Information about the natural world comes from many sources. In controlled experiments, the responses of similar groups to a treatment are compared, and differences in the responses suggest that the treatment may have had an effect. Where controlled experiments would be impossible or unethical studies that compare conditions in two or more similar situations that differ in place or time may be appropriate. Statistical analysis allows investigators to evaluate the probability that observed results are due to chance. Historical records, natural records such as fossils, oral traditions, traditional ecological knowledge, and observations from citizen scientists and parataxonomists are also important. Researchers often develop models to predict how a system behaves under specified conditions. This is useful when a system, such as the Earth’s climate, cannot be observed directly. Science provides a framework within which results can be compared to predictions and conclusions can be modified as new evidence becomes available. Arguments and information about the natural world should be evaluated critically for misleading statements and potential bias.

A quick introduction to the standard model of particle physics is given. The general concepts of elementary particles, interactions and fields are outlined. The experimental side of particle physics is also briefly discussed: how elementary particles are produced with accelerators or from cosmic rays and how to observe them with detectors via the interactions of particles with matter. The various detector technologies leading to particle identification are briefly presented. The way in which the data collected by the sensors is analysed is also presented: the most frequent probability density functions encountered in particle physics are outlined. How measurements can be used to estimate a quantity from some data and the question of the best estimate of that quantity and its uncertainty are explained. As measurements can also be used to test a hypothesis based on a particular model, the hypothesis testing procedure is explained.

This chapter examines suitable statistics questions for investigation by children of different ages, using a cycle of problem, plan, data, analysis and conclusion (PPDAC) (Wild & Pfannkuch 1999). The importance of variation in data and different types of variables and the difference between a population and a sample are investigated. Readers will explore different ways of displaying data to ‘tell a story’. The importance of drawing inferences from data and the uncertainty associated with these inferences are discussed. Readers will engage in activities that use technology to support the development of statistical understanding.

In this chapter we identify issues pertinent to ‘out of field’ teachers of mathematics. Strategies are offered to assist ‘out of field’ teachers of mathematics while considering the invaluable knowledge a primary-trained teacher can bring to the secondary mathematics classroom. Examples are presented of teachers’ critical pedagogical content knowledge that has a high impact on students’ growth and development across the main strands of the curriculum.

This chapter details the practical, theoretical, and philosophical aspects of experimental science. It discusses how one chooses a project, performs experiments, interprets the resulting data, makes inferences, and develops and tests theories. It then asks the question, "are our theories accurate representations of the natural world, that is, do they reflect reality?" Surprisingly, this is not an easy question to answer. Scientists assume so, but are they warranted in this assumption? Realists say "yes," but anti-realists argue that realism is simply a mental representation of the world as we perceive it, that is, metaphysical in nature. Regardless of one's sense of reality, the fact remains that science has been and continues to be of tremendous practical value. It would have to be a miracle if our knowledge and manipulation of the nature were not real. Even if they were, how do we know they are true in an absolute sense, not just relative to our own experience? This is a thorny philosophical question, the answer to which depends on the context in which it is asked. The take-home message for the practicing scientist is "never assume your results are true."

This first chapter introduces our unique approach to teaching statistics. We note that while we review the statistical formulas for each method, we focus on the practical component of statistical analysis. We teach the readers how to apply and interpret the statistical methods and results. We then briefly describe the book’s content, which includes a concise explanation of the statistical techniques covered in each chapter. We end the chapter with suggestions on using the book to gain maximum benefit.

When very young children are brought to a doctor or hospital with signs and symptoms consistent with head injury, it is important to determine the cause. For almost 50 years, the triad of subdural haematoma (SDH), retinal haemorrhage (RH) and encephalopathy has been regarded as an accurate predictor of deliberate shaking and widely used to diagnose shaken baby syndrome (SBS). Statistical analyses by Cardiff University researchers and others claim to show that certain combinations of findings are highly predictive of abuse and as a result of this conclusion, protocols such as mandatory reporting to police are invoked in the name of protecting the child. However, concerns have been raised about the circularity of approach used in the statistical analyses which requires each case to be classified explicitly as either abuse or non-abuse. By producing a causal model of the problem, we show that these findings are actually a poor predictor of SBS, even where there is some evidence of risk factors indicative of abuse.

This chapter can serve either as a starting point or a recharging point for instructors who are preparing to teach research methods and/or statistics at the college or graduate level. Using empirical work and experience, I’ll discuss the importance of these classes and then provide a list of what I perceive to be the most important recommendations and biggest challenges related to teaching these courses. Because so many classes include projects, I have dedicated half of the recommendations and challenges to the ones that involve student projects. It is my hope that a person reading this takes away a set of ideas and feels empowered to teach these courses well. For all the challenges, teaching these classes can be rewarding for the instructor and transformative for the student.

Working in applied settings presents unique challenges and complexities with respect to research. Researchers have often commented on the scientist–practitioner divide, but there is a lack of information about the specific challenges and constraints of doing applied work that may contribute to this divide. As a group of applied social and behavioral scientists, we discuss what individuals should know, understand, and expect regarding the work practitioners conduct in applied settings. We describe the challenges of applied work as they relate to some topics covered earlier in this volume and identify other unique aspects of applied work. We conclude by discussing how an individual can approach deciding whether applied work is a fit with one’s interests.

Volume 2 of The Cambridge History of Global Migrations presents an authoritative overview of the various continuities and changes in migration and globalization from the 1800s to the present day. Despite revolutionary changes in communication technologies, the growing accessibility of long-distance travel, and globalization across major economies, the rise of nation-states empowered immigration regulation and bureaucratic capacities for enforcement that curtailed migration. One major theme worldwide across the post-1800 centuries was the differentiation between “skilled” and “unskilled” workers, often considered through a racialized lens; it emerged as the primary divide between greater rights of immigration and citizenship for the former, and confinement to temporary or unauthorized migrant status for the latter. Through thirty-one chapters, this volume further evaluates the long global history of migration; and it shows that despite the increased disciplinary systems, the primacy of migration remains and continues to shape political, economic, and social landscapes around the world.

Many of the problems that human minds need to solve – including learning concepts, causal relationships, and languages – require making informed inferences from limited data. Bayesian models of cognition consider how an ideal agent should solve these problems, drawing on ideas from probability theory, statistics, machine learning, and artificial intelligence.  The resulting models can then be used to understand human behavior, identifying in formal terms the knowledge that human minds draw on when solving these problems and identifying potential mechanisms by which their solutions might be implemented. This chapter provides an introduction to Bayesian models of cognition, starting with the basic principles of probability theory and then considering more advanced topics such as graphical models, causal learning, hierarchical Bayesian models, and Markov chain Monte Carlo. The chapter ends with a brief review of recent theoretical developments.

This chapter focuses on the mechanics of collecting and analyzing outcome data. It reviews the foundational functions of data management as they pertain to measuring outcomes. Then it discusses different data collection mechanisms such as using spreadsheets, REDCap, registries, and electronic health records. Additional considerations for data collection are outlined such as establishing the measurement timeline and ethical and legal considerations when establishing an outcome measurement program. This chapter also discusses the steps of integrating and validating data as well as extracting and analyzing outcome data. The primary audience for this chapter is individual clinicians who want to start measuring outcomes in their clinical practice.