The normal (Gaussian) distribution plays an essential role in statistical theory and is often referred to in applied statistical analysis, unfortunately sometimes in an inappropriate manner. We first describe the properties of this distribution and its two parameters (mean and variance), paying particular attention to the standardized normal distribution. We then discuss deviations of observed distributions from the normal distribution, measured by their skewness and kurtosis. Another important part of this chapter is the description of specialised graphs and of the tests allowing us to check whether a set of values is likely to originate from a normal distribution. But we generally discourage the reader from performing statistical tests when checking for normality of observed distributions. The methods described in this chapter are accompanied by a carefully-explained guide to the R code needed for their use.

We start by focusing on the important assumption of additivity for the effects of predictors in ANOVA models. Using a practical example, we show how the predictors used to explain response variables in biology oftentimes operate on a multiplicative scale, and thus stress the need to take this into account when choosing an appropriate data transformation. We introduce three important monotonic transformations, namely the log transformation, arcsine transformation, and square-root transformation. We thoroughly discuss the advantages and possible dangers of individual transformation types. The methods described in this chapter are accompanied by a carefully-explained guide to the R code needed for their use.

In this chapter, we discuss the general finite element analysis procedure for 2-D and 3-D linear scalar field problems. A scalar field problem is a problem whose primary unknown physical quantity is a scalar at any spatial location in the computational domain. We demonstrate the finite element analysis procedure by solving 2-D and 3-D steady state heat transfer problems. The steady state heat transfer problems are solved step by step in the same fashion as solving 1-D problems. Strong and weak forms of the governing equations are derived from the law of energy conservation and the method of weighted residuals. 2-D and 3-D finite element approximations and elements are described in detail. Numerical integration over multi-dimensional elements is also described in detail. Convergence considerations are discussed. MATLAB codes for solving these problems are presented.

This chapter explains the meaning of finite element analysis (FEA) and why it is a popular computational method for engineering analysis. By using a structural analysis of a thin plate as an example, the procedure of a typical FEA is illustrated. The history of the development of the method, its applications, and software commercialization are introduced briefly, followed by a description of some of the trends in the current development of the method. The chapter also provides a list of commercial and open-source FEA codes that are popular today.

Chapter 9 reviews fold terminology, describes fold profiles at outcrop scales, uses differential geometry to quantify folds in three dimensions at crustal scales, and builds canonical models for folding due to bending and buckling. For two-dimensional profiles of folds in sedimentary, metamorphic, and igneous rocks, we introduce the concept of curvature to characterize fold shapes. Then we describe the crustal-scale fold at Sheep Mountain, WY, and use a modern technology called Airborne Laser Swath Mapping (ALSM) to map the fold geometry in three dimensions. We employ differential geometry to characterize a three-dimensional bedding surface in this fold in terms of the principal curvatures at every point. The fundamental shapes at a given point on such a surface can be planar, elliptic, parabolic, or hyperbolic. These distinct shapes are used to define a classification scheme for folded geological surfaces based on curvature.

Chapter 3 ended with a discussion of the community survey approach to needs assessment. If you have taken a course on research methods, you probably learned that a survey is a way to collect data that most commonly involves attempting to describe the characteristics of a population on the basis of responses from a sample of people from that population to a series of written or oral questions about their characteristics and views. When surveying needs, those views typically pertain to how people feel about what they need or what their community needs. Surveys also can be used to assess views regarding how satisfied clients feel about the services an agency provides or does not provide, but should provide. Early in your career you may well be involved in planning or carrying out such surveys.

Now that you’ve learned the ins and outs of designing and conducting an evaluation, here comes what might be for you the hard part: communicating your work in such a way as to have an impact on your target audience. Just how hard will depend on how well you have comprehended the previous chapters of this book and whether you have successfully completed courses in which you had to write and then receive critical appraisals of your writing. If you did complete such courses, you probably learned that good writing does not come easy. Often the thing you write seems perfectly clear to you, because you know what you are thinking and trying to say, and you understand your topic. But your readers might not share your expertise, and they can’t read your mind. Consequently, if you are receiving feedback on your drafts, you might have to go through several revisions before the feedback reassures you that your writing is clear, understandable, and interesting to read.

In Chapters 18 and 19, we introduced a statistical formalization of causal effects using potential outcomes, focusing on the estimation of average causal effects and interactions using data from controlled experiments. In practice, logistic, ethical, or financial constraints can make it difficult or impossible to externally assign treatments, and simple estimates of the treatment effect based on differences or regressions can be biased when selection into treatment and control group is not random. To estimate effects when there is imbalance and lack of overlap between treatment and control groups, you should include as regression predictors all the confounders that explain this selection. The present chapter discusses methods for causal inference in the presence of systematic pre-treatment differences between treatment and control groups. A key difficulty is that there can be many pre-treatment variables with mismatch, hence the need for adjustment on many variables.

No matter how rigorous and sophisticated an outcome evaluation design might be, various political and practical agency factors can interfere with its successful completion. This chapter will discuss those factors and what can be done to try to enhance the likelihood of successful completion of an evaluation and utilization of its findings and recommendations. To be a successful evaluator, you will need to be able to anticipate how practical realities in service-oriented settings can pose barriers to particular evaluation designs and data collection methods and how vested interests in the results of an outcome evaluation can affect compliance with an evaluation protocol and utilization of the report and recommendations of an evaluation.