Learning Outcomes supporting the integration of Ethical Reasoning into quantitative courses: Three tasks for use in three general contexts

This paper gives a brief overview of cognitive and educational sciences' perspectives on learning outcomes (LOs) to facilitate the integration of LOs specific to ethical reasoning into any mathematics or quantitative course. The target is undergraduate (adult) learners but these LOs can be adapted for earlier and later stages of learning. Core contents of Ethical Reasoning are: 1. its six constituent knowledge, skills, and abilities; 2. a stakeholder analysis; and 3. ethical practice standards or guidelines. These are briefly summarized. Five LOs are articulated at each of three levels of cognitive complexity (low/med/high), and a set of assignment features that can be adapted repeatedly over a term are given supporting these LOs. These features can support authentic development of the knowledge, skills, and abilities that are the target of ethical reasoning instruction in math and quantitative courses at the tertiary level. Three contexts by which these can be integrated are Assumption (what if the assumption fails?), Approximation (what if the approximation does not hold?), and Application (is the application appropriate? what if it is not?). One or more of the three core contents of Ethical Reasoning can be added to any problem already utilized in a course (or new ones) by asking learners to apply the core to the context. Engagement with ethical reasoning can prepare students to assume their responsibilities to promote and perpetuate the integrity of their profession across their careers using mathematics, statistics, data science, and other quantitative methods and technologies.Comment: 21 pages; 8 tables, 1 Figur

Stewardship of Mathematics: Essential Training for Contributors to, and Users of, the Practice of Mathematics

A steward of the discipline was originally defined as an individual to whom “we can entrust the vigor, quality, and integrity of the field”, and more specifically, as “someone who will creatively generate new knowledge, critically conserve valuable and useful ideas, and responsibly transform those understandings through writing, teaching, and application” [8]. Originally articulated for doctoral education, in 2019 the construct of stewardship was expanded so that it can also be applied to non-academic practitioners in any field, and can be initiated earlier than doctoral education [18]. In this paper, we apply this construct to the context of mathematics, and argue that even for those early in their training in mathematics, stewardly practice of mathematics can be introduced and practiced. Postsecondary and tertiary education in mathematics — for future mathematicians as well as those who will use math at work — can include curriculum-spanning training, and documented achievement in stewardship. Even before a formal ethical practice standard for mathematics is developed and deployed to help inculcate math students with a “tacit responsibility for the quality and integrity of their own work”, higher education can begin to shape student attitudes towards stewardly professional identities. Learning objectives to accomplish this are described, to assist math instructors in facilitating the recognition and acceptance of responsibility for the quality and integrity of their own work and that of colleagues in the practice of mathematics

How does international guidance for statistical practice align with the ASA Ethical Guidelines?

Gillikin (2017) defines a 'practice standard' as a document to 'define the way the profession's body of knowledge is ethically translated into day-to-day activities' (Gillikin 2017, p. 1). Such documents fulfill three objectives: they 1) define the profession; 2) communicate uniform standards to stakeholders; and 3) reduce conflicts between personal and professional conduct (Gillikin, 2017 p. 2). However, there are many guidelines - this is due to different purposes that guidance writers may have, as well as to the fact that there are different audiences for the many guidance documents. The existence of diverse statements do not necessarily make it clear that there are commonalities; and while some statements are explicitly aspirational, professionals as well as the public need to know that ethically-trained practitioners follow accepted practice standards. This paper applies the methodological approach described in Tractenberg (2023) and demonstrated in Park and Tractenberg (2023) to study alignment among international guidance for official statistics, and between these guidance documents and the ASA Ethical Guidelines for Statistical Practice functioning as an ethical practice standard (Tractenberg, 2022-A, 2022-B; after Gillikin 2017). In the spirit of exchanging experiences and lessons learned, we discuss how our findings could inform closer examination, clarification, and, if beneficial, possible revision of guidance in the future.Comment: 53 pages; 28 page document with 11 summary tables; the 2022 ASA Ethical Guidelines for Statistical Practice and 10 detailed tables. arXiv admin note: text overlap with arXiv:2309.0718

How do ASA Ethical Guidelines Support U.S. Guidelines for Official Statistics?

