I first review and critique the prevailing use of hypothesis tests to compare treatments. I then describe my application of statistical decision theory. I compare Bayes, maximin, and minimax regret decisions. I consider choice of sample size in randomized trials from the minimax regret perspective.

In Chapter 31 we study three commonly used techniques for proving minimax lower bounds, namely, Le Cam’s method, Assouad’s lemma, and Fano’s method. Compared to the results in Chapter 29, which are geared toward large-sample asymptotics in smooth parametric models, the approach here is more generic, less tied to mean-squared error, and applicable in non-asymptotic settings such as nonparametric or high-dimensional problems. The common rationale of all three methods is reducing statistical estimation to hypothesis testing.

Chapter 6 introduces the hypothesis-testing process and relevance of standard error in reaching statistical conclusions about whether to accept or reject the null hypothesis using the z-test statistic. Type I and Type II errors, along with the types of statistical tests researchers apply in testing hypotheses, are presented; these include one-tailed (directional) versus two-tailed (nondirectional) tests. Three important decision rules are the sampling distribution of means, the level of significance, and critical regions. Type I and Type II errors influence the decisions we make about our predictions of relationships between variables. Statistical decision-making is never error-free, but we have some control in reducing these types of errors.

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.