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This study investigates the correlates of statistics anxiety. Considering that statistics anxiety and spatial anxiety have been separately correlated with related constructs (e.g., mathematics anxiety, academic performance, etc.), the possibility that spatial anxiety plays a role in statistics anxiety is explored. When facing statistics or mathematics operations, people may imagine or visualize the task operations they must do to obtain the result. To examine this hypothesis, 778 students in a Social or Health Sciences program, enrolled in a--often mandatory--statistics course from Canadian, French and Belgian universities completed an online survey. The results show moderate to strong positive correlations between all three types of anxiety (spatial, mathematics, and statistics). In addition, a mediation analysis reveals the intermediate role played by mathematics anxiety in the relationship between spatial and statistics anxieties. Nonetheless, the direct link from spatial anxiety to statistics anxiety is non-negligible in the model. Finally, the results also indicate that women report higher levels of statistics anxiety, which may be partly explained by their higher level of spatial anxiety.

There is widespread misuse of statistics in research, particularly in the life sciences, which is one of the contributing factors to reproducibility concerns in research. However, the formal quantitative training that life sciences research trainees receive is often quite limited. Our survey of statistics requirements in undergraduate life sciences programmes offered by the top research-intensive universities in Canada, the U15 Group of Canadian Research Universities, confirmed that training in statistics tends to be limited and more general in nature. To help raise awareness and address these limitations, this paper shares findings of this statistics requirements survey and describes the evidence-based framework for a second-year undergraduate course at the University of Toronto, which was introduced to integrate statistics instruction with the life sciences research process. We hope these insights will inform future quantitative course offerings, and ultimately, better prepare students to effectively engage with statistics in life sciences research.

On the lookout for and with a vested interest in Canadian mathematics education matters, this article is dedicated to hockey cards. More specifically, the statistics found on the back of hockey cards. The combination of taking a trip down memory lane, thrifting in British Columbia, traipsing around Toronto, and having coffee (one cream) at Tim Hortons resulted in an investigation as to whether or not hockey card statistics have changed over the last half century. Long story short, they have not. The addition of power play goals and the plus/minus statistic are the only major developments. Although this can be considered an improvement, I consider it a shame. First, the statistics do not reflect changes to the game of hockey. Second, they do not include any of the plethora of statistics readily available at National Hockey League Stats (dot com) and Records (dot com). In other words, I contend that the standard statistics (Games Played, Goals, Assists, Points, Plus/Minus, Penalty in Minutes and Power Play Goals), found on the back of every type of hockey card, do not well enough paint a statistical picture of the hockey player photographed on the front of the card. To cement my contention, I detail my Build-a-Card exercise (akin to Build-a-Bear, yes), which is where one uses a blank back of the card as a canvas with which to paint a proper statistical portrait of a hockey player, albeit beer league hockey style.

Statistics play an important role in psychology, but statistics modules are notoriously unpopular amongst psychology students. We examined attitudes toward statistics and attitudes toward the statistical software package R in both undergraduate and postgraduate students across the duration of a statistics module. Participants' responses were analysed using both quantitative and qualitative techniques. Results demonstrated that, on average, students in introductory level modules held neutral (not negative) attitudes, but students at higher study levels held somewhat positive attitudes towards R and statistics. While not all students enjoyed learning R, our findings demonstrate that many students enjoyed statistics or R, most students found statistics/R valuable and they generally reported feeling competent using software by the end of their module. These results challenge the argument that R is not suitable for undergraduate psychology students. Consequently, benefits, challenges, and implications of teaching R to psychology students are discussed.

During the COVID-19 pandemic, people across the globe have been exposed to large amounts of statistical data. Previous studies have shown that individuals' mathematical understanding of health-related information affects their attitudes and behaviours. Here, we investigate the relation between: (1) basic numeracy; (2) COVID-19 health numeracy; and (3) COVID-19 health-related attitudes and behaviours. An online survey measuring these three variables was distributed in Canada, the United States (US) and the United Kingdom (UK) (n = 2032). In line with predictions, basic numeracy was positively related to COVID-19 health numeracy. However, predictions, neither basic numeracy nor COVID-19 health numeracy was related to COVID-19 health related attitudes and behaviours (e.g. follow experts' recommendations on social distancing, wearing masks etc.). Multi-group analysis was used to investigate mean differences and differences in the strength of the correlation across countries. Results indicate there were no between-country differences in the correlations between the main constructs but there were between-country differences in latent means. Overall, results suggest that while basic numeracy is related to one's understanding of data about COVID-19, better numeracy alone is not enough to influence a population's health-related attitudes about disease severity and to increase the likelihood of following public health advice.

