The goal of public health is to improve the overall health of a population by reducing the burden of disease and premature death. In order to monitor our progress towards eliminating existing problems and to identify the emergence of new problems, we need to be able to quantify the levels of ill health or disease in a population. Researchers and policy makers use many different measures to describe the health of populations. In this chapter we introduce more of the most commonly used measures so that you can use and interpret them correctly. We first discuss the three fundamental measures that underlie both the attack rate and most of the other health statistics that you will come across in health-related reports, the incidence rate, incidence proportion (also called risk or cumulative incidence) and prevalence, and then look at how they are calculated and used in practice. We finish by considering other, more elaborate measures that attempt to get closer to describing the overall health of a population. As you will see, this is not always as straightforward as it might seem.

Chapter 4 examines efforts in the nineteenth and early twentieth centuries to better understand Britain’s rain. Meteorologists had attempted to investigate the distribution of rain prior to the 1850s, but observation points remained few and inadequately distributed. The solution to answering questions about the geographies of the rain was the establishment of a rainfall observatory network that covered the entirety of the British Isles. The network of rainfall observing stations was established by George Symons and became known as the British Rainfall Organisation. It relied almost exclusively on volunteer labour. The first section of the chapter details the early years of Symons’s Rainfall Organisation and its key administrative features, before moving on to discussions about rain gauges and station exposures. The chapter then examines a series of experimental trials that ran from 1863 to 1890 and discusses the ensuing controversy regarding the value of the experiments and of the observatory network more generally. The chapter then looks at contemporary discussions about the value of various statistical treatments of rain data, before finishing with Alexander Buchan’s and Hugh Robert Mill’s rainfall maps and the maps’ contributions to data management and public utility.

Network science is a broadly interdisciplinary field, pulling from computer science, mathematics, statistics, and more. The data scientist working with networks thus needs a broad base of knowledge, as network data calls for—and is analyzed with—many computational and mathematical tools. One needs good working knowledge in programming, including data structures and algorithms to effectively analyze networks. In addition to graph theory, probability theory is the foundation for any statistical modeling and data analysis. Linear algebra provides another foundation for network analysis and modeling because matrices are often the most natural way to represent graphs. Although this book assumes that readers are familiar with the basics of these topics, here we review the computational and mathematical concepts and notation that will be used throughout the book. You can use this chapter as a starting point for catching up on the basics, or as reference while delving into the book.

This chapter introduces the reader to facial recognition technology (FRT) history and the development of FRT from the perspective of science and technologies studies. Beginning with the traditionally accepted origins of FRT in 1964–1965, developed by Woody Bledsoe, Charles Bisson, and Helen Wolf Chan in the United States, Simon Taylor discusses how FRT builds on earlier applications in mug shot profiling, imaging, biometrics, and statistical categorisation. Grounded in the history of science and technology, the chapter demonstrates how critical aspects of FRT infrastructure are aided by scientific and cultural innovations from different times of locations: that is, mugshots in eighteenth-century France; mathematical analysis of caste in nineteenth-century British India; innovations by Chinese closed-circuit television companies and computer vision start-ups conducting bio-security experiments on farm animals. This helps to understand FRT development beyond the United States-centred narrative. The aim is to deconstruct historical data, mathematical, and digital materials that act as ‘back-stage elements’ to FRT and are not so easily located in infrastructure yet continue to shape uses today. Taylor’s analysis lays a foundation for the kinds of frameworks that can better help regulate and govern FRT as a means for power over populations in the following chapters.

The Coda sketches how the distinctive tradition of uncertainty in nineteenth-century literature and culture changes with the rise of literary modernism. Uncertainty remains of vital interest to writers like Henry James, D. H. Lawrence, James Joyce, Virginia Woolf, and E. M. Forster. Yet a more self-conscious embrace of chance, contingency, and randomness, alongside a more thoroughgoing skepticism, disengages this writing from the earlier literature’s concerns. Further valences acquired by the concept of uncertainty in the early twentieth century – as radical indeterminacy in physics and contrast class to risk in economics – both intensify cultural interest in the topic and disarticulate its nineteenth-century framework. In a reading of Joseph Conrad’s novel Chance (1914), I argue that his emphasis on the value of momentary judgments, on knowledge as mercurial and provisional, and on the role of accident in literary plots all reprise Victorian tactics.

The Introduction provides an overview of the book’s argument about how novels in nineteenth-century Britain (by George Eliot, Wilkie Collins, William Thackeray, and Thomas Hardy) represented modes of thinking, judging, and acting in the face of uncertainty. It also offers a synopsis of key intellectual contexts: (1) the history of probability in logic and mathematics into the Victorian era, the parallel rise of statistics, and the novelistic importance of probability as a dual concept, geared to both the aleatory and the epistemic, to objective frequencies and subjective degrees of belief; (2) the school of thought known as associationism, which was related to mathematical probability and remained influential in the nineteenth century, underwriting the embodied account of mental function and volition in physiological psychology, and representations of deliberation and action in novels; (3) the place of uncertainty in treatises of rhetoric, law, and grammar, where considerations of evidence were inflected by probability’s epistemological transformation; and (4) the resultant shifts in literary probability (and related concepts like mimesis and verisimilitude) from Victorian novel theory to structuralist narratology, where understandings of probability as a dual concept were tacitly incorporated.

National censuses are rarely interested in those who know and use two or more languages, and they seldom make available statistics that reflect the bi- or multilingualism of their population. The author recounts how, over the years, he researched how many bilinguals there are in various countries. He contacted national statistical offices and census bureaus, studied their data, and perused national and transnational reports. He also interacted with official statisticians, who answered his questions and sent him unpublished data. And sometimes he went on specific quests to hunt down particular numbers or percentages that were being passed around. Here he concentrates on the results he obtained for the United States, Canada, Switzerland, and France. He ends with the holy grail many have been searching for – the proportion of bilinguals in the world. He gave an estimate back in 1982 – about half of the world’s population – and discusses how, with time, even 65 percent was proposed by some. Understanding why that was so was an adventure in its own right.

To effectively target public health interventions for greatest impact, it is essential that public health practitioners have a clear understanding of the populations they work with. As described in Chapter 1, understanding these populations, their health status and health needs draws on skills from several disciplines, including demography, epidemiology and statistics. Brought together, these skills allow the practitioner to understand the characteristics of the population of interest, the key health issues that it faces and the broader factors that have a particular influence on the health of that population. These broader factors are generally referred to as the wider determinants of health or the social determinants of health. Information is also vital in allowing practitioners to assess the impact of public health interventions.

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.