Data Display

Abstract

A data display is an external visual representation of data — a chart, graph, map, or diagram — engineered so that quantitative relations can be read off by the visual system rather than computed in the head. Cognitive psychology treats such displays as instruments of external cognition: they move work off working memory onto fast, parallel perception, but only when their encodings match how vision operates. This article surveys the elementary-perceptual-task hierarchy that ranks graphical encodings by accuracy; the preattentive features that make some patterns pop out; the top-down processes that govern how graphs are comprehended and misread; and the science of how displays shape judgment. Three interactive demonstrations compare position and angle encodings, contrast feature and conjunction search across set size, and strip non-data ink from a chart to raise its data-ink ratio.

Keywords: data display, graphical perception, attention, external cognition, data visualization

A data display is the visual representation of data through a manufactured system: a bar chart, a scatterplot, a line graph, a map, a network diagram. In cognitive terms a display is a device for external cognition — it externalizes information into a spatial arrangement so that relations which would be effortful to compute symbolically can instead be seen. Jill Larkin and Herbert Simon made the classic argument for why this works: a diagram and a sentential description can be informationally equivalent yet differ enormously in computational efficiency, because a good diagram groups together the information needed for an inference and lets perceptual operators substitute for slow symbolic search (Larkin & Simon, 1987). The display does not add information; it reorganizes it so that the eye does work the mind would otherwise have to do.

Why bother, when a few summary numbers seem to say it all? Francis Anscombe answered with four small datasets — Anscombe's quartet — that share almost identical means, variances, correlations, and regression lines yet look completely different when plotted: one linear, one curved, one dominated by a single outlier (Anscombe, 1973). The statistics conceal what the display reveals at a glance. This is the founding intuition of the field: a display can expose structure — clusters, trends, gaps, outliers — that no reasonable summary preserves, provided the structure is encoded in a form the visual system reads well.

Types of Data Display

The Medical Subject Headings vocabulary files Data Display (D003626) under Ergonomics in tree F02.784.412.221, and also under Information Science (L01.296), and lists three narrower descriptors directly beneath it, shown in Table 1. These subtypes are an artifact of indexing practice rather than a cognitive taxonomy of displays: MeSH is a controlled vocabulary for retrieving literature, so it groups display technologies (immersive and computer-generated media) as kinds of data display, a classification largely orthogonal to the perceptual dimensions — encoding, attention, comprehension — along which cognitive psychology analyzes displays. Each entry below is glossed from its MeSH sense tightened to one line; none yet has its own article on this site, so none is linked.

Graphical Perception and the Encoding Hierarchy

The central empirical discovery of the field is that encoding channels are not interchangeable. William Cleveland and Robert McGill defined a set of elementary perceptual tasks — the basic acts of extracting a quantity from a graph, such as judging position along a common scale, length, angle, slope, area, or color saturation — and measured how accurately people perform each (Cleveland & McGill, 1984). The result is a hierarchy: judgments of position along a common scale are the most accurate, followed by position on non-aligned scales, then length, then angle and slope, with area, volume, and color among the least accurate. The practical corollary is direct: the quantities most in need of precise reading should be encoded in the highest-ranked channel available. A dot plot or bar chart, which uses aligned position and length, supports more accurate value extraction than a pie chart, which forces the eye to judge angle and area. Cleveland and McGill's Science paper carried the argument beyond statistics into the wider scientific community (Cleveland & McGill, 1985), and Cleveland's later monograph developed a full program of display design grounded in perception (Cleveland, 1993).

The hierarchy is not merely a lab curiosity. Jeffrey Heer and Michael Bostock re-ran Cleveland and McGill's proportion-judgment experiments as crowdsourced studies on hundreds of online participants and recovered the same ordering, showing the effect is robust and replicable at scale and establishing crowdsourcing as a method for evaluating displays (Heer & Bostock, 2010). The first demonstration lets a reader read the same proportion off a position encoding and an angle encoding and feel why the ranking holds.

Position versus angle: the encoding hierarchy

Both panels encode the identical quantities. In the bars you can line up the tops against the common baseline and read the ratio directly; in the pie you must compare two wedge angles, a judgment Cleveland and McGill found markedly less accurate. That difference in the eye, not in the data, is the encoding hierarchy: position on a common scale sits at the top, angle and area near the bottom.

Underneath the hierarchy lies a vocabulary of visual variables. Jacques Bertin's Sémiologie graphique systematized the channels a mark can vary along — position, size, shape, value, color hue, orientation, and texture — and analyzed which are suited to ordered versus categorical data, a framework that still organizes how encodings are chosen. Edward Tufte added a normative layer of design principles: maximize the share of ink devoted to data, strip away decorative chartjunk, and preserve graphical integrity so that the visual magnitude of an effect matches its magnitude in the data (Tufte, 2001). Bertin's descriptive taxonomy and Tufte's prescriptions converge on the same point that graphical-perception experiments quantify: the form of the encoding, not just its content, determines what a viewer can extract.