Histories of statistics and quantification have demonstrated that systems of statistical knowledge participate in the construction of the objects that are measured. However, the pace, purpose, and scope of quantification in state bureaucracy have expanded greatly over the past decades, fuelled by (neoliberal) societal trends that have given the social phenomenon of quantification a central place in political discussions and in the public sphere. This is particularly the case in the field of education. In this article, we ask what is at stake in state bureaucracy, professional practice, and individual pupils as quantification increasingly permeates the education field. We call for a theoretical renewal in order to understand quantification as a social phenomenon in education. We propose a sociology-of-knowledge approach to the phenomenon, drawing on different theoretical traditions in the sociology of knowledge in France (Alain Desrosières and Laurent Thévenot), England (Barry Barnes and Donald MacKenzie), and Canada (Ian Hacking), and argue that the ongoing quantification practice at different levels of the education system can be understood as cultural processes of self-fulfilling prophecies.

This paper analyses introductory statistics students' verbal and gestural expressions as they interacted with a dynamic sketch (DS) designed using "Sketchpad" software. The DS involved numeric data points built on the number line whose values changed as the points were dragged along the number line. The study is framed on aggregate reasoning with quantitative data, but it also draws on the Vygotskian social cultural and historical perspective of learning, particularly, how cultural artefacts including language support learning. Three concepts, namely, data distribution, the mean and standard deviation were analyzed in the study. Tasks were designed such that students first talked about their informal understanding of the three concepts before interacting with the DS; then they interacted with the DS and discussed the connections among the three concepts as they dragged the data points along the horizontal axis. Analysis of students' verbal, gestural and other expressions suggest firstly, that the dynamic sketch mediated the informal meaning of data variability for them, particularly the meaning of standard deviation, which most students only recalled through a formula. Secondly, the interactions with the DS drew students' attention away from focusing on formulas and calculations which was clearly evident in their statements before the DS was introduced, to investigating the connections among concepts. These findings support previous studies that have proposed that the use of dynamic computing tools strongly support students' informal understanding of abstract concepts. Implications for teaching and learning introductory statistics concepts at the tertiary level are discussed.

In this study we assessed the usefulness of a multifaceted teaching framework in an advanced statistics course. We sought to expand on past findings by using this framework to assess changes in anxiety and self-efficacy, and we collected focus group data to ascertain whether students attribute such changes to a multifaceted teaching approach. Statistics anxiety significantly decreased and students' current statistics self-efficacy increased. Further, course performance was positively correlated with self-efficacy and a strong negative relationship between statistics anxiety and self-efficacy was documented. Focus group data suggested students appreciated aspects of this teaching framework and that they thought it served to reduce anxiety. In addition to this teaching framework, two instructional techniques were used to teach two specific statistical concepts. These techniques did not result in significant performance differences; however, students reported enjoying the activities and encouraged their use in future classes. Overall, this study suggests a multifaceted teaching framework may be useful in helping graduate students overcome anxiety and increase self-efficacy when completing an advanced statistics course. The research presented here adds to the growing literature concerning the importance of non-cognitive factors when teaching statistics. Limitations and directions for future research are discussed.

This study examined the experiences of and challenges faced by students when completing a statistics course. As part of the requirement for this course, students completed a learning check-in, which consisted of an individual meeting with the instructor to discuss questions and the completion of a learning reflection and study plan. Forty psychology students enrolled in two sections of an introductory statistics course volunteered for the research study. The types of questions raised by students during their meetings and the themes found in their learning reflections are presented. Results from this study provide information about the content, affective, and behavioral challenges faced by students learning statistics.

Two controversial topics related to the teaching of statistics to psychology students are (a) when to introduce statistical software and (b) which statistical software package to use. The current research looked at the use of statistical software in statistics classes from every university with a psychology program in Canada. Researchers collected data from 321 statistics courses offered to psychology students at 65 Canadian universities and coded the type of statistical software used (if any) in each course. Results show that slightly more than half of all universities introduce software at the introductory level. Point-and-click software is most popular, particularly SPSS. There is a considerable amount of variability in when and which software is introduced to students. Departments can use these data to inform their own practices.

