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This paper compares the use of confidence intervals (CIs) and a sensitivity analysis called the number needed to disturb (NNTD), in the analysis of research findings expressed as 'effect' sizes. Using 1,000 simulations of randomised trials with up to 1,000 cases in each, the paper shows that both approaches are very similar in outcomes, and each one is highly predictable from the other. CIs are supposed to be a measure of likelihood or uncertainty in the results, showing a range of possible effect sizes that could have been produced by random sampling variation alone. NNTD is supposed to be a measure of the robustness of the effect size to any variation, including that produced by missing data. Given that they are largely equivalent and interchangeable under the conditions tested here, the paper suggests that both are really measures of robustness. It concludes that NNTD is to be preferred because it requires many fewer assumptions, is more tolerant of missing data, is easier to explain, and directly addresses the key question of whether the underlying effect size is zero or not.

There is continuing concern about the paucity of social science graduates who have the quantitative skills required by academia and industry. Not only do students often lack the confidence to explore, and use, statistical techniques, the dominance of qualitative research in many disciplines has also often constrained programme-level integration of more quantitative material. However, whilst the topic of statistical literacy is relatively well researched within the more general educational literature, the evidence-base with respect to the effectiveness of teaching and learning of quantitative research methods in the social science remains somewhat limited. This paper describes the development, integration and evaluation of a series of student-led inquiry-based quantitative workbooks within a sociology/social policy undergraduate degree. It outlines how the workbooks were constructively aligned within a "methods spine" and offers some insight into quantitative teaching and learning generally. The paper also discusses some of the opportunities and challenges of taking both an aligned and IBL approach to the teaching of quantitative methods. In doing so it adds to growing evidence that 'problem-based pedagogies' tend to increase educational gain over and above more didactic approaches to learning and teaching. It highlights three key findings: programme-level approaches to curriculum design can be crucial in improving quantitative skills, particularly where they are tailored to student needs; a general indifference to quantitative methods is likely to be due to a process of disenfranchisement that happens before and during students' engagement with university; and, meaningfully engaging students as partners in the process of designing, integrating and evaluating curricula can help to overcome some of the barriers associated with the learning and teaching of quantitative skills.

Statistics is one of the important branches of mathematics taught in schools, colleges and universities. It is also an important tool in public policy discussions. This paper focuses on the use of statistics in the latter context, rather than its use in adult mathematics education research. I review the key characteristics of the statistical approach to constructing public knowledge, and give a very brief history of key points in its development. I discuss how what I call the "overt crisis of statistics," the apparent disenchantment of large sections of the public with the "expert" statistical methods, outputs and pronouncements, leads to dilemmas both for citizens and for democratic governments. Recently "Big Data" and data analytics seem to many to offer new solutions to problems resulting from the essential lack of certainty surrounding efforts to understand society, and from the need to make quick decisions in a rapidly changing world. These approaches have potential, but also limitations. This leads me to consider a second, "covert" crisis of statistics, resulting from a struggle between proponents of freely available public information and public argument, and those aiming to profit from the appropriation and sequestering of information for private ends. I finish by considering what can be done by ourselves, as citizens, as adult mathematics teachers, and as researchers.

Statistics anxiety is extremely common in undergraduate psychology students. The Statistics Anxiety Rating Scale (STARS) is at present the most widely used measure to assess statistics anxiety, measuring six distinct scales: test and class anxiety, interpretation anxiety, fear of asking for help, worth of statistics, fear of statistics teachers and computational self-concept. In this paper we first review the existing research that uses the STARS with psychology undergraduates. We then provide an analysis of the factor and reliability analysis of the STARS measure using a sample of undergraduate psychology students (N=315). Factor analysis of the STARS yielded nine factors, rather than the six it is intended to measure, with some items indicating low reliability, as demonstrated by low factor loadings. On the basis of these data, we consider the further development and refinement of measures of statistics anxiety in psychology students. Keywords: STARS, psychology, statistics anxiety.

Preparing students to be critical thinkers and effective communicators is essential in today's multinational and technologically sophisticated environment. New electronic technologies provide opportunities for creating learning environments that extend the possibilities of "old" but still essential technologies: books, blackboards, and linear, one-way communication media. Such technologies contribute to engagement and meaningful learning in the higher education sector. Greater understanding in educational psychology and the effectiveness of educational interventions has motivated the development of various student-centred pedagogies (e.g. Problem-Based Learning [PBL]) addressing perceived shortcomings of traditional didactic instruction. PBL as a pedagogy promotes meaningful learning due largely to its power to stimulate critical, reflective and creative thinking. Can teaching staff, then, adopt technology-based approaches to create multi-disciplinary interactive PBL environments that enhance learning and excite students, inspiring them to take ownership of their own education? This paper presents a cross-case analysis of four cases that explore how classroom-based learning activities have been transferred to online formats in universities to improve critical thinking, problem-solving skills, and other learning attributes across a range of disciplines.

