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Small multiple
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 | This article includes a list of general references, but it lacks sufficient corresponding inline citations. (June 2016) |
A small multiple (sometimes called trellis chart, lattice chart, grid chart, or panel chart) is a series of similar graphs or charts using the same scale and axes, allowing them to be easily compared. It uses multiple views to show different partitions of a dataset. The term was popularized by Edward Tufte.
According to Tufte,
At the heart of quantitative reasoning is a single question: Compared to what? Small multiple designs, multivariate and data bountiful, answer directly by visually enforcing comparisons of changes, of the differences among objects, of the scope of alternatives. For a wide range of problems in data presentation, small multiples are the best design solution.[1]
Modern example
[edit]In the example, the departmental salary expense is charted by month with a dashed line indicating the average for each department. The scales on each panel are different to emphasize the relative change over time compared to the range. Standardizing the scales could provide insight into comparisons in magnitude between the different departments. Two independent Y axes may be utilized when presenting data with different numeric scales in each panel.[2][3]
Historical examples
[edit]
Some of the earliest known examples of this type of visualization include the photographic series Horse In Motion by Eadweard Muybridge, around 1886, and Francis Amasa Walker's chart of citizen's occupations in census year 1870 appearing in the Statistical Atlas of the United States.[4][5]
Muybridge's work not only proved for the first time that all four of a horse's hooves left the ground during gallop (see upper central plates), but it also broke new ground in terms of artistic expression and became foundational to the development of the motion picture. Muybridge went on to produce many more examples of small multiples showing animal locomotion through the medium of stop-motion photography, including boys playing leapfrog and a bison cantering.
Sketched graphic examples can be found in Francis Amasa Walker's charts appearing in the 1870 Statistical Atlas of the United States. Superintendent of the US Census at the time of its creation, Walker was determined to modernize the Census collection and analysis methods and used the Atlas to present the final data set using unprecedented visual forms, including many beautiful examples of small multiples.
Adjacent is a chart showing the population broken down by occupation, including a count of those attending school, according to the 1870 Census. This graphic is innovative in its use of both a treemap display and a latticed layout of small multiples. Additional examples appearing in the Atlas include side-by-side geographic maps showing the changes in population over time, as well as tiled mosaic charts showing population demographic breakdowns, and diverging bar graphs showing deaths broken down by age and gender, tiled by state.[5]
Thematic maps
[edit]
Small multiples are a popular technique in cartographic design for multivariate mapping. As with the small multiple chart, each panel uses the same underlying two-dimensional space, but in this case that is a geographic space. Typically, the variables being mapped are of a similar type, such as types of agricultural products, so that the same strategy of map symbol can be used on each panel, enabling rapid comparison between the maps.
Another common use of small multiples is to show change in spatial patterns over time, as an alternative to an animated map.[6] Several tests of the effectiveness of each method have generally concluded that they have distinct advantages, with animation being better for seeing trends, especially movement, and small multiples being better for making comparisons between times.[7]
References
[edit]- ^ Tufte, Edward (1990). Envisioning Information. Graphics Press. p. 67. ISBN 978-0961392116.
- ^ "Plotting a Trellis Plot with Double Y Axis". Origin Blog. 2018-10-18. Retrieved 2019-04-25.
- ^ R.bhabuk, U. (2013-05-02). "R graph gallery: RG#102: Double Y axis trellis plot (weather data example)". R graph gallery. Retrieved 2019-04-25.
- ^ Herbert, Alan. "Horse in Motion, Eadweard Muybridge, ca. 1886". Harry Ransom Center, The University of Texas at Austin. Retrieved 10 February 2019.
- ^ a b United States, Bureau of the Census. "Statistical Atlas of the United States : Based on the Results of the Ninth Census 1870". FRASER St. Louis Fed. Retrieved 10 February 2019.
- ^ Griffin, Amy L.; MacEachren, Alan M.; Hardisty, Frank; Steiner, Erik; Li, Bonan (2006). "A Comparison of Animated Maps with Static Small-Multiple Maps for Visually Identifying Space-Time Clusters". Annals of the Association of American Geographers. 96 (4): 740–753. Bibcode:2006AAAG...96..740G. CiteSeerX 10.1.1.474.2385. doi:10.1111/j.1467-8306.2006.00514.x. S2CID 53356363.