The purpose of this study was to test three pathways from achievement goals to academic performance in statistics classes. Participants were 247 undergraduate students in psychology taking an introductory course on statistics. They completed questionnaires shortly after the midterm, and their final grades were provided by their professors at the end of the semester. Structural equation modeling results reveal three distinct paths from achievement goals to academic performance. Results suggest that the more participants adopted mastery goals in the context of their statistics course, the less they experienced anxiety and the better they performed in the course at the end of the semester.

Statistics educators have long recognized the importance of empowering students with statistical thinking skills that could be applied beyond the classroom. However, there is a dearth of research on how students deem statistical topics as having practical future relevance after they complete introductory courses. Focusing on student interest in and perceived value of statistics, this study reports findings from a qualitative study that examined students' written reflections to explore the nature and extent of the perceived future relevance of statistics among undergraduate students who completed a first-year introductory statistics course online. Findings show that students deemed statistics topics as important if they could be applied to their everyday lives or their academic- and career-related interests. We conclude with recommendations for instructors of introductory statistics courses that enroll students with diverse interests and goals.

In this paper we examine the ultimatum game's income distribution and efficiency implications and modify the game to investigate the impact of re-distributional policies imposed on the parties.

The purpose of this annual report is to provide a summary of measurement in physical education and exercise science-related activities in 2017. A recent trend for an annual increase in manuscript submissions to measurement in physical education and exercise science continued in 2017. Twenty-nine countries were represented (i.e., corresponding author) with the United States of America, Canada, the United Kingdom, Brazil, Spain, and Australia collectively accounting for slightly more than two-thirds of the submissions. Measurement in physical education and exercise science continues to welcome high-quality submissions from around the world in 2018. More than three-quarters of the manuscripts that were submitted to measurement in physical education and exercise science in 2017 were submitted to the exercise science section or the physical activity section or the research methodology and statistics section. Measurement in physical education and exercise science continues to welcome high-quality submissions within each of the seven sections that comprise the journal in 2018. We also gratefully acknowledge the many scholars from around the world who served as a reviewer for measurement in physical education and exercise science in 2017. Twenty-two countries were represented with the United States, Australia, Hong Kong, Spain, the United Kingdom, Canada, and Germany collectively accounting for more than 85% of the total number of reviewers. Measurement in physical education and exercise science continues to welcome high-quality manuscript reviews from around the world in 2018. Volume 21 (i.e., the volume published in 2017) of measurement in physical education and exercise science published a total of 26 manuscripts. More than three-quarters of the published manuscripts were submitted to the research methodology and statistics section or the physical education pedagogy section or the exercise science section or the physical activity section. Twelve countries were represented with the United States of America, the United Kingdom, Canada, and Australia collectively accounting for approximately three-fourths of the publications. Measurement in physical education and exercise science continues to strive for publishing high-quality manuscripts from around the world in 2018.

In this study, we follow students' modeling and covariational reasoning in the context of learning about big data. A three-week unit was designed to allow 12th grade students in a mathematics course to explore big and mid-size data using concepts such as trend and scatter to describe the relationships between variables in multivariate settings. Students' emergent ideas were followed along a varied learning trajectory that included computer-supported collaborative and inquiry-based approaches, using visualization tools and statistical software to explore data and fit a suitable trend, and student presentations of investigations. Findings show progress in some components of students' reasoning and modeling of covariation, and indicate which features of the unit design might contribute to it.

This article is a critical discourse analysis of coverage in the "National Post" and the "Globe and Mail" concerning the Organisation for Economic Co-operation and Development's 2000 Programme for International Student Assessment (PISA). In this article, I have shown how numbers are interpreted through statistics to create a reality and analyzed the mechanisms used, through which information is constructed and reconstructed by and for the media. I have also explored how diverse voices are represented. The discourses of neoliberalism were embedded in the coverage of the PISA results and discourses that accentuated regional stereotypes were in use. (Contains 1 note.)

Using data from recent national disability surveys in Australia, Canada, France, the Netherlands, South Africa, and the United States, an international team of researchers coded indicators of several types of disability using the International Classification of Functioning, Disability, and Health. This article discusses the Disability Tabulations (DISTAB) project and presents and evaluates the estimates of the prevalence of visual impairments.