As a component of the ongoing development of the mathematics curriculum in China, we compare the country's high school mathematics textbooks with those of several other countries. We base our analysis on the assumption that textbooks, as primary printed teaching resources, are key tools for interpreting educational policy. In this paper, we compare what content is selected and how that content is presented in series of high school textbooks from China, France, Germany, Japan, Russia, the United Kingdom, and the United States according to four core domains: algebra, geometry, statistics and probability, and calculus. We then discuss the implications of the analysis for the reform of the high school mathematics curriculum in China, particularly as it applies to the development of textbooks within that process of reform. The comparative results provide us with the opportunity to recognise the distinguishing features of the content and presentation of the Chinese mathematics curriculum and lead to some suggestions for future curriculum development.

Drawing on the traditions of critical race theory, the paper is presented as a chronicle--a narrative--featuring two invented characters with different histories and expertise. Together they explore the strengths and weaknesses of quantitative approaches to race equality in education. In societies that are structured in racial domination, such as the USA and the UK, quantitative approaches often encode particular assumptions about the nature of social processes and the generation of educational inequality that reflect a generally superficial understanding of racism. Statistical methods can obscure the material reality of racism and the more that statisticians manipulate their data, the more it is likely that majoritarian assumptions will be introduced as part of the fabric of the calculations themselves and the conclusions that are drawn. Focusing on the case of recent national data on the secondary education of minoritized children in England, the paper highlights statisticians' ability to define what counts as a "real" inequality without public challenge or scrutiny; reflects on the dangers of statistical "explanations" in the realm of public debate and policy outcomes; and questions quantitative assumptions about the intersectional relationships between different forms of oppression, including gender, class and race. (Contains 19 notes and 2 tables.)

Although our health professional students have some experience of simple charts, such as pie and bar, and some intuition of histograms, they do not appear to have much knowledge or understanding about box and whisker plots and their relation to the data they are describing or compared to histograms. The boxplot is a versatile charting tool, useful for presenting data from surveys and any other projects, where a reasonable quantity of data has been collected. An opportunity arose to create a reusable learning object (RLO) to describe, explore, and interpret boxplots, especially in relation to their data and summary statistics. Examples included interprofessional learning, as this was the main remit of the Centre for Excellence in Teaching and Learning, from which funding was obtained. The RLO is aimed at both undergraduate and post-graduate HP students, who would be able to use the resource flexibly, to augment their limited exposure to statistical techniques, and add to their appreciation of IP learning and working. The RLO includes animation and opportunities for students to interact with the resource. Existing, available "real" data, collected as part of research projects concerning (IP) learning, as well as generated data, is used as illustrative material. This paper explores some of the issues raised during the creation of the RLO, and presents limited feedback from users. Issues raised include the working of the project team, delivery platform, copyright and intellectual property rights and software incompatibilities. To date, feedback from colleagues and students has been very positive and has encouraged further improvements. The creation of this RLO has been a longer and more time-consuming experience than anticipated, and has highlighted the importance of a team approach, with constant reviewing. It will be interesting to see how the RLO will be used, and usage will be evaluated in the future.

The issue of poor statistical literacy amongst undergraduates in the United Kingdom is well documented. At university level, where poor statistics skills impact particularly on social science programmes, embedding is often used as a remedy. However, embedding represents a surface approach to the problem. It ignores the barriers to learning that students bring to class, which may not always be addressed solely through embedding, such as, mathematics anxiety. Instead, embedding can only work within a much deeper pedagogic model that places students at its heart, as active participants in learning. This paper examines the development of such a model within a large sociology programme, where there was an implementation of a range of pedagogic strategies to support the development of students' statistical literacy.

Full Fact is an independent, non-partisan fact-checking charity. A particular focus is the analysis of factual claims in political debate in the UK; for example, fact-checking claims and counterclaims made during Prime Minister's questions. Facts do not appear in a vacuum as they are often used as key elements in an effort to make a coherent argument. This paper describes a number of case histories where facts are disputed, drawn from our election work, to give an overview of the contemporary state of statistical literacy among politicians and the media. Common pitfalls in politicians' claims are set out, along with descriptions of our attempts to close the communication gap between different communities.

