Statistical graphics

Data visualization
Part of a series on Statistics

Major dimensions Exploratory data analysis • Information design Interactive data visualization Descriptive statistics • Inferential statistics Statistical graphics • Plot Data analysis • Infographic Data science
Thought leaders John W. Tukey • Edward Tufte • Hadley Wickham • Drew Conway
Information graphic types Line chart • Bar chart Histogram • Scatterplot Boxplot • Pareto chart Pie chart • Area chart Control chart • Run chart Stem-and-leaf display • Cartogram Small multiple • Sparkline Table
Related Topics Data • Information Big data • Database Chartjunk • Visual perception Regression analysis • Statistical model Misleading graph

Statistical graphics, also known as graphical techniques, are graphics in the field of statistics used to visualize quantitative data.

Overview

Whereas statistics and data analysis procedures generally yield their output in numeric or tabular form, graphical techniques allow such results to be displayed in some sort of pictorial form. They include plots such as scatter plots, histograms, probability plots, spaghetti plots, residual plots, box plots, block plots and biplots.^[1]

Exploratory data analysis (EDA) relies heavily on such techniques. They can also provide insight into a data set to help with testing assumptions, model selection and regression model validation, estimator selection, relationship identification, factor effect determination, and outlier detection. In addition, the choice of appropriate statistical graphics can provide a convincing means of communicating the underlying message that is present in the data to others.^[1]

Graphical statistical methods have four objectives:^[2]

The exploration of the content of a data set
The use to find structure in data
Checking assumptions in statistical models
Communicate the results of an analysis.

If one is not using statistical graphics, then one is forfeiting insight into one or more aspects of the underlying structure of the data.

History

Statistical graphics have been central to the development of science and date to the earliest attempts to analyse data. Many familiar forms, including bivariate plots, statistical maps, bar charts, and coordinate paper were used in the 18th century. Statistical graphics developed through attention to four problems:^[3]

Spatial organization in the 17th and 18th century
Discrete comparison in the 18th and early 19th century
Continuous distribution in the 19th century and
Multivariate distribution and correlation in the late 19th and 20th century.

Since the 1970s statistical graphics have been re-emerging as an important analytic tool with the revitalisation of computer graphics and related technologies.^[3]

Examples

William Playfair's trade-balance time-series chart, published in his Commercial and Political Atlas, 1786

John Snow's Cholera map in dot style, 1854.

Famous graphics were designed by:

William Playfair who produced what could be called the first line, bar, pie, and area charts. For example, in 1786 he published the well known diagram that depicts the evolution of England's imports and exports,^[4]
Florence Nightingale, who used statistical graphics to persuade the British Government to improve army hygiene,^[5]
John Snow who plotted deaths from cholera in London in 1854 to detect the source of the disease,^[6] and
Charles Joseph Minard who designed a large portfolio of maps of which the one depicting Napoleon's campaign in Russia is the best known.^[7]

See the plots page for many more examples of statistical graphics.

References

1 2 The Role of Graphics in: NIST/SEMATECH e-Handbook of Statistical Methods, 2003-2010. Accessed May 5, 2011.
↑ William G. Jacoby (1997). Statistical Graphics for Univariate and Bivariate Data: Statistical Graphics pp.2–4
1 2 James R. Beniger and Dorothy L. Robyn (1978). "Quantitative graphics in statistics: A brief history". In: The American Statistician. 32: pp. 1–11.
↑ Tufte, Edward (1983). The Visual Display of Quantitative Information. Cheshire, Connecticut: Graphics Press. ISBN 0961392142.
↑ Small, Hugh. "Florence Nightingale's statistical diagrams".
↑ Crosier, Scott. "John Snow: The London Cholera Epidemic of 1854". University of California, Santa Barbara.
↑ Corbett, John. "Charles Joseph Minard: Mapping Napoleon's March, 1861". Center for Spatially Integrated Social Science. Retrieved 21 September 2014.

Attribution

This article incorporates public domain material from the National Institute of Standards and Technology website http://www.nist.gov.

External links

Wikimedia Commons has media related to Statistical charts.

