Discusses statistical methods, covering random variables and variates, sample and population, frequency distributions, moments and moment measures, probability and stochastic processes, discrete and continuous probability distributions, return periods and quantiles, probability density functions, parameter estimation, hypothesis testing, confidence intervals, covariance, regression and correlation analysis, time-series analysis.

This chapter covers ways to explore your network data using visual means and basic summary statistics, and how to apply statistical models to validate aspects of the data. Data analysis can generally be divided into two main approaches, exploratory and confirmatory. Exploratory data analysis (EDA) is a pillar of statistics and data mining and we can leverage existing techniques when working with networks. However, we can also use specialized techniques for network data and uncover insights that general-purpose EDA tools, which neglect the network nature of our data, may miss. Confirmatory analysis, on the other hand, grounds the researcher with specific, preexisting hypotheses or theories, and then seeks to understand whether the given data either support or refute the preexisting knowledge. Thus, complementing EDA, we can define statistical models for properties of the network, such as the degree distribution, or for the network structure itself. Fitting and analyzing these models then recapitulates effectively all of statistical inference, including hypothesis testing and Bayesian inference.

This chapter elaborates on the calibration and validation procedures for the model. First, we describe our calibration strategy in which a customised optimisation algorithm makes use of a multi-objective function, preventing the loss of indicator-specific error information. Second, we externally validate our model by replicating two well-known statistical patterns: (1) the skewed distribution of budgetary changes and (2) the negative relationship between development and corruption. Third, we internally validate the model by showing that public servants who receive more positive spillovers tend to be less efficient. Fourth, we analyse the statistical behaviour of the model through different tests: validity of synthetic counterfactuals, parameter recovery, overfitting, and time equivalence. Finally, we make a brief reference to the literature on estimating SDG networks.

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.

For this book, we assume you’ve had an introductory statistics or experimental design class already! This chapter is a mini refresher of some critical concepts we’ll be using and lets you check you understand them correctly. The topics include understanding predictor and response variables, the common probability distributions that biologists encounter in their data, the common techniques, particularly ordinary least squares (OLS) and maximum likelihood (ML), for fitting models to data and estimating effects, including their uncertainty. You should be familiar with confidence intervals and understand what hypothesis tests and P-values do and don’t mean. You should recognize that we use data to decide, but these decisions can be wrong, so you need to understand the risk of missing important effects and the risk of falsely claiming an effect. Decisions about what constitutes an “important” effect are central.

Abstract: In this chapter, I discuss an alternative perspective on interpreting the results of joint and constrained inversions of geophysical data. Typically such inversions are performed based on inductive reasoning (i.e. we fit a limited set of observations and conclude that the resulting model is representative of the Earth). While this has seen many successes, it is less useful when, for example, the specified relationship between different physical parameters is violated in parts of the inversion domain. I argue that in these cases a hypothesis testing perspective can help to learn more about the properties of the Earth. I present joint and constrained inversion examples that show how we can use violations of the assumptions specified in the inversion to study the subsurface. In particular I focus on the combination of gravity and magnetic data with seismic constraints in the western United States. There I see that high velocity structures in the crust are associated with relatively low density anomalies, a possible indication of the presence of melt in a strong rock matrix. The concepts, however, can be applied to other types of data and other regions and offer an extra dimension of analysis to interpret the results of geophysical inversion algorithms.

Finding one’s niche in any scientific domain is often challenging, but there are certain tips and steps that can foster a productive research program. In this chapter, we use terror management theory (TMT) as an exemplar of what designing a successful line of research entails. To this end, we present an overview of the development and execution of our research program, including testing of original hypotheses, direct and conceptual replications, identification of moderating and mediating variables, and how efforts to understand failures to replicate mortality salience effects led to important conceptual refinements of the theory. Our hope is that recounting the history of terror management theory and research will be useful for younger scholars in their own research pursuits in the social and behavioral sciences.

Writing the paper is one of the most challenging aspects of a project, and learning to write the report well is one of the most important skills to master for the success of the project and for sustaining a scholarly career. This chapter discusses challenges in writing and ways to overcome these challenges in the process of writing papers in the social and behavioral sciences. Two main principles emphasized are that writing is (a) a skill and (b) a form of communication. Skills are developed through instruction, modeling, and practice. In terms of communication, the research report can be conceived as a narrative that tells a story. Sections of the chapter focus on identifying common barriers to writing and ways to overcome them, developing a coherent and appropriate storyline, understanding the essential elements of a research paper, and valuing and incorporating feedback.

