Part 3. Intermediate methods
While part 2 covered basic graphical and statistical methods, section 3 offers coverage of intermediate methods. We move from describing the relationship between two variables, to modeling the relationship between a numerical outcome variable and a set of numeric and/or categorical predictor variables.
Chapter 8 introduces regression methods for modeling the relationship between a numeric outcome variable and a set of one or more predictor variables. Modeling data is typically a complex, multistep, interactive process. Chapter 8 provides step-by-step coverage of the methods available for fitting linear models, evaluating their appropriateness, and interpreting their meaning.
Chapter 9 considers the analysis of basic experimental and quasi-experimental designs through the analysis of variance and its variants. Here we’re interested in how treatment combinations or conditions affect a numerical outcome variable. The chapter introduces the functions in R that are used to perform an analysis of variance, analysis of covariance, repeated measures analysis of variance, multi-factor analysis of variance, and multivariate analysis of variance. Methods for assessing the appropriateness of these analyses, and visualizing the results are also discussed.
In designing experimental and quasi-experimental studies, it’s important to determine if the sample size is adequate for detecting the effects of interest (power analysis). Otherwise, why conduct the study? A detailed treatment of power analysis is provided in chapter 10. Starting with a discussion of hypothesis testing, the presentation focuses on how to use R functions to determine the sample size necessary to detect a treatment effect of a given size with a given degree of confidence. This can help you to plan studies that are likely to yield useful results.
Chapter 11 expands on the material in chapter 5 by covering the creation of graphs that help you to visualize relationships among two or more variables. This includes the various types of two- and three-dimensional scatter plots, scatter plot matrices, line plots, and bubble plots. It also introduces the useful, but less well-known, correlograms and mosaic plots.
The linear models described in chapters 8 and 9 assume that the outcome or response variable is not only numeric, but also randomly sampled from a normal distribution. There are situations where this distributional assumption is untenable. Chapter 12 presents analytic methods that work well in cases where data are sampled from unknown or mixed distributions, where sample sizes are small, where outliers are a problem, or where devising an appropriate test based on a theoretical distribution is mathematically intractable. They include both resampling and bootstrapping approaches—computer intensive methods that are powerfully implemented in R. The methods described in this chapter will allow you to devise hypothesis tests for data that do not fit traditional parametric assumptions.
After completing part 3, you’ll have the tools to analyze most common data analytic problems encountered in practice. And you will be able to create some gorgeous graphs!