- ^ Slocum, Terry A.; Sluter, R.S.; Kessler, Fritz C.; Yoder, S.C. (2004). "A qualitative evaluation of MapTime, a program for exploring spatiotemporal point data". Cartographica. 39 (3): 43–68. doi:10.3138/92T3-T928-8105-88X7.
- Tufte, Edward (1983). Visual Display of Quantitative Information. Graphics Press. ISBN 978-1930824133.
Small multiple
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Concept and Principles
Definition
Small multiples are a data visualization technique comprising an array of similar charts or graphs that employ identical scales, axes, and graphical elements, with variations introduced across panels to represent changes in one specific data dimension, such as time periods, categories, or geographic regions. This arrangement in a grid or lattice format enables viewers to discern patterns and differences through direct visual juxtaposition without the need to mentally superimpose disparate elements.[7][2] The concept was introduced by Edward Tufte in his 1990 book Envisioning Information, where he defined small multiples as compact, repetitive displays—often thumbnail-sized—that leverage self-similarity to highlight subtle variations, thereby facilitating efficient pattern recognition and comparison while eschewing decorative distractions that dilute data integrity. By maintaining consistency across panels except for the varying data slice, the technique aligns with perceptual principles that minimize cognitive effort in interpreting multivariate relationships, prioritizing high data density over singular, overloaded representations.[3]Key Design Principles
Small multiples achieve effective visualization through strict uniformity in design elements across all panels, including identical scales, axes limits, and graphic forms such as line plots or scatter diagrams. This consistency enforces "inevitable comparability," where observed differences stem directly from data variations rather than arbitrary scaling or representational choices that could introduce distortions or mislead interpretations.[2][8] A core principle emphasizes minimalism to maximize the data-ink ratio, prioritizing ink devoted to data representation over non-essential chart junk like repeated legends, dense gridlines, or ornate frames in each panel. Non-data elements are stripped to essentials, with color applied sparingly—typically to highlight the single varying dimension—thus minimizing cognitive load and enhancing the clarity of patterns amid multiplicity.[9][7] Panels must be rendered at small physical sizes, sufficiently compact to array dozens on a single display while exploiting peripheral vision for holistic scanning rather than sequential inspection. Grid-based layouts, organized in rows or columns, align with the data's categorical or temporal dimensions, promoting parallel visual processing of variances without overwhelming the viewer.[7][10] To support causal realism, designs isolate one controlled varying factor per sequence of panels—such as time, category, or condition—while standardizing all others, enabling differences to reveal potential causal mechanisms through direct, unconfounded visual contrasts grounded in empirical variation.[7][11]History
Early Precursors
In the 17th century, Jesuit astronomer Christopher Scheiner produced one of the earliest arrays resembling small multiples in his 1630 treatise Rosa Ursina sive Sol, depicting configurations of sunspots observed between October 23 and December 19, 1611, as a grid of 12 similar schematic images grouped into seven categories.[12] This grid format enabled direct comparison of positional changes over time, leveraging repetitive visual elements to reveal patterns without overlay, a constraint imposed by the era's manual illustration techniques.[13] The 19th century saw expanded applications in meteorology and statistics, driven by growing data volumes from systematic observations. In 1863, Francis Galton presented a 3x3 trellis of schematic maps charting barometric pressure, wind direction, rainfall, and temperature across Europe for 15 consecutive days in December 1861, allowing side-by-side scrutiny of synoptic weather evolution.[14] Similarly, Florence Nightingale's 1858 report Notes on Matters Affecting the Health, Efficiency, and Hospital Administration of the British Army featured multiple adjacent coxcomb (polar area) diagrams comparing monthly mortality causes in British military hospitals from April 1854 to March 1856, with wedge areas scaled to death counts to emphasize preventable diseases over battle wounds—16,000 died from disease versus 3,500 in combat.[15][16] Statistical atlases further exemplified the approach amid expanding census data. The U.S. Census Bureau's 1870 Statistical Atlas included grids of small, parallel charts, such as state-level breakdowns of gainful occupations by age and school attendance, with 38 states represented in uniform bar or pyramid formats for regional labor comparisons.