While some Canadian universities have a long history in the provision of data services, that was not the norm in Canada, especially in small universities and colleges. To maximize the use of data by students and researchers in academia, it was evident that increased education, resources, and tools were required to support those delivering data services on their campuses. To this end, the Data Liberation Initiative (DLI) Survival Guide was designed as a comprehensive reference tool, which complements an established regional training curriculum, whereby enabling librarians to effectively fulfill their role as a DLI Contact in their academic institutions. This case study will examine the history, current state, and recommended future direction of the Survival Guide. This article will also examine the challenges in understanding the drivers shaping academic service delivery and the ways in which the guide has evolved to remain current to the needs of the Canadian data community.

Students in psychology generally have difficulties to successfully accomplish mandatory courses in statistics. Group peer-tutoring is a pedagogical strategy to support them with a peer that has already successfully mastered the content of such a course. In order to specifically tailor group peer-tutoring to the needs of students and to sustain tutees' participation, it is important to understand how they conceptualize tutoring. The aim of this study was to provide an empirical investigation of psychology students' conceptualization regarding cross-year group peer-tutoring in statistics. A multivariate concept mapping analysis generated a relevant three-cluster structure ("Tutoring setup," "Tutor knowledge, interpersonal skills, and relational dynamics" and "Student role and commitment to the course") that underlies students' cognitive structure regarding group peer-tutoring. The implications of the results for selecting and training peer-tutors are discussed. [Marie-Ève Martel provided the English revision of the manuscript.]

Statistics is taught in mathematics courses in all school levels. We suggest that using rich tasks in statistics can develop statistical reasoning and create both intra and interdisciplinary links in students. In this paper, we present three case studies where middle school mathematics teachers used different tasks in lessons on pie charts. We analyzed the actions implemented/performed/attempted by teachers to support the development of statistical reasoning and the creation of intra and interdisciplinary links in their lessons. Results show that their procedural vision of statistics led them to focus more on graphical representation, neglecting aspects of statistical reasoning. Results also reveal an interdisciplinary intersection between mathematics and statistics, which may prevent the development of statistical reasoning.

We followed established best practices in concept inventory design and developed a 12-item inventory to assess student ability in statistical reasoning in biology (Statistical Reasoning in Biology Concept Inventory [SRBCI]). It is important to assess student thinking in this conceptual area, because it is a fundamental requirement of being statistically literate and associated skills are needed in almost all walks of life. Despite this, previous work shows that non-expert-like thinking in statistical reasoning is common, even after instruction. As science educators, our goal should be to move students along a novice-to-expert spectrum, which could be achieved with growing experience in statistical reasoning. We used item response theory analyses (the one-parameter Rasch model and associated analyses) to assess responses gathered from biology students in two populations at a large research university in Canada in order to test SRBCI's robustness and sensitivity in capturing useful data relating to the students' conceptual ability in statistical reasoning. Our analyses indicated that SRBCI is a unidimensional construct, with items that vary widely in difficulty and provide useful information about such student ability. SRBCI should be useful as a diagnostic tool in a variety of biology settings and as a means of measuring the success of teaching interventions designed to improve statistical reasoning skills.

We surveyed researchers in the health and exercise sciences to explore different areas and magnitudes of bias in researchers' decision making. Participants were presented with scenarios (testing a central hypothesis with p = 0.06 or p = 0.04) in a random order and surveyed about what they would do in each scenario. Participants showed significant bias in deciding to randomize additional participants when p = 0.06 (24.5%) compared to when p = 0.04 (6.5%), ?[superscript 2] = 19.86, odds ratio (OR) = 13.5. Based on this bias to randomize additional participants, we present statistical simulations showing the cumulative negative effect this bias has on the false positive rate for a field. While it is important for researchers to have flexibility in their data-processing decisions, there is a cost/benefit trade-off to experimenter degrees of freedom and it is important that these decisions be unbiased. These data highlight the importance of a priori analysis plans in research.

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.