In 2022, the American Statistical Association revised its Ethical Guidelines for Statistical Practice. Originally issued in 1982, these Guidelines describe responsibilities of the 'ethical statistical practitioner' to their profession, to their research subjects, as well as to their community of practice. These guidelines are intended as a framework to assist decision-making by statisticians working across academic, research, and government environments. For the first time, the 2022 Guidelines describe the ethical obligations of organizations and institutions that use statistical practice. This paper examines alignment between the ASA Ethical Guidelines and other long-established normative guidelines for US official statistics: the OMB Statistical Policy Directives 1, 2, and 2a NASEM Principles and Practices, and the OMB Data Ethics Tenets. Our analyses ask how the recently updated ASA Ethical Guidelines can support these guidelines for federal statistics and data science. The analysis uses a form of qualitative content analysis, the alignment model, to identify patterns of alignment, and potential for tensions, within and across guidelines. The paper concludes with recommendations to policy makers when using ethical guidance to establish parameters for policy change and the administrative and technical controls that necessarily follow.Comment: 74 pages total; 25 page manuscript with 4 summary tables, the 2022 ASA Ethical Guidelines for Statistical Practice, and 10 detailed tables in Anne

The Mastery Rubric for Statistics and Data Science: promoting coherence and consistency in data science education and training

Consensus based publications of both competencies and undergraduate curriculum guidance documents targeting data science instruction for higher education have recently been published. Recommendations for curriculum features from diverse sources may not result in consistent training across programs. A Mastery Rubric was developed that prioritizes the promotion and documentation of formal growth as well as the development of independence needed for the 13 requisite knowledge, skills, and abilities for professional practice in statistics and data science, SDS. The Mastery Rubric, MR, driven curriculum can emphasize computation, statistics, or a third discipline in which the other would be deployed or, all three can be featured. The MR SDS supports each of these program structures while promoting consistency with international, consensus based, curricular recommendations for statistics and data science, and allows 'statistics', 'data science', and 'statistics and data science' curricula to consistently educate students with a focus on increasing learners independence. The Mastery Rubric construct integrates findings from the learning sciences, cognitive and educational psychology, to support teachers and students through the learning enterprise. The MR SDS will support higher education as well as the interests of business, government, and academic work force development, bringing a consistent framework to address challenges that exist for a domain that is claimed to be both an independent discipline and part of other disciplines, including computer science, engineering, and statistics. The MR-SDS can be used for development or revision of an evaluable curriculum that will reliably support the preparation of early e.g., undergraduate degree programs, middle e.g., upskilling and training programs, and late e.g., doctoral level training practitioners.Comment: 40 pages; 2 Tables; 4 Figures. Presented at the Symposium on Data Science & Statistics (SDSS) 202

Agreement of Immunoassay and Tandem Mass Spectrometry in the Analysis of Cortisol and Free T4: Interpretation and Implications for Clinicians

Objective. To quantify differences in results obtained by immunoassays (IAs) and tandem mass spectrometry (MSMS) for cortisol and free thyroxine (FT4). Design & Patients. Cortisol was measured over 60 minutes following a standard ACTH stimulation test (n = 80); FT4 was measured over time in two cohorts of pregnant (n = 57), and nonpregnant (n = 28) women. Measurements. Samples were analyzed with both IA and MSMS. Results. Results for cortisol by the two methods tended to agree, but agreement weakened over the 60-minute test and was worse for higher (more extreme) concentrations. The results for FT4 depended on the method. IA measurements tended to agree with MSMS measurements when values fell within “normal levels”, but agreement was not constant across trimester in pregnant women and was poorest for the extreme (low/high) concentrations. Correlations between MSMS measurements and the difference between MSMS and IA results were strong and positive (0.411 < r < 0.823; all P < .05). Conclusions. IA and MSMS provide different measures of cortisol and FT4 at extreme levels, where clinical decision making requires the greatest precision. Agreement between the methods is inconsistent over time, is nonlinear, and varies with the analyte and concentrations. IA-based measurements may lead to erroneous clinical decisions

Leveraging guidelines for ethical practice of statistics and computing to develop standards for ethical mathematical practice: A White Paper

