of Jesus Christ has implications for the entire world.

http://inallthings.org/lies-statistics-mathematics-and-the-truth/

Assessing The Association Between Quantitative Maturity And Student Performance In Simulation-Based And Non-Simulation Based Introductory Statistics, Nathan L. Tintle

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The recent simulation-based inference movement in algebra-based introductory statistics courses has provided preliminary evidence of improved student conceptual understanding and retention of key statistical concepts. However, little is known about whether these positive effects in courses using simulation-based inference are preferentially distributed across different types of students. Recent studies investigating predictors of student performance in traditional, algebra-based introductory statistics courses (Stat 101) have focused primarily on mathematical achievement or competencies in high school and early college. Little consideration has been given to how prior experience and competency with statistical thinking may be associated with student performance in college-level courses. In …

Effects Of Growth Mindset Training On Undergraduate Statistics Students, Valorie L. Zonnefeld

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Undergraduate introductory statistics courses have experienced numerous changes in the past century, for instance, increased enrollment and diversification of students required to take the courses. Promising research has been conducted on mathematical mindsets, however, no research is available for introductory statistics courses. This presentation addresses the effect of growth mindset training on students in mathematics.

Broadening The Impact And Effectiveness Of Simulation-Based Curricula For Introductory Statistics, Nathan L. Tintle, Beth Chance, George Cobb, Allan Rossman, Soma Roy, Todd Swanson, Jill Vanderstoep

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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 …

Student Performance In Curricula Centered On Simulation-Based Inference: A Preliminary Report, Beth Chance, Jimmy Wong, Nathan L. Tintle

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"Simulation-based inference"(e.g., bootstrapping and randomization tests) has been advocated recently with the goal of improving student understanding of statistical inference, as well as the statistical investigative process as a whole. Preliminary assessment data have been largely positive. This article describes the analysis of the first year of data from a multi-institution assessment effort by instructors using such an approach in a college-level introductory statistics course, some for the first time. We examine several pre-/post-measures of student attitudes and conceptual understanding of several topics in the introductory course. We highlight some patterns in the data, focusing on student level and instructor …

Combating Anti-Statistical Thinking Using Simulation-Based Methods Throughout The Undergraduate Curriculum, Nathan L. Tintle, Beth Chance, George Cobb, Soma Roy, Todd Swanson, Jill Vanderstoep

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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/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, …

Mindsets, Attitudes, And Achievement In Undergraduate Statistics Courses, Valorie L. Zonnefeld

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The purpose of this study was to determine the effects of theories of intelligence and an intervention of incremental mindset training on students’ attitudes toward statistics and their mastery of content in an introductory statistics college course. The sample was 547 undergraduate students at a small, faith-based, liberal arts college in the Midwest.

A pretest-posttest design was used for the three instruments implemented. The Comprehensive Assessment of Outcomes in a first Statistics course (CAOS) assessed students’ statistical literacy. The Student Attitudes Towards Statistics – 36© (SATS©) assessed six components of students’ attitudes toward statistics including affect, cognitive competence, difficulty, effort, …

Students Learning From Atlanta Public Schools Cheating Scandal, Thomas M. Van Soelen

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Access full-text article on publisher's site:

http://exclusive.multibriefs.com/content/students-learning-from-atlanta-public-schools-cheating-scandal/education

Emphasizing The Entire Research Process Throughout The Curriculum: The Next Step In Real Data Integration In Introductory Statistics Courses, Nathan L. Tintle

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Access blog post at publisher's site:

https://www.causeweb.org/sbi/?p=617

Simulation-Based Inference In Statistics Education: Exciting Progress And Future Directions, Nathan L. Tintle

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Statistics Views asked Dr Tintle to explain more about simulation-based inference in statistics education and some of the exciting progress that has been made to date and future directions within the undergraduate curriculum.

General Approaches For Combining Multiple Rare Variant Associate Tests Provide Improved Power Across A Wider Range Of Genetic Architecture, Nathan L. Tintle, Brian Greco, Allison Hainline, Keli Liu, Jaron Arbet, Alejandra Benitez, Kelsey Grinde

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In the wake of the widespread availability of genome sequencing data made possible by way of nextgeneration technologies, a flood of gene‐based rare variant tests have been proposed. Most methods claim superior power against particular genetic architectures. However, an important practical issue remains for the applied researcher—namely, which test should be used for a particular association study which may consider multiple genes and/or multiple phenotypes. Recently, tests have been proposed which combine individual tests to minimize power loss while improving the robustness to a wide range of genetic architectures. In our analysis, we propose an expansion of these approaches, by …