Statistics

Descriptive statistics

Continuous data

Center	Mean arithmetic geometric harmonic Median Mode

Dispersion	Variance Standard deviation Coefficient of variation Percentile Range Interquartile range

Shape	Moments Skewness Kurtosis L-moments

Count data

Index of dispersion

Summary tables

Dependence

Graphics

Data collection

Study design	Population Statistic Effect size Statistical power Sample size determination Missing data

Survey methodology	Sampling Standard error stratified cluster Opinion poll Questionnaire

Controlled experiments	Design control optimal Controlled trial Randomized Random assignment Replication Blocking Interaction Factorial experiment

Uncontrolled studies	Observational study Natural experiment Quasi-experiment

Statistical inference

Statistical theory

Frequentist inference

Point estimation	Estimating equations Maximum likelihood Method of moments M-estimator Minimum distance Unbiased estimators Mean-unbiased minimum-variance Rao–Blackwellization Lehmann–Scheffé theorem Median unbiased Plug-in

Interval estimation	Confidence interval Pivot Likelihood interval Prediction interval Tolerance interval Resampling Bootstrap Jackknife

Testing hypotheses	1- & 2-tails Power Uniformly most powerful test Permutation test Randomization test Multiple comparisons

Parametric tests	Likelihood-ratio Wald Score

Specific tests

Z (normal) Student's t-test F

Goodness of fit	Chi-squared Kolmogorov–Smirnov Anderson–Darling Normality (Shapiro–Wilk) Likelihood-ratio test Model selection Cross validation AIC BIC

Rank statistics	Sign Sample median Signed rank (Wilcoxon) Hodges–Lehmann estimator Rank sum (Mann–Whitney) Nonparametric anova 1-way (Kruskal–Wallis) 2-way (Friedman) Ordered alternative (Jonckheere–Terpstra)

Bayesian inference

Correlation	Pearson product–moment Partial correlation Confounding variable Coefficient of determination

Regression analysis	Errors and residuals Regression model validation Mixed effects models Simultaneous equations models Multivariate adaptive regression splines (MARS)

Linear regression	Simple linear regression Ordinary least squares General linear model Bayesian regression

Non-standard predictors	Nonlinear regression Nonparametric Semiparametric Isotonic Robust Heteroscedasticity Homoscedasticity

Generalized linear model	Exponential families Logistic (Bernoulli) / Binomial / Poisson regressions

Partition of variance	Analysis of variance (ANOVA, anova) Analysis of covariance Multivariate ANOVA Degrees of freedom

Categorical / Multivariate / Time-series / Survival analysis

Categorical

Multivariate

Time-series

General	Decomposition Trend Stationarity Seasonal adjustment Exponential smoothing Cointegration Structural break Granger causality

Specific tests	Dickey–Fuller Johansen Q-statistic (Ljung–Box) Durbin–Watson Breusch–Godfrey

Time domain	Autocorrelation (ACF) partial (PACF) Cross-correlation (XCF) ARMA model ARIMA model (Box–Jenkins) Autoregressive conditional heteroskedasticity (ARCH) Vector autoregression (VAR)

Frequency domain	Spectral density estimation Fourier analysis Wavelet

Survival

Survival function	Kaplan–Meier estimator (product limit) Proportional hazards models Accelerated failure time (AFT) model First hitting time

Hazard function	Nelson–Aalen estimator

Test	Log-rank test

Applications

Biostatistics	Bioinformatics Clinical trials / studies Epidemiology Medical statistics

Engineering statistics	Chemometrics Methods engineering Probabilistic design Process / quality control Reliability System identification

Social statistics	Actuarial science Census Crime statistics Demography Econometrics National accounts Official statistics Population statistics Psychometrics

Spatial statistics	Cartography Environmental statistics Geographic information system Geostatistics Kriging

Category
Portal
Commons
WikiProject

Visualization of technical information

Fields	Biological data visualization Chemical imaging Crime mapping Data visualization Educational visualization Flow visualization Geovisualization Information visualization Mathematical visualization Medical imaging Molecular graphics Product visualization Scientific visualization Software visualization Technical drawing User interface design Visual culture Volume visualization

Image types	Chart Diagram Engineering drawing Graph of a function Ideogram Map Photograph Pictogram Plot Schematic Statistical graphics Table Technical drawings Technical illustration User interface

People	Jacques Bertin Stuart Card Thomas A. DeFanti Michael Friendly George Furnas Nigel Holmes Alan MacEachren Jock D. Mackinlay Michael Maltz Bruce H. McCormick Charles Joseph Minard Gaspard Monge Otto Neurath Florence Nightingale Clifford A. Pickover William Playfair Adolphe Quetelet George G. Robertson Arthur H. Robinson Lawrence J. Rosenblum Ben Shneiderman Edward Tufte Fernanda Viégas Howard Wainer

Related topics	Cartography Chartjunk Computer graphics in computer science Graph drawing Graphic design Graphic organizer Imaging science Information graphics Information science Mental visualisation Misleading graph Neuroimaging Patent drawing Scientific modelling Spatial analysis Visual analytics Visual perception Volume cartography

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