Overview and State-of-the-Art of Uncertainty Visualization - Scientific Visualization: Uncertainty, Multifield, Biomedical, and Scalable Visualization - page 13

Fig. 1.2 Variations of the boxplot. a The construction of the boxplot [ 103 ]. b Range plot [ 94 ].
c Innerquartile plot [ 102 ]. d Histplot [ 4 ]. e Vaseplot [ 4 ]. f Box-percentile plot [ 26 ]. g Violin plot [ 39 ].
h Variable width notched boxplot [ 67 ]. i Skewplot [ 16 ]. j Summary plot [ 82 ]
information, typically through changes to the sides of the plot. The hist plot [ 4 ]
extends the width of the cross bars at the quartiles and median to express density
at these three locations. The vase plot [ 4 ] instead varies the “box” continuously
to reflect the density at each point in the innerquartile range. Similarly, the box-
percentile plot [ 26 ] and violin plot [ 39 ] show density information for the entire range
of the data set. Density can also be shown by adding dot plots [ 106 ], which graph data
samples using a circular symbol. The sectioned density plot [ 17 ] completely recon-
structs the box plot by creating rectangles whose colors and size indicate cumulative
density, and placement express the location of the quartiles. Sample size and confi-
dence levels can be expressed through changing or notching the width of the plot [ 67 ]
(Fig. 1.2 h) or by using dot-box plots, which overlay dot plots onto box plots [ 107 ].
Other descriptors, such as skew and modality, can be added by modifying the width
of the median line [ 67 ], thickening the quartile lines [ 16 ], (Fig. 1.2 i) adding beam
and fulcrum displays [ 23 ] alongside, or overlaying additional glyphs [ 82 ] (Fig. 1.2 j).
1.5.1.2 2D
Standard implementations of the boxplot focus on univariate data distributions. The
five-number summary is a useful descriptor of not only univariate, but also bivariate
data distributions. The main challenge in extending the boxplot for use with higher
dimensional data is how to translate the five-number summary values, which are
vector values in the bivariate case, into visual metaphors with meaningful spatial
positions, while maintaining the simplicity of the original boxplot. A rangefinder
boxplot [ 3 ], as seen as the solid back lines in Fig. 1.3 a, is a simple extension of the
boxplot into 2Dwhich determines boxplots for the two dimensions independently and
draws lines to show the interquartile ranges and extrema of those plots. This idea was
further improved upon, as shown as the thick gray lines in Fig. 1.3 a, to emphasize the
quartiles rather than the range, by moving the perpendicular lines from the extrema
values to the upper and lower quartile positions and extending whisker lines to the