Leland Wilkinson

The History of the Cluster Heat Map

The cluster heat map is an ingenious display that simultaneously reveals row and column hierarchical cluster structure in a data matrix. It consists of a rectangular tiling, with each tile shaded on a color scale to represent the value of the corresponding element of the data matrix. The rows (columns) of the tiling are ordered such that similar rows (columns) are near each other. On the vertical and horizontal margins of the tiling are hierarchical cluster trees. This cluster heat map is a synthesis of several different graphic displays developed by statisticians over more than a century. We locate the earliest sources of this display in late 19th century publications, and trace a diverse 20th century statistical literature that provided a foundation for this most widely used of all bioinformatics displays.

Nominal, Ordinal, Interval, and Ratio Typologies are Misleading

Abstract The psychophysicist S.S. Stevens developed a measurement scale typology that has dominated social statistics methodology for almost 50 years. During this period, it has generated considerable controversy among statisticians. Recently, there has been a renaissance in the use of Stevenss scale typology for guiding the design of statistical computer packages. The current use of Stevenss terminology fails to deal with the classical criticisms at the time it was proposed and ignores important developments in data analysis over the last several decades.

Graph-theoretic scagnostics

We introduce Tukey and Tukey scagnostics and develop graph-theoretic methods for implementing their procedure on large datasets.

An Analytic Approximation to the Distribution of Lilliefors's Test Statistic for Normality

Abstract Table 1 corrects the critical values for testing normality reported by Lilliefors (1967). The corrected table allows us to derive a simple analytic approximation to the upper tail probabilities of his test statistic for probabilities less than .10. With few exceptions, the approximation is more accurate than Lillieforss original table.

Exact and Approximate Area-Proportional Circular Venn and Euler Diagrams

Scientists conducting microarray and other experiments use circular Venn and Euler diagrams to analyze and illustrate their results. As one solution to this problem, this paper introduces a statistical model for fitting area-proportional Venn and Euler diagrams to observed data. The statistical model outlined in this paper includes a statistical loss function and a minimization procedure that enables formal estimation of the Venn/Euler area-proportional model for the first time. A significance test of the null hypothesis is computed for the solution. Residuals from the model are available for inspection. As a result, this algorithm can be used for both exploration and inference on real data sets. A Java program implementing this algorithm is available under the Mozilla Public License. An R function venneuler () is available as a package in CRAN and a plugin is available in Cytoscape.

High-Dimensional Visual Analytics: Interactive Exploration Guided by Pairwise Views of Point Distributions

We introduce a method for organizing multivariate displays and for guiding interactive exploration through high-dimensional data. The method is based on nine characterizations of the 2D distributions of orthogonal pairwise projections on a set of points in multidimensional Euclidean space. These characterizations include such measures as density, skewness, shape, outliers, and texture. Statistical analysis of these measures leads to ways for 1) organizing 2D scatterplots of points for coherent viewing, 2) locating unusual (outlying) marginal 2D distributions of points for anomaly detection and 3) sorting multivariate displays based on high-dimensional data, such as trees, parallel coordinates, and glyphs

Tests of Significance in Forward Selection Regression With an F-to-Enter Stopping Rule

A Monte Carlo simulation is used to estimate the upper percentage points of the null distribution of the sample squared multiple correlation coefftcient (R 2) when the number of predictors selected is determined by a stopping rule. In the study, the sample size n and the number of candidate predictors m satisfy 2 ≤ m ≤ 20 and 10 ≤ n – m – 1 ≤ 200, while the F threshold ranges from two to four. Tables of the upper five percent and upper one percent sample R* values are presented and an example is given to illustrate the use of the tables.

Stacking Graphic Elements to Avoid Over-Plotting

An ongoing challenge for information visualization is how to deal with over-plotting forced by ties or the relatively limited visual field of display devices. A popular solution is to represent local data density with area (bubble plots, treemaps), color(heatmaps), or aggregation (histograms, kernel densities, pixel displays). All of these methods have at least one of three deficiencies:1) magnitude judgments are biased because area and color have convex downward perceptual functions, 2) area, hue, and brightnesshave relatively restricted ranges of perceptual intensity compared to length representations, and/or 3) it is difficult to brush or link toindividual cases when viewing aggregations. In this paper, we introduce a new technique for visualizing and interacting with datasets that preserves density information by stacking overlapping cases. The overlapping data can be points or lines or other geometric elements, depending on the type of plot. We show real-dataset applications of this stacking paradigm and compare them to other techniques that deal with over-plotting in high-dimensional displays.

Revising the Pareto Chart

The Pareto chart is a bar chart of frequencies sorted by frequency. The most popular incarnation of the chart puts the highest bars on the left and includes a line showing the scores produced by adding the heights in order from left to right. This chart is used widely in quality control settings to identify critical factors leading to failure or defects in a process. This article presents revisions that remedy problems with the chart and improve its usability in diagnostic settings.

Admission decisions and performance during medical school.

This study compared a group of 24 applicants who were interviewed and accepted at the Yale University School of Medicine but went to other medical schools (AYEs) with a group of 27 applicants who attended the same schools but had been rejected at Yale following an interview and committee deliberation (NAYs). Measures of performance during medical school included scores on Parts I and II of the examinations of the National Board of Medical Examiners and evaluations from the deans office at each students medical school. No relationship was found between admission decisions and performance during medical school when AYEs and NAYs attending the same medical schools were compared.