Data Analysis Using Regression and Multilevel/Hierarchical Models

Statistical graphics are sometimes summarized as “exploratory data analysis” or “presentation” or “data display.” But these only capture part of the story. Graphs are a way to communicate graphical and spatial information to ourselves and others. Long before worrying about how to convince others, you first have to understand what's happening yourself.

Why to graph

Going back through the dozens of examples in this book, what are our motivations for graphing data and fitted models? Ultimately, the goal is communication (to self or others). More immediately, graphs are comparisons (to zero, to other graphs, to horizontal lines, and so forth). We “read” a graph both by pulling out the expected (for example, the slope of a fitted regression line, the comparisons of a series of confidence intervals to zero and each other) and the unexpected.

In our experience, the unexpected is usually not an “outlier” or aberrant point but rather a systematic pattern in some part of the data. For example, consider the binned residual plots in Section 5.6 for the well-switching models. There was an unexpectedly low rate of switching from wells that were just barely over the dangerous level for arsenic, possibly suggesting that people were moderating their decisions when in this ambiguous zone, or that there was other information not included in the model that could explain these decisions.