Recent concerns about a shortage of capacity for statistical and numerical analysis skills among social science students and researchers have prompted a range of initiatives aiming to improve teaching in this area. However, these projects have rarely re-evaluated the content of what is taught to students and have instead focussed primarily on delivery. The emphasis has generally been on increased use of complex techniques, specialist software and, most importantly in the context of this paper, a continued focus on inferential statistical tests, often at the expense of other types of analysis. We argue that this "business as usual" approach to the content of statistics teaching is problematic for several reasons. First, the assumptions underlying inferential statistical tests are rarely met, meaning that students are being taught analyses that should only be used very rarely. Secondly, all of the most common outputs of inferential statistical tests--p-values, standard errors and confidence intervals--suffer from a similar logical problem that renders them at best useless and at worst misleading. Eliminating inferential statistical tests from statistics teaching (and practice) would avoid the creation of another generation of researchers who either do not understand, or knowingly misuse, these techniques. It would also have the benefit of removing one of the key barriers to students' understanding of statistical analysis. [For a response to this article, "A Response to White and Gorard: against Inferential Statistics: How and Why Current Statistics Teaching Gets It Wrong," see EJ1152509. For the rejoinder, "Still against Inferential Statistics: Rejoinder to Nicholson and Ridgway," see EJ1152510.]

Graduates with well-developed capabilities in finance are invaluable to our society and in increasing demand. Universities face the challenge of designing finance programmes to develop these capabilities and the essential knowledge that underpins them. Our research responds to this challenge by identifying threshold concepts that are central to the mastery of finance and by exploring their potential for informing curriculum design and pedagogical practices to improve student outcomes. In this paper, we report the results of an online survey of finance academics at multiple institutions in Australia, Canada, New Zealand, South Africa and the United Kingdom. The outcomes of our research are recommendations for threshold concepts in finance endorsed by quantitative evidence, as well as a model of the finance curriculum incorporating finance, modelling and statistics threshold concepts. In addition, we draw conclusions about the application of threshold concept theory supported by both quantitative and qualitative evidence. Our methodology and findings have general relevance to the application of threshold concept theory as a means to investigate and inform curriculum design and delivery in higher education.

Learning to talk about motion in a second language is very difficult because it involves restructuring deeply entrenched patterns from the first language. In this paper we argue that statistical learning can explain why L2 learners are only partially successful in restructuring their second language grammars. We explore to what extent L2 learners make use of two mechanisms of statistical learning, entrenchment and pre-emption to acquire target-like expressions of motion and retreat from overgeneralisation in this domain. Paying attention to the frequency of existing patterns in the input can help learners to adjust the frequency with which they use path and manner verbs in French but is insufficient to acquire the boundary crossing constraint and learn what not to say. We also look at the role of language proficiency and exposure to French in explaining the findings.

This paper summarizes the evaluation of a project that involved undergraduate mathematics students in the development of teaching and learning resources for statistics modules taught in various departments of a university. This evaluation regards students' participation in the project and its impact on their learning of statistics, as characterized in terms of statistical reasoning, statistical thinking, and skills for statistical consultancy. The participation of students is evaluated from the viewpoint of communities of practice. The evaluation resulted in a characterization of the benefits of such a project and suggestions for implementations of future projects, and in addition brought to light new theoretical elements both as regards the learning of statistics and as regards communities of practice. In particular, the analysis highlighted contributions of the students involved to resource development practice in the community of university statistics teachers, as well as contributions to students' learning as a result of participation in this community.

In this paper we report the results from a major UK government-funded project, started in 2005, to review statistics and handling data within the school mathematics curriculum for students up to age 16. As a result of a survey of teachers we developed new teaching materials that explicitly use a problem-solving approach for the teaching and learning of statistics through real contexts. We also report the development of a corresponding assessment regime and how this works in the classroom. Controversially, in September 2006 the UK government announced that coursework was to be dropped for mathematics exams sat by 16-year-olds. A consequence of this decision is that areas of the curriculum previously only assessed via this method will no longer be assessed. These include the stages of design, collection of data, analysis and reporting which are essential components of a statistical investigation. The mechanism outlined here could provide some new and useful ways of coupling new teaching methods with learning and doing assessment--in short, they could go some way towards making up for the educational loss of "not" doing coursework. Also, our findings have implications for teaching, learning and assessing statistics for students of the subject at all ages. (Contains 4 tables and 15 figures.)

This discussion of experimental information retrieval focuses on the mathematical and statistical skills needed by students in librarianship and information studies. Theoretical approaches to document representation, query representation, database searching, and evaluation are reviewed, and changes in library schools' curriculum are suggested. (Author/LRW)

Examines the use of small-scale databases for introductory economic and social science statistics in higher education. The results of a research project at Portsmouth Polytechnic that used a specially written database are reported, the use of spreadsheets is discussed, and future considerations are suggested. (17 references) (LRW)