We describe an activity that introduces students to population modelling, enables them to use estimates obtained from a sample to infer back to the population, and understands how the findings are translatable via penguins and their poo!

Testing whether items fit the assumptions of an item response theory model is an important step in evaluating a test. In the literature, numerous item fit statistics exist, many of which show severe limitations. The current study investigates the root mean squared deviation (RMSD) item fit statistic, which is used for evaluating item fit in…

While various studies suggest that informal statistical inference (ISI) can be developed by young students, more research is needed to translate this claim into a well-founded learning trajectory (LT). As a contribution, this paper presents the results of a cycle of design research that focuses on the design, implementation, and evaluation of the…

Statistics education reform efforts emphasize the importance of informal inference in the learning of statistics. Research suggests statistics teachers experience similar difficulties understanding statistical inference concepts as students and how teacher knowledge can impact student learning. This study investigates how teachers reinvented an…

The omega (?) statistic is reputed to be one of the best indices for detecting answer copying on multiple choice tests, but its performance relies on the accurate estimation of copier ability, which is challenging because responses from the copiers may have been contaminated. We propose an algorithm that aims to identify and delete the suspected…

For many years, students have been taught to visualise data by drawing graphs. Recently, there has been a growing trend to teach statistics, particularly statistical concepts, using interactive and dynamic visualisation tools. Free down-loadable teaching and simulation software designed specifically for schools, and more general data visualisation…

This study focuses on the development of four tertiary introductory statistics students' informal inferential reasoning while engaging in data driven repeated sampling and resampling activities. Through the use of hands-on manipulatives and simulations with technology, the participants constructed empirical sampling distributions in order to…

Most questions in social and biomedical sciences are causal in nature: what would happen to individuals, or to groups, if part of their environment were changed? In this groundbreaking text, two world-renowned experts present statistical methods for studying such questions. This book starts with the notion of potential outcomes, each corresponding…

Formal inference, which makes theoretical assumptions about distributions and applies hypothesis testing procedures with null and alternative hypotheses, is notoriously difficult for tertiary students to master. The debate about whether this content should appear in Years 11 and 12 of the "Australian Curriculum: Mathematics" has gone on…

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…

Establishing model parsimony is an important component of structural equation modeling (SEM). Unfortunately, little attention has been given to developing systematic procedures to accomplish this goal. To this end, the current study introduces an innovative application of the jackknife approach first presented in Rensvold and Cheung (1999). Unlike…

This is the first report from a new initiative called TLRI Project Plus. It aims to add value to the Teaching and Learning Research Initiative (TLRI), which NZCER manages on behalf of the government, by synthesising findings across multiple projects. This report focuses on two projects in statistics education and explores the factors that…

Nearly all introductory statistics textbooks include a chapter on data collection methods that includes a detailed discussion of both random sampling methods and randomized experiments. But when statistical inference is introduced in subsequent chapters, its justification is nearly always based on principles of random sampling methods. From the…

In this article we describe a semester-long project, based on the popular video game series Guitar Hero, designed to introduce upper-level undergraduate statistics students to statistical research. Some of the goals of this project are to help students develop statistical thinking that allows them to approach and answer open-ended research…

This paper identifies key concepts and issues associated with the reasoning of informal statistical inference. I focus on key ideas of inference that I think all students should learn, including at secondary level as well as tertiary. I argue that a fundamental component of inference is to go beyond the data at hand, and I propose that statistical…