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The Grammar of Graphics

:	Leland Wilkinson
:	The Grammar of Graphics
:	Springer-Verlag
:	9780387286952
:	2
:	CHF 145.80
:

:	Wahrscheinlichkeitstheorie, Stochastik, Mathematische Statistik
:	English

:	693
:	Wasserzeichen/DRM
:	PC/MAC/eReader/Tablet
:	PDF

resents a unique foundation for producing almost every quantitative graphic found in scientific journals, newspapers, statistical packages, and data visualization systems

The new edition features six new chapters and has undergone substantial revision.

The first edition has sold more than 2200 copies.

Four color throughout.

7 Statistics(p.111-112)

Statistics state the status of the state. All these s words derive from the Greek statis and Latinstatus, 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.

	Preface	7
	Contents	13
	1 Introduction	17
	1.1 Graphics Versus Charts	18
	1.2 Object-Oriented Design	19
	1.2.1 What is OOD?	19
	1.2.2 What is not OOD?	20
	1.2.3 Why OOD?	21
	1.3 An Object-Oriented Graphics System	22
	1.3.1 Specification	22
	1.3.2 Assembly	23
	1.3.3 Display	23
	1.4 An Example	24
	1.4.1 Specification	25
	1.4.2 Assembly	25
	1.4.3 Display	26
	1.4.4 Revision	27
	1.5 What This Book Is Not	29
	1.5.1 Not a Command Language	29
	1.5.2 Not a Taxonomy	30
	1.5.3 Not a Drafting Package	30
	1.5.4 Not a Book of Virtues	31
	1.5.5 Not a Heuristic System	32
	1.5.6 Not a Geographic Information System	33
	1.5.7 Not a Visualization System	33
	1.6 Background	34
	1.7 Sequel	34
	Part I	37
	2 How To Make a Pie	39
	2.1 Definitions	41
	2.1.1 Sets	41
	2.1.2 Relations	43
	2.1.3 Functions	43
	2.1.4 Graphs	44
	2.1.5 Compositions	44
	2.1.6 Transformations	45
	2.1.7 Algebras	45
	2.1.8 Variables	45
	2.1.9 Varsets	46
	2.1.10 Frames	46
	2.2 Recipe	47
	2.2.1 Create Variables	47
	2.2.2 Apply Algebra	48
	2.2.3 Apply Scales	49
	2.2.4 Compute Statistics	50
	2.2.5 Construct Geometry	50
	2.2.6 Apply Coordinates	51
	2.2.7 Compute Aesthetics	52
	2.3 Notation	54
	2.3.1 Specifications	54
	2.3.2 Functions	56
	2.4 Sequel	56
	3 Data	57
	3.1 Data Functions	58
	3.2 Empirical Data	60
	3.2.1 Reshaping Data	61
	3.2.2 Bootstrapping	63
	3.3 Abstract Data	64
	3.3.1 Time Series	64
	3.3.2 Counts	65
	3.4 Metadata	67
	3.5 Data Mining	67
	3.5.1 MOLAP	68
	3.5.2 ROLAP	69
	3.5.3 Visual Query of Databases	70
	3.6 Sequel	70
	4 Variables	71
	4.1 Transforms	72
	4.2 Examples	73
	4.2.1 Sorting	73
	4.2.2 Probability Plots	74
	4.2.3 Aggregating Variables	75
	4.2.4 Regression Residuals	76
	4.3 Sequel	77
	5 Algebra	79
	5.1 Syntax	79
	5.1.1 Symbols	79
	5.1.2 Operators	79
	5.1.3 Rules	84
	5.2 Examples	89
	5.2.1 Cross	89
	5.2.2 Nest	91
	5.2.3 Blend	92
	5.3 Other Algebras	96
	5.3.1 Design Algebra	96
	5.3.2 Relational Algebra	96
	5.3.3 Functional Algebra	98
	5.3.4 Table Algebra	99
	5.3.5 Query Algebra	99
	5.3.6 Display Algebra	99
	5.4 Sequel	99
	6 Scales	101
	6.1 Scaling Theory	101
	6.1.1 Axiomatic Measurement	101
	6.1.2 Unit Measurement	102
	6.1.3 Applied Scaling	105