Graphics, Statistical

Statistical graphics provide visual displays of quantitative information. While graphs have been an [Page 1044]important tool in the statistical sciences, their role and applications have evolved over time. In the past, graphical displays were generally employed for pedagogical purposes and to present the final results of an analysis. Currently, graphs are being incorporated more directly into data analysis itself, where they are used to provide insights and directions for further investigation. In this entry, the basic elements, major advantages, and recent developments of statistical graphics are presented.

Statistical graphs are used for several purposes. First, they provide a tool for exploring the contents of a data set; in effect, graphical displays enable researchers to interact directly with the “raw material” for their analyses. Second, graphs enable researchers to look for structure in their data; they provide a ready means to identify interesting features such as concentrations of observations at particular data values, covariance across variables, outliers in distributions, and so on. Third, graphical displays are useful for checking the assumptions of statistical models; for example, they can be used to examine distributional shapes of constituent variables or to search for systematic patterns among model residuals. Fourth, graphs remain an excellent vehicle for communicating the results of statistical analyses; they provide fairly intuitive representations of complex models that can be understood by broad audiences.

Of course, all of the preceding objectives could also be achieved through numerical methods, such as equations and tabular representations. But graphs have several advantages. For one thing, an enormous amount of information can be represented directly or summarized in a single well-constructed graph; therefore, graphical displays are useful for depicting large, complex data sets. At the same time, graphs are not as reliant on underlying assumptions as are numerical summaries of data such as descriptive statistics or model coefficients. And graphs almost inherently encourage greater interaction between the researcher and the data; interesting features stand out immediately and graphs provide the means to pursue them to gain further insights.