Despite decades of theoretical conceptualization of racism’s complexity as a multilevel and multidimensional construct, the measurement of racism has largely ignored these important nuances. Prior empirical research has largely focused on interpersonal racism, its antecedents, and its consequences. The present chapter summarizes the variety of methodological tools that have been used to evaluate youths’ experiences with interpersonal racism. We highlight opportunities to advance the scientific rigor of each method and technique, with particular considerations for measurement inclusive of the Intersectionality framework. We also argue for measuring racism beyond the individual level. Cultural, institutional, and structural racism are delineated, and tangible recommendations are provided for advancing the measurement of each type of racism among marginalized youth populations. The chapter concludes with promising avenues of future research to support the triangulation of measurement and enhance the scientific understanding of the impact of racism.

In this chapter, we review the current state of this science for the measurement of daily ethnic and racial discrimination among ethnoracially minoritized youth. The goal of this chapter is to provide an understanding of the primary theoretical and empirical foundations for this research, to review the most recent findings and advancements in ethnic and racial discrimination measurement, and to highlight future directions that may prove important to understanding the daily experiences and health of ethnoracially minoritized youth. We highlight the foundation of this research in critical race theory, stress and coping research, and developmental and socioecological frameworks, we discuss the importance of daily methods in researching quotidian ethnic and racial discrimination, we review the health research that has contributed to our understanding of daily ethnic and racial discrimination assessment, and we highlight how measurement approaches should continue to evolve as social spaces, online contexts, and US society and institutions continually to shift.

This chapter provides a critical reflection on past and current research on ethnic and racial discrimination and youth development with recommendations for future research directions. First and foremost, I emphasize the need for positionality, reflexivity, and representational ethics to avoid advancing false or problematic narratives and to advance research that is more transparent and accountable. It also is necessary to distinguish and better contextualize ethnic discrimination (rooted in ethnocentrism) and racial discrimination (rooted in modern imperialism and White supremacy) rather than conflate these two constructs and measure them in ahistorical ways. These considerations require researchers to select or develop critically appropriate measurement tools, moving beyond commonly used measures that may not be relevant or appropriate to all racialized groups. Ethnic and racial discrimination during youth development requires special considerations, as discrimination coincides with identity formation and pubertal development. Yet there remains limited research on the ways in which these developmental tasks and experiences interplay. Given the complexities of how ethnic and racial discrimination manifest during youth development, researchers may want to consider novel methods like storytelling to embody discriminatory experiences and strengthen ecological validity.

Chapter 9 focuses on how students develop foundational understandings of Measurement and Space in the early years (Foundation to Year 2). It explores how young learners engage with concepts such as length, area, time, and mass through hands-on experiences and everyday contexts. You will consider how to structure learning experiences that build conceptual understanding, support spatial reasoning, and introduce key mathematical vocabulary and thinking processes.

Chapter 10 builds on earlier learning and explores how students extend their understanding of Measurement and Space in the middle and upper primary years (Years 3 to 6). It focuses on the development of key concepts such as units of measure, angles, transformations, and geometric properties. You will investigate strategies for using precise mathematical language, addressing common misconceptions, and applying spatial and measurement thinking to solve purposeful, real-world problems.

Chapter 2 explains how the Economist Mental Model (EMM) is measured by capturing two key dimensions: familiarity with core economic concepts (e.g., inflation, supply–demand, market dynamics) and the application of economic reasoning tools (e.g., cost–benefit analysis, opportunity costs, marginal analysis). This measurement approach uses an index of “economic knowledge,” drawn from original surveys in the US, Italy, and the UK. By assessing both factual economic knowledge and the ability to apply it to hypothetical scenarios, the index distinguishes EMM users (high economic knowledge) from those with Alternative Mental Models (AMMs) (low economic knowledge). Descriptive findings reveal that older, educated, wealthier men tend to score higher, with no strong partisan gap. Notably, EMM adopters do not value economic objectives more than those with AMMs, highlighting that differences in policy choices likely stem from how trade-offs are interpreted rather than divergent fundamental values. Demonstrating strong consistency across contexts, these measures set the stage for subsequent empirical analyses.