Quantitative Evidence For The Use Of Simulation And Randomization In The Introductory Statistics Course, Nathan L. Tintle, Ally Rogers, Beth Chance, George Cobb, Allan Rossman, Soma Roy, Todd Swanson, Jill Vanderstoep

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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 …

Evaluation Of The Power And Type 1 Error Of Recently Proposed Family-Based Tests Of Assocations For Rare Variants, Allison Hainline, Carolina Alvarez, Alexander Luedtke, Brian Greco, Andrew Beck, Nathan L. Tintle

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Until very recently, few methods existed to analyze rare-variant association with binary phenotypes in complex pedigrees. We consider a set of recently proposed methods applied to the simulated and real hypertension phenotype as part of the Genetic Analysis Workshop 18. Minimal power of the methods is observed for genes containing variants with weak effects on the phenotype. Application of the methods to the real hypertension phenotype yielded no genes meeting a strict Bonferroni cutoff of significance. Some prior literature connects 3 of the 5 most associated genes (p <1 × 10−4) to hypertension or related phenotypes. Further methodological development is needed to extend these methods to handle covariates, and to explore more powerful test alternatives.

Evaluating The Concordance Between Sequencing, Imputation And Microarray Genotype Calls In The Gaw18 Data, Ally Rogers, Andrew Beck, Nathan L. Tintle

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Genotype errors are well known to increase type I errors and/or decrease power in related tests of genotypephenotype association, depending on whether the genotype error mechanism is associated with the phenotype. These relationships hold for both single and multimarker tests of genotype-phenotype association. To assess the potential for genotype errors in Genetic Analysis Workshop 18 (GAW18) data, where no gold standard genotype calls are available, we explored concordance rates between sequencing, imputation, and microarray genotype calls. Our analysis shows that missing data rates for sequenced individuals are high and that there is a modest amount of called genotype discordance between …

Genetic Analysis Workshop 18: Methods And Strategies For Analyzing Human Sequence And Phenotype Data In Members Of Extended Pedigrees, Heike Bickeboller, Julia N. Bailey, Joseph Beyene, Rita M. Cantor, Heather J. Cordell, Robert C. Culverhouse, Corinne D. Engelman, David W. Fardo, Saurabh Ghosh, Inke R. Konig, Justo Lorenzo Bermejo, Phillip E. Melton, Stephanie A. Santorico, Glen A. Satten, Lei Sun, Nathan L. Tintle, Andreas Ziegler, Jean W. Maccluer, Laura Almasy

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Genetic Analysis Workshop 18 provided a platform for developing and evaluating statistical methods to analyze whole-genome sequence data from a pedigree-based sample. In this article we present an overview of the data sets and the contributions that analyzed these data. The family data, donated by the Type 2 Diabetes Genetic Exploration by Next-Generation Sequencing in Ethnic Samples Consortium, included sequence-level genotypes based on sequencing and imputation, genome-wide association genotypes from prior genotyping arrays, and phenotypes from longitudinal assessments. The contributions from individual research groups were extensively discussed before, during, and after the workshop in theme-based discussion groups before being submitted …

Application Of Family-Based Tests Of Association For Rare Variants To Pathways, Brian Greco, Alexander Luedtke, Allison Hainline, Carolina Alvarez, Andrew Beck, Nathan L. Tintle

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Pathway analysis approaches for sequence data typically either operate in a single stage (all variants within all genes in the pathway are combined into a single, very large set of variants that can then be analyzed using standard “gene-based” test statistics) or in 2-stages (gene-based p values are computed for all genes in the pathway, and then the gene-based p values are combined into a single pathway p value). To date, little consideration has been given to the performance of gene-based tests (typically designed for a smaller number of single-nucleotide variants [SNVs]) when the number of SNVs in the gene …

Evaluating The Impact Of Genotype Errors On Rare Variant Tests Of Association, Kaitlyn Cook, Alejandra Benitez, Casey Fu, Nathan L. Tintle

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The new class of rare variant tests has usually been evaluated assuming perfect genotype information. In reality, rare variant genotypes may be incorrect, and so rare variant tests should be robust to imperfect data. Errors and uncertainty in SNP genotyping are already known to dramatically impact statistical power for single marker tests on common variants and, in some cases, inflate the type I error rate. Recent results show that uncertainty in genotype calls derived from sequencing reads are dependent on several factors, including read depth, calling algorithm, number of alleles present in the sample, and the frequency at which an …

Risk Factors For Physical Violence Against Partners In The U.S., K. Daniel O'Leary, Nathan L. Tintle, Evelyn Bromet