In previous infant studies on statistics-based word segmentation, the unit of statistical computation was always aligned with the syllabic edge, which had a consonant onset. The current study addressed whether the learning system imposes a constraint that favors word forms beginning with a consonant onset over those beginning with an onsetless sub-syllable, by examining infants' segmentation of vowel-initial non-words in French liaison. French-learning 20- and 24-month-old infants ("N" = 64) were familiarized with sentences containing variable liaison consonants preceding the same vowel-initial non-word (e.g., /n/"onche", /z/"onche", /r/"onche", /t/"onche"), such that the distributional cues supported the sub-syllabic target (e.g., "onche"). After familiarization, we tested sub-syllabic statistical segmentation by presenting the vowel-initial target (e.g., "onche") versus another non-familiarized vowel-initial word (e.g., "èque"). Another group of infants was tested with a consonant-initial mis-segmentation of the target (e.g., "zonche") versus another non-familiarized consonant-initial word (e.g., "zèque"). Results showed that 20-month-olds failed to segment the vowel-initial targets, but they mis-segmented the targets as consonant-initial, indicating that the onset bias dominated over sub-syllabic statistics for word segmentation at this age. Twenty-four-month-olds showed ambiguous interpretations (i.e., both vowel-initial segmentation and consonant-initial mis-segmentation), suggesting that the use of statistics to segment sub-syllabic words was emerging while the onset bias continued to have an impact.

Base-rate neglect refers to the tendency for people to underweight base-rate probabilities in favor of diagnostic information. It is commonly held that base-rate neglect occurs because effortful (Type 2) reasoning is required to process base-rate information, whereas diagnostic information is accessible to fast, intuitive (Type 1) processing (e.g., Kahneman & Frederick, 2002). To test this account, we instructed participants to respond to base-rate problems on the basis of "beliefs" or "statistics," both in free time (Experiments 1 and 3) and under a time limit (Experiment 2). Participants were given problems with salient stereotypes (e.g., "Jake lives in a beautiful home in a posh suburb") that either conflicted or coincided with base-rate probabilities (e.g., "Jake was randomly selected from a sample of 5 doctors and 995 nurses for conflict; 995 doctors and 5 nurses for nonconflict"). If utilizing base-rates requires Type 2 processing, they should not interfere with the processing of the presumably faster belief-based judgments, whereas belief-based judgments should always interfere with statistics judgments. However, base-rates interfered with belief judgments to the same extent as the stereotypes interfered with statistical judgments, as indexed by increased response time and decreased confidence for conflict problems relative to nonconflict. These data suggest that base-rates, while typically underweighted or neglected, do not require Type 2 processing and may, in fact, be accessible to Type 1 processing.

Office hours provide time outside of class for students to consult with instructors about course material, progress, and evaluation. Yet office hours, at times, remain an untapped source of academic support. The current study examined whether office hour attendance in combination with a learning reflection would help students learn material in an introductory statistics course. Psychology students were randomly assigned to meet in person with the course instructor and complete a learning reflection form prior to a test. Students who completed these tasks prior to the second test in the course outperformed other students. Office hour attendance combined with reflection may be a useful way to improve students' understanding of statistics.

Students' informal inferential reasoning (IIR) is often inconsistent with the normative logic underlying formal statistical methods such as Analysis of Variance (ANOVA), even after instruction. In two experiments reported here, student's IIR was assessed using an intuitive ANOVA task at the beginning and end of a statistics course. In both experiments, students were provided feedback regarding the normative logic underlying ANOVA and how their reasoning compared with it. Additionally, students in Experiment 2 were given an assignment in which they analyzed and interpreted other students' performance on the intuitive ANOVA task. Results indicate that the feedback combined with the assignment (which required active explanation of both normative and non-normative reasoning applied to the task) led to more normative inferential reasoning at the end of the course, whereas providing feedback alone did not. Implications are discussed for using the intuitive ANOVA task as a formative classroom tool to help students improve their conceptual understanding of ANOVA.

The arithmetic mean is a fundamental statistical concept. Unfortunately, social science students rarely develop an intuitive understanding of the mean and rely on the formula to describe or define it. According to constructivist pedagogy, educators that have access to a variety of conceptualizations of a particular concept are better equipped to teach that concept in a meaningful way. With this in mind, this article outlines five conceptualizations of the arithmetic mean and discusses how each conceptualization can be presented in the classroom. Educators can use these conceptualizations in order to foster insight into the mean. (Contains 5 figures.)

The purpose of this paper is to report the results of a quantitative analysis exploring the interaction and relationship between the online database and electronic journal collections at the J. N. Desmarais Library of Laurentian University. A very strong relationship exists between the number of searches and the size of the online database collection where the larger a database collection, the greater its usage. Another very strong relationship was observed between the number of searches and the number of articles downloaded. The more searches that were performed on the database collection, the more the e-journal collection was utilized. (Contains 2 tables and 4 figures.)