Hipparchus realised that for calculation to be effective and useful it must proceed from good observational practice. Without accuracy in the latter, the former, however sophisticated, cannot provide usable answers. Accordingly, he would have made many observations of astronomical facts and phenomena for himself, and for this he would have needed instrumentation. Very little is known for sure about what tools he used. The Antikythera Mechanism, which is roughly contemporary with Hipparchus, demonstrates the engineering skills that were available in his time, and on the reasonable assumption that such skills did not advance much by the time of Ptolemy, the latter’s description of his own instruments provides a basis for discussion. Also important in this context are notions of accuracy, precision and units of measurement. Evidence is brought to bear on these issues in relation to Hipparchus, and how they should be interpreted in the context of his works, using information gleaned from both him and from Ptolemy.

This chapter explores the application of large language models (LLMs) in empirical legal studies, with a focus on their potential to advance research on EU law at scale. The chapter provides a non-technical introduction to LLMs and the role they can play in legal information retrieval, including the classification of case characteristics and outcomes, which constitutes one of the most common research tasks in legal scholarship. The chapter stresses the importance of validation – researchers cannot treat the output of LLMs as automatically correct and instead must demonstrate the relevance and reliability of measures and results obtained through the use of LLMs in the context of their research topic. While LLMs are capable of significantly reducing the cost of doing legal research, their use will place growing demands on scholars to ensure the integrity of their findings. The chapter also reflects on the distinction between closed- and open-source models and how ethical and replicability imperatives might influence model choices in an increasingly crowded field.

Not everything we know about numbers can be interpreted as true of what they represent, so this chapter explores how far we can go in applying the numbers to real problems, and how we can be sure they are meaningful.

Empirical legal studies in EU law routinely, if not inevitably, engage with text. From the decisions of national courts applying EU law, applicants’ case filings, to the Court’s own jurisprudence, these texts are an invaluable source of information for researchers seeking to understand the dynamics involved in the shaping of EU law and its broader societal impact. Distilling relevant information from legal texts, however, is anything but trivial. Intended to serve as a reference manual, the chapter offers detailed guidelines to researchers of both law and political science interested in employing a text-as-data approach to the study of EU law. To this end, we elaborate on how to conceptualise real-life phenomena in a way that renders them conducive to measurement, providing practical guidance on hand-coding and the use of deep learning classifiers. Further, we address potential challenges arising in the specific context of EU law. This includes limitations to access to relevant documents, as well as ensuring inter-coder reliability in data collection efforts that require specialised legal expertise.

Typologies are well-established analytic tools in the social sciences. They can be “put to work” in forming concepts, refining measurement, exploring dimensionality, and organizing explanatory claims. Yet some critics, basing their arguments on what they believe are relevant norms of quantitative measurement, consider typologies old-fashioned and unsophisticated. This critique is methodologically unsound, and research based on typologies can and should proceed according to high standards of rigor and careful measurement. These standards are summarized in guidelines for careful work with typologies, and an illustrative inventory of over 100 typologies is included at the end of the chapter.

The challenge of finding appropriate tools for measurement validation is an abiding concern in political science. This chapter considers four traditions of validation, using examples from cross-national research on democracy: the levels-of-measurement approach, structural-equation modeling with latent variables, the pragmatic tradition, and the case-based method. Methodologists have sharply disputed the merits of alternative traditions. The chapter encourages scholars – and certainly analysts of democracy – to pay more attention to these disputes and to consider strengths and weaknesses in the validation tools they adopt. An appendix summarizes the evaluation of six democracy data sets from the perspective of alternative approaches to validation.

This chapter focuses on teaching the formation and analysis of concepts in research, emphasizing the importance of clarity in defining and measuring concepts. It presents a structured approach to conceptual thinking, outlining four steps: formulation, contextualization, operationalization, and measurement. Bussell highlights the role of examples and typologies to deepen understanding and discusses challenges in concept analysis, using “democracy” and “corruption” as primary examples. The chapter underscores the iterative process of concept development and its role in fostering rigorous academic research.

It is well past time to take scholarly disputes about words seriously, for where there’s smoke, there’s fire. Conceptual disagreement is a manifestation of disagreements about ideas. Yet no attempt has been made to measure the degree of conceptual disagreement that exists or to track those concepts identified as essentially contested. Accordingly, it is unclear how one might distinguish contested from uncontested concepts or test propositions about the causes of contestation. This chapter begins by introducing an approach to measuring conceptual contestation within social science. Next, the chapter explore factors that may help to explain variation in conceptual contestation. The characteristics of concepts – their value, abstraction, and normativity – explain most of the variability in conceptual contestation.