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Objective: To examine unique and relative predictive values of demographic, social learning, developmental, psychopathology, and dyadic variables as risk factors for perpetration of intimate partner physical aggression in a national sample of married or cohabiting individuals. Method: Men (n = 798) and women (n = 770) were selected from the public use data file of the 2003 National Comorbidity Survey Replication (NCS-R) which used a multistage cluster sampling design. Results: Eight percent of women and 5% of men reported perpetrating physical aggression in the past year. Based on multivariable regression analyses, among men, the unique risk factors for perpetrating physical …

Value Of Mendelian Laws Of Segregation In Families: Data Quality Control, Imputation, And Beyond, Elizabeth M. Blue, Lei Sun, Nathan L. Tintle, Ellen M. Wijsman

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When analyzing family data, we dream of perfectly informative data, even whole-genome sequences (WGSs) for all family members. Reality intervenes, and we find that next-generation sequencing (NGS) data have errors and are often too expensive or impossible to collect on everyone. The Genetic Analysis Workshop 18 working groups on quality control and dropping WGSs through families using a genome-wide association framework focused on finding, correcting, and using errors within the available sequence and family data, developing methods to infer and analyze missing sequence data among relatives, and testing for linkage and association with simulated blood pressure. We found that single-nucleotide …

Pathway Analysis Approaches For Rare And Common Variants: Insights From Genetic Analysis Workshop 18, Stella Aslibekyan, Marcio Almeida, Nathan L. Tintle

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Pathway analysis, broadly defined as a group of methods incorporating a priori biological information from public databases, has emerged as a promising approach for analyzing high-dimensional genomic data. As part of Genetic Analysis Workshop 18, seven research groups applied pathway analysis techniques to whole-genome sequence data from the San Antonio Family Study. Overall, the groups found that the potential of pathway analysis to improve detection of causal variants by lowering the multiple-testing burden and incorporating biologic insight remains largely unrealized. Specifically, there is a lack of best practices at each stage of the pathway approach: annotation, analysis, interpretation, and follow-up. …

Assessing Methods For Assigning Snps To Genes In Gene-Based Tests Of Association Using Common Variants, Ashley Petersen, Carolina Alvarez, Scott Declaire, Nathan L. Tintle

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Gene-based tests of association are frequently applied to common SNPs (MAF>5%) as an alternative to single-marker tests. In this analysis we conduct a variety of simulation studies applied to five popular gene-based tests investigating general trends related to their performance in realistic situations. In particular, we focus on the impact of non-causal SNPs and a variety of LD structures on the behavior of these tests. Ultimately, we find that non-causal SNPs can significantly impact the power of all gene-based tests. On average, we find that the “noise” from 6–12 non-causal SNPs will cancel out the “signal” of one causal …

Geometric Framework For Evaluating Rare Variant Tests Of Association, Keli Liu, Shannon Fast, Matthew Zawistowski, Nathan L. Tintle

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The wave of next-generation sequencing data has arrived. However, many questions still remain about how to best analyze sequence data, particularly the contribution of rare genetic variants to human disease. Numerous statistical methods have been proposed to aggregate association signals across multiple rare variant sites in an effort to increase statistical power; however, the precise relation between the tests is often not well understood. We present a geometric representation for rare variant data in which rare allele counts in case and control samples are treated as vectors in Euclidean space. The geometric framework facilitates a rigorous classification of existing rare …

Optimal Methods For Using Posterior Probabilities In Association Testing, Keli Liu, Alexander Luedtke, Nathan L. Tintle

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Objective: The use of haplotypes to impute the genotypes of unmeasured single nucleotide variants continues to rise in popularity. Simulation results suggest that the use of the dosage as a one-dimensional summary statistic of imputation posterior probabilities may be optimal both in terms of statistical power and computational efficiency; however, little theoretical understanding is available to explain and unify these simulation results. In our analysis, we provide a theoretical foundation for the use of the dosage as a one-dimensional summary statistic of genotype posterior probabilities from any technology. Methods: We analytically evaluate the dosage, mode and the more general set …

Assessing The Impact Of Differential Genotyping Errors On Rare Variant Tests Of Association, Morgan Mayer-Jochimsen, Shannon Fast, Nathan L. Tintle

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Genotyping errors are well-known to impact the power and type I error rate in single marker tests of association. Genotyping errors that happen according to the same process in cases and controls are known as non-differential genotyping errors, whereas genotyping errors that occur with different processes in the cases and controls are known as differential genotype errors. For single marker tests, non-differential genotyping errors reduce power, while differential genotyping errors increase the type I error rate. However, little is known about the behavior of the new generation of rare variant tests of association in the presence of genotyping errors. In …