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.

Statistical inference can be formulated as a set of operations on data that yield estimates and uncertainty statements about predictions and parameters of some underlying process or population. From a mathematical standpoint, these probabilistic uncertainty statements are derived based on some assumed probability model for observed data. In this chapter, we sketch the basics of probability modeling, estimation, bias and variance, and the interpretation of statistical inferences and statistical errors in applied work. We introduce the theme of uncertainty in statistical inference and discuss how it is a mistake to use hypothesis tests or statistical significance to attribute certainty from noisy data.

Chapter 7 focuses on fractures in rock by describing outcrops of joints, veins, and dikes, introducing a canonical model for opening fractures, and considering fracture initiation and propagation using linear elastic fracture mechanics. The outcrop descriptions serve to highlight the characteristic geometric features of these structures, and provides the background necessary to build a conceptual model for opening fractures in rock. The canonical fracture model is based on a pure opening fracture in an elastic rock mass. With attention focused on the fracture tips, we explore the stress concentration there that leads to fracture propagation, and identify the three modes of fracture tip deformation. We explain how fractures initiate at flaws in rock and propagate when the stress intensity in the near-tip region reaches a critical value called the fracture toughness. Although many opening fractures are approximately planar, we describe how minor amounts of shearing can alter the propagation path and lead to kinked or echelon fractures. These interesting geometries provide evidence for interpreting the state of stress at the time the fractures formed.

You’ve come a long way since Chapter 1. You’ve learned about the different purposes and types of evaluation, how to assess needs, how to survey clients and program staff, how to measure program outcomes, the logic and utility of feasible outcome designs, how to strengthen the causal logic of feasible outcome designs, how to conduct and interpret single-case outcome designs, practical and political pitfalls in outcome evaluations, how to analyze and present data from formative and process evaluations and from outcome evaluations, and how to write an evaluation report in a manner that will improve its chances of being read and utilized. This epilogue will examine things that you can do throughout the evaluation process to increase the chances that your report and evaluation will be successful. Some of the tips were mentioned in previous chapters, but warrant repeating because of their importance. Other tips will be new.

This introductory chapter lays out the key challenges of statistical inference in general and regression modeling in particular. We present a series of applied examples to show how complex and subtle regression can be, and why a book-length treatment is needed, not just on the mathematics of regression modeling but on how to apply and understand these methods.