Wilkinson The Grammar of Graphics
2. Auflage 2005
ISBN: 978-0-387-28695-2
Verlag: Springer US
Format: PDF
Kopierschutz: 1 - PDF Watermark
E-Book, Englisch, 693 Seiten, eBook
Reihe: Statistics and Computing
ISBN: 978-0-387-28695-2
Verlag: Springer US
Format: PDF
Kopierschutz: 1 - PDF Watermark
Preface to First Edition Before writing the graphics for SYSTAT in the 1980’s, I began by teaching a seminar in statistical graphics and collecting as many different quantitative graphics as I could find. I was determined to produce a package that could draw every statistical graphic I had ever seen. The structure of the program was a collection of procedures named after the basic graph types they p- duced. The graphics code was roughly one and a half megabytes in size. In the early 1990’s, I redesigned the SYSTAT graphics package using - ject-based technology. I intended to produce a more comprehensive and - namic package. I accomplished this by embedding graphical elements in a tree structure. Rendering graphics was done by walking the tree and editing worked by adding and deleting nodes. The code size fell to under a megabyte. In the late 1990’s, I collaborated with Dan Rope at the Bureau of Labor Statistics and Dan Carr at George Mason University to produce a graphics p- duction library called GPL, this time in Java. Our goal was to develop graphics components. This book was nourished by that project. So far, the GPL code size is under half a megabyte.
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7 Statistics (p.111-112)
Statistics state the status of the state. All these s words derive from the Greek statis and Latin status, or standing. Standing (for humans) is a state of being, a condition that represents literally or figuratively the active status of an individual, group, or state. Modern statistics as a discipline arose in the early 18th century, when collection of data about the state was recognized as essential to serving the needs of its constituents. This Enlightenment perspective gave rise not only to the modern social sciences, but also to mathematical methods for analyzing data measured with error (Stigler, 1983).
In a graphical system, statistics are methods that alter the position of geometric graphs. We are accustomed to think of a chart as a display of a statistic or a statistical function (e.g., a bar chart of budget expenditures). As such, it would seem that we should begin by aggregating data, computing statistics, and drawing a chart. This would be wrong, however. By putting statistics under control of graphing functions, rather than whole charts under the control of statistics, we accomplish several things. First, we can represent more than one statistic in a frame. One graphic can represent a mean and another a median, in the same frame. Second, making statistics into graphing methods forces them to be views or summaries of the raw data rather than data themselves. In other words, the casewise data and a graphic are inextricably bound because we never break the connection between the variables and the graphics that represent them.
This allows us to drill-down, brush, and investigate values with other dynamic tools. This functions would be lost if we pre-aggregated the data. Finally, by putting statistics under the control of graphing functions, we can modularize and localize computations in a distributed system. Adding graphics to a frame is easy when we do not have to worry about the structure of the data and how aggregations were computed. We will return to this issue in Section 7.3 at the end of this chapter.
The simplest graphing method is the one students first learn for plotting algebraic functions: for every x, compute f(x) so that one may draw a graph based on the tuples of the form (x, f(x)) that comprise the graph. Students learn to construct a list of these tuples (a finite subset of the graph of the function) in order to plot selected points in Cartesian coordinates. In the functional no tation of this book, students usually draw graphs of algebraic functions using the graphing function line(position(f()).
While students learn graphing methods for polynomial and other simple algebraic functions, most charts are based on statistical functions of observed values of one or more variables. In our notation, examples of statistical graphs are produced by the functions
point(position(summary.mean())) and
line(position(smooth.linear())),
which implement the statistical graphing functions summary.mean() and smooth.linear(), respectively. Statistical functions can be complicated, but their output looks the same to their geometric clients as the output of algebraic functions. A line does not care who produced the points it needs to plot itself.