This chapter discusses the key elements involved when building a study. Planning empirical studies presupposes a decision about whether the major goal of the study is confirmatory (i.e., tests of hypotheses) or exploratory in nature (i.e., development of hypotheses or estimation of effects). Focusing on confirmatory studies, we discuss problems involved in obtaining an appropriate sample, controlling internal and external validity when designing the study, and selecting statistical hypotheses that mirror the substantive hypotheses of interest. Building a study additionally involves decisions about the to-be-employed statistical test strategy, the sample size required by this strategy to render the study informative, and the most efficient way to achieve this so that study costs are minimized without compromising the validity of inferences. Finally, we point to the many advantages of study preregistration before data collection begins.

From observed data, statistical inference infers the properties of the underlying probability distribution. For hypothesis testing, the t-test and some non-parametric alternatives are covered. Ways to infer confidence intervals and estimate goodness of fit are followed by the F-test (for test of variances) and the Mann-Kendall trend test. Bootstrap sampling and field significance are also covered.

Prior chapters relied on elementary statistical calculations and base R functions to analyze and visualize experimental results. This chapter builds on this foundation by showing how covariate adjustment using regression can be used to improve the precision with which treatment effects are estimated. Readers are shown how to apply regression to actual experimental data and to visualize multivariate regression results using R packages. This chapter also introduces the concepts of substantive and statistical “significance,” calling attention to the distinction between estimates of the average treatment effect that are large enough to be meaningful, even if they are not statistically distinguishable from zero. Examples of this distinction are provided using actual experimental data.

Hypothetical thinking involves imagining possibilities and mentally exploring their consequences. This chapter overviews a contemporary, integrative account of such thinking in the form of Jonathan Evans’s hypothetical thinking theory. This default-interventionist, dual–process theory operates according to three principles: relevance, singularity, and satisficing. To illustrate the explanatory strength of the theory a range of empirical evidence is considered that has arisen from extensive research on hypothesis testing, which involves individuals generating and evaluating hypotheses as they attempt to derive a more general understanding of information. The chapter shows how key findings from hypothesis-testing research undertaken in both laboratory and real-world studies (e.g. in domains such as scientific reasoning) are readily explained by the principles embedded in hypothetical thinking theory. The chapter additionally points to important new directions for future research on hypothetical thinking, including the need for: (1) further studies of real-world hypothesis testing in collaborative contexts, including ones outside of the domain of scientific reasoning; (2) increased neuroscientific analysis of the brain systems underpinning hypothetical thinking so as to inform theoretical developments; and (3) systematic individual-differences investigations to explore the likely association between people’s capacity to think creatively and their ability to engage in effective hypothetical thinking.

The appropriate method of data analysis depends upon a variety of factors that have been specified in the research question and as part of the research design. One key issue is whether the data are qualitative or quantitative, and this depends upon the underlying research approach. If the research approach is deductive, then most of the data are likely to be expressed as numbers and the key issue will be selecting the appropriate statistical techniques for describing and analysing the data. In this chapter, we will concentrate on techniques for describing quantitative data and for providing simple preliminary analyses.

The most commonly used technique for the analysis of quantitative data in business research is multiple regression analysis. This is a powerful technique for understanding the relationships between variables, which variables have the most impact, and for prediction. In this chapter, we consider how to specify regression models, how to estimate the models, and how to use the estimated models to undertake some simple hypothesis tests. We emphasize that the researcher has to exercise his/her judgement in deciding not only the specification of the initial model but also in how to adapt and interpret the model in response to the various statistical tests.

The most commonly used technique for the analysis of quantitative data in business research is multiple regression analysis. This is a powerful technique for understanding the relationships between variables, which variables have the most impact, and for prediction. In this chapter, we consider how to specify regression models, how to estimate the models, and how to use the estimated models to undertake some simple hypothesis tests. We emphasize that the researcher has to exercise his/her judgement in deciding not only the specification of the initial model but also in how to adapt and interpret the model in response to the various statistical tests.

The appropriate method of data analysis depends upon a variety of factors that have been specified in the research question and as part of the research design. One key issue is whether the data are qualitative or quantitative, and this depends upon the underlying research approach. If the research approach is deductive, then most of the data are likely to be expressed as numbers and the key issue will be selecting the appropriate statistical techniques for describing and analysing the data. In this chapter, we will concentrate on techniques for describing quantitative data and for providing simple preliminary analyses.