[17] By 1874, statistician Francis Amasa Walker extended this in visualizations of occupational distributions, using matrices of similar graphics to juxtapose economic activities across U.S. states and territories.[18] These repetitions prioritized pattern detection over narrative embellishment, necessitated by engraving limitations that favored discrete units over intricate superimpositions. Chronophotography provided another precursor in motion analysis. In 1878, Eadweard Muybridge captured sequential photographs of a trotting horse named Sallie Gardner, producing a series of 12 small, identically framed images triggered by 12 cameras spaced along a track, resolving whether all hooves leave the ground simultaneously during gait—a bet won by railroad magnate Leland Stanford.[19] This linear array of frames facilitated frame-by-frame comparison of limb positions, influencing subsequent studies in biomechanics and animation.[20] Such 19th-century practices underscored small multiples' utility in empirical sciences, where parallel visuals clarified causal sequences in temporal or categorical data amid technological constraints on complexity.Popularization by Edward Tufte
Edward Tufte first articulated the concept of small multiples in his 1983 book The Visual Display of Quantitative Information, presenting them as a method for displaying multivariate data through repeated, simplified graphical elements that facilitate direct visual comparisons across variations.[21][22] Tufte emphasized their utility in revealing patterns and changes without overwhelming the viewer, using examples such as time-series data partitioned into adjacent panels sharing common scales and frames.[23] In his 1990 follow-up, Envisioning Information, Tufte expanded on small multiples with a dedicated chapter, illustrating their application to high-dimensional data and complex phenomena like spatial arrangements and temporal sequences.[1][24] He advocated their use alongside principles of graphical integrity, which prioritize undistorted representations and high data density while condemning "chartjunk"—non-informative decorative elements that obscure evidence and invite misinterpretation.[23][25] Small multiples, by contrast, support rigorous, evidence-driven analysis through parallel views that minimize distortion and enable perceptual judgments over numerical recall.[26][27] Tufte's framework elevated small multiples from ad hoc techniques to a foundational principle in data visualization, influencing standards in statistics and graphic design by the mid-1990s.[28] His ideas resonated in works like William S. Cleveland's The Elements of Graphing Data (1994), which echoed multipanel approaches for comparative plotting while building on Tufte's emphasis on clarity and perceptual accuracy.[28] This codification shifted visualization practice toward designs that prioritize causal inference and empirical scrutiny over aesthetic or persuasive embellishments.[29]Evolution in Digital Tools
In the 2000s, statistical computing environments like R incorporated small multiples through packages such as lattice, which introduced trellis graphics for conditioning plots that automate the division of data into comparative panels.[30] The ggplot2 package, released in 2009, further advanced this with faceting functions likefacet_wrap() and facet_grid(), enabling scalable creation of small multiples for multivariate data analysis without manual repetition.[31] These tools democratized access by automating layout and scaling, reducing the need for custom programming in exploratory data visualization.[32]
During the 2010s, business intelligence software like Tableau facilitated small multiples via table calculations and grid layouts, allowing users to generate panel charts for dimensional comparisons, though often requiring calculated fields for dividers and indexing.[33] This integration supported broader adoption in professional reporting, with features evolving to handle larger datasets through drag-and-drop interfaces.[34]
In the 2020s, Microsoft Power BI added native small multiples capabilities, introduced around 2020, which split visuals into side-by-side versions based on categorical dimensions while maintaining shared axes for consistent scaling.[35] Recent updates, such as those in 2024, extended this to card visuals and dynamic row/column configurations, enhancing scalability for real-time dashboards in big data environments.[36] Libraries like Plotly have incorporated interactive facets since the mid-2010s, with ongoing enhancements supporting uniform scale preservation during zooming and panning across panels, applicable to web-based applications.[37]
These digital evolutions have shifted toward hybrid forms with constrained interactivity, such as linked brushing across panels, preserving Tufte's emphasis on rapid visual comparison amid growing data volumes.[38] Automated faceting in these tools has empirically improved efficiency, as evidenced by their widespread use in scalable analytics workflows.[39]