Scagnostics

Scatterplot diagnostics measures

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Scatterplot matrix of the scagnostics measures for the 91 scatterplots of the variables of the Boston Housing data set

Scagnostics (scatterplot diagnostics) is a series of measures that characterize certain properties of a point cloud in a scatter plot. The term and idea was coined by John Tukey and Paul Tukey, though they didn't publish it; later it was elaborated by Wilkinson, Anand, and Grossman. The following nine dimensions are considered:^[1]^[2]

For the outliers in the data:
1. outlying
For the density of data points:
1. skewed
2. clumpy
3. sparse
4. striated
For the shape of the point cloud:
1. convex
2. skinny
3. stringy
For trends in the data:
1. monotony

References

^ Wilkinson, Leland (23 April 2008). "Scagnostics". Retrieved 25 March 2022. {{cite journal}}: Cite journal requires |journal= (help)
^ Wilkinson, Leland; Anand, Anushka; Grossman, Robert (2005). "Graph-theoretic scagnostics". In Proc. 2005 IEEE Symp. On Information Visualization (INFOVIS: 157–164. CiteSeerX 10.1.1.329.1315.

External links

Python library pyscagnostics
R package scagnostics

Statistics

Outline
Index

Descriptive statistics

Continuous data

Center	Mean Arithmetic Arithmetic-Geometric Cubic Generalized/power Geometric Harmonic Heronian Heinz Lehmer Median Mode
Dispersion	Average absolute deviation Coefficient of variation Interquartile range Percentile Range Standard deviation Variance
Shape	Central limit theorem Moments Kurtosis L-moments Skewness

Count data

Index of dispersion

Summary tables

Dependence

Graphics

Data collection

Study design	Effect size Missing data Optimal design Population Replication Sample size determination Statistic Statistical power
Survey methodology	Sampling Cluster Stratified Opinion poll Questionnaire Standard error
Controlled experiments	Blocking Factorial experiment Interaction Random assignment Randomized controlled trial Randomized experiment Scientific control
Adaptive designs	Adaptive clinical trial Stochastic approximation Up-and-down designs
Observational studies	Cohort study Cross-sectional study Natural experiment Quasi-experiment

Statistical inference

Statistical theory

Population
Statistic
Probability distribution
Sampling distribution
- Order statistic
Empirical distribution
- Density estimation
Statistical model
- Model specification
- L^p space
Parameter
- location
- scale
- shape
Parametric family
- Likelihood (monotone)
- Location–scale family
- Exponential family
Completeness
Sufficiency
Statistical functional
- Bootstrap
- U
- V
Optimal decision
- loss function
Efficiency
Statistical distance
- divergence
Asymptotics
Robustness

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 Score/Lagrange multiplier Wald

Specific tests

Z-test (normal) Student's t-test F-test
Goodness of fit	Chi-squared G-test Kolmogorov–Smirnov Anderson–Darling Lilliefors Jarque–Bera 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) Van der Waerden test

Bayesian inference

Correlation	Pearson product-moment Partial correlation Confounding variable Coefficient of determination
Regression analysis	Errors and residuals Regression 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 Least-squares spectral analysis Wavelet Whittle likelihood

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 Jurimetrics National accounts Official statistics Population statistics Psychometrics
Spatial statistics	Cartography Environmental statistics Geographic information system Geostatistics Kriging