Fan chart (statistics)

A dispersion fan diagram (left) in comparison with a box plot

A fan chart is made of a group of dispersion fan diagrams, which may be positioned according to two categorising dimensions. A dispersion fan diagram is a circular diagram which reports the same information about a dispersion as a box plot: namely median, quartiles, and two extreme values.

Elements

The elements of a dispersion fan diagram^[1] are:

a circular line as scale
a diameter which indicates the median
a fan (a segment of a circle) which indicates the quartiles
two feathers which indicate the extreme values.

The scale on the circular line begins at the left with the starting value (e. g. with zero). The following values are applicated clockwise. The white tail of diameter indicates the median. The dark fan indicates the dispersion of the middle half of the observed values; thus it encompasses the values from the first to the third quartile. The white feathers indicate the dispersion of the middle 90% of the observed values.

The length of the white part of the diameter corresponds with the number of observations.

Application

A fan chart gives a quick summary of observed values which depend from two variables. This is possible thanks of a dense representation and a constant size which does not depend on the size of the single dispersion fan diagrams.

An essential advantage compared to a sequence of box plots is the possibility to compare dispersion fan diagrams not only within one direction but within two directions (horizontally and vertically).

Example

The following example presents data from the data set MathAchieve which is part of the R package nlme of José Pinheiro et al.^[2] It contains mathematics achievement scores of 7185 students. The students are categorised according to sex and membership of a minority ethnic group.

The graphics show the mathematics achievement scores in dependency on the socio-economic status of the students (x axis) and on the average socio-economic status of all students at the same school (y axis). The four graphic panels differentiate the students according to sex and membership of a minority ethnic group.

The fan charts reveals clearly how the median value is partially following a big main tendency while the values of the single subgroups (with the cells) scatter largely what could lead to doubts about a possible correlation.

References

↑ Fischer, Wolfram (2010). Neue Grafiken zur Datenvisualisierung. Band 1. Speichengrafiken, Streuungsfächerkarten, Differenz-, Sequenz- und Wechseldiagramme [New Graphics For Data Visualisation. Volume 1. Spoke Plots, Fan Charts, Difference, Sequence and Change Diagrams]. Wolfertswil: ZIM. ISBN 978-3-905764-06-2.
↑ Pinheiro, José; Bates, Douglas; et al. (2013) [1999]. "nlme: Linear and Nonlinear Mixed Effects Models". CRAN (The Comprehensive R Archive Network).

External links

Fischer, Wolfram (2012): Streuungsfächerkarten und pseudogeografische Anordnungen. Mit Beispielen zum verfügbaren Einkommen und zu Krankenkassenprämien in der Schweiz. Swiss Days of Official Statistics, Vaduz LI, 2012.
Fischer, Wolfram (2010): Visualising Twofold Dependencies by Fan Charts. ZIM.

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

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