We report the results of our NSF-funded project in which we alpha- and beta- tested a survey comprising all aspects of the ethical practice standards from two disciplines with relevance to mathematics, the American Statistical Association (ASA) and Association of Computing Machinery (ACM). Items were modified so that text such as "A computing professional should..." became, "The ethical mathematics practitioner...". We also removed elements that were duplicates or were deemed unlikely to be considered relevant to mathematical practice even after modification. Starting with more than 100 items, plus 10 demographic questions, the final survey included 52 items (plus demographics), and 142 individuals responded to our invitations (through listservs and other widespread emails and announcements) to participate in this 30-minute survey. This white paper reports the project methods and findings regarding the community perspective on the 52 items, specifically, which rise to the level of ethical obligations, which do not meet this level, and what is missing from this list of elements of ethical mathematical practice. The results suggest that the community of mathematicians perceives a much wider range of behaviors to be subject to ethical practice standards than is currently represented.Comment: 48 pages including 6 Tables, plus Appendi

Willingness to Share Research Data Is Related to the Strength of the Evidence and the Quality of Reporting of Statistical Results

Background The widespread reluctance to share published research data is often hypothesized to be due to the authors' fear that reanalysis may expose errors in their work or may produce conclusions that contradict their own. However, these hypotheses have not previously been studied systematically. Methods and Findings We related the reluctance to share research data for reanalysis to 1148 statistically significant results reported in 49 papers published in two major psychology journals. We found the reluctance to share data to be associated with weaker evidence (against the null hypothesis of no effect) and a higher prevalence of apparent errors in the reporting of statistical results. The unwillingness to share data was particularly clear when reporting errors had a bearing on statistical significance. Conclusions Our findings on the basis of psychological papers suggest that statistical results are particularly hard to verify when reanalysis is more likely to lead to contrasting conclusions. This highlights the importance of establishing mandatory data archiving policies

Using the Guttman Scale to Define and Estimate Measurement Error in Items over Time: The Case of Cognitive Decline and the Meaning of “Points Lost”

We used a Guttman model to represent responses to test items over time as an approximation of what is often referred to as “points lost” in studies of cognitive decline or interventions. To capture this meaning of “point loss”, over four successive assessments, we assumed that once an item is incorrect, it cannot be correct at a later visit. If the loss of a point represents actual decline, then failure of an item to fit the Guttman model over time can be considered measurement error. This representation and definition of measurement error also permits testing the hypotheses that measurement error is constant for items in a test, and that error is independent of “true score”, which are two key consequences of the definition of “measurement error” –and thereby, reliability- under Classical Test Theory. We tested the hypotheses by fitting our model to, and comparing our results from, four consecutive annual evaluations in three groups of elderly persons: a) cognitively normal (NC, N = 149); b) diagnosed with possible or probable AD (N = 78); and c) cognitively normal initially and a later diagnosis of AD (converters, N = 133). Of 16 items that converged, error-free measurement of “cognitive loss” was observed for 10 items in NC, eight in converters, and two in AD. We found that measurement error, as we defined it, was inconsistent over time and across cognitive functioning levels, violating the theory underlying reliability and other psychometric characteristics, and key regression assumptions

What the CERAD Battery Can Tell Us about Executive Function as a Higher-Order Cognitive Faculty

Executive function (EF) is believed to control or influence the integration and application of cognitive functions such as attention and memory and is an important area of research in cognitive aging. Recent studies and reviews have concluded that there is no single test for EF. Results from first-order latent variable modeling have suggested that little, if any, variability in cognitive performance can be directly (and uniquely) attributed to EF; so instead, we modeled EF, as it is conceptualized, as a higher-order function, using elements of the CERAD neuropsychological battery. Responses to subtests from two large, independent cohorts of nondemented elderly persons were modeled with three theoretically plausible structural models using confirmatory factor analysis. Robust fit statistics, generated for the two cohorts separately, were consistent and support the conceptualization of EF as a higher-order cognitive faculty. Although not specifically designed to assess EF, subtests of the CERAD battery provide theoretically and empirically robust evidence about the nature of EF in elderly adults