Attention and Preattentive Processing

Before deliberate reading begins, a display has already been processed by early vision. Christopher Healey and James Enns review how certain visual features are preattentive — detected rapidly, in parallel, across the whole field without focused attention — and how visualization can exploit them (Healey & Enns, 2012). A point that differs from all others in a single feature such as hue or orientation pops out: the time to find it is roughly constant no matter how many distractors surround it. But a target defined by a conjunction of features — the one item that is both red and a circle among red squares and blue circles — has no unique preattentive signature, so it must be sought by slower, serial, attention-demanding search whose time grows with the number of items. This feature-versus-conjunction contrast is the empirical core of Anne Treisman's feature-integration theory, which holds that individual features are registered preattentively and in parallel across the field, whereas binding several features into a single object requires focal attention deployed serially from item to item (Treisman & Gelade, 1980). The design lesson is that a well-chosen encoding lets the reader's parallel visual machinery do the finding, while a poor one forces effortful item-by-item scanning. The second demonstration contrasts these two regimes and shows search time flatten or climb as the set size grows.

Pop-out versus serial search

Estimated search time: 468 ms (420 + 2 × 24)

In feature mode the target is the only object of its hue, so early vision flags it in parallel and the estimated time barely moves as items are added (slope ≈ 2 ms/item). In conjunction mode the target shares its colour with the red squares and its shape with the blue circles, so no single feature isolates it; attention must visit items one by one and time grows steeply with set size (slope ≈ 26 ms/item). The same data, differently encoded, is either found at a glance or hunted for.

Which channels carry meaning cleanly, and which mislead, is itself an empirical question. Danielle Szafir catalogs the systematic ways visualizations distort perception — misjudged color scales, area encodings that understate large values, ensemble effects in which the average of many marks is read differently than any one — and shows these are not user errors but predictable consequences of how the visual system samples a display (Szafir, 2018). Encoding accuracy, in this light, is a property to be measured and engineered, not assumed.

How Graphs Are Comprehended

Extracting a value is only the first step; understanding a graph means building a mental representation of the relations it depicts, and that process is heavily top-down. Priti Shah and Patricia Carpenter showed conceptual limitations in reading line graphs: viewers encode the relations the graph's format makes salient and struggle to reorganize the same data along a different axis, so the choice of which variable goes on the x-axis constrains what relations are noticed at all (Shah & Carpenter, 1995). David Simkin and Reid Hastie gave an information-processing account of the elementary judgments — anchoring, scanning, projection — that comprehension of bar and pie charts is built from, linking perceptual tasks to the chart types that support them (Simkin & Hastie, 1987). Stephen Kosslyn proposed a framework analyzing a chart at the syntactic, semantic, and pragmatic levels, treating a graph as a visual language whose comprehension can break down at any of these levels (Kosslyn, 1989).

Graphic conventions carry meaning of their own. Jeff Zacks and Barbara Tversky found that the form of a graph cues the kind of relation viewers infer: bars, which depict discrete bounded quantities, prompt discrete comparisons (“A is more than B”), while lines, which connect points, prompt trend and continuity readings (“it rises”) — even when the two encode identical data, so that switching bars for lines changes the message people take away (Zacks & Tversky, 1999). Mary Hegarty situates these findings in a broader cognitive science of visual-spatial displays, arguing that a display is effective only when its spatial structure is congruent with the structure of the concept it represents and with the inferences the viewer must draw (Hegarty, 2011). Comprehension, across these accounts, is an interaction between the display's form and the viewer's knowledge, task, and expectations — not a passive reading-off.

Displays and Decision Making

Because displays shape what is understood, they also shape what is decided. Lace Padilla and colleagues offer a cognitive framework spanning disciplines for decision making with visualizations, modeling how a viewer's bottom-up perception of a display and top-down goals combine, through working memory and prior knowledge, to produce a judgment — and where in that pipeline predictable errors enter (Padilla et al., 2018). Steven Franconeri and colleagues synthesize the evidence on what works in visual data communication, distilling how attention, perception, and prior belief determine whether a display informs or misleads, and translating the science into design guidance (Franconeri et al., 2021).

A striking demonstration that displays are not neutral is the curse of knowledge in communication. Cindy Xiong, Franconeri, and colleagues showed that once a viewer knows the intended message of a chart, they systematically overestimate how obvious that message is to a naive viewer, so a designer who already grasps the data misjudges what an audience will actually see in it (Xiong et al., 2020). The finding sharpens the field's central claim: the meaning a reader takes from a display is a psychological outcome, contingent on perception and prior knowledge, not a property inherent in the picture.

Design Principles and the Economy of Ink

The perceptual findings converge on a small set of design commitments. Tufte's data-ink ratio — the fraction of a graphic's ink that represents data, as opposed to frames, gridlines, shading, and decoration — captures one of them quantitatively: within reason, erase non-data ink and redundant data ink, and what remains shows the data more clearly (Tufte, 2001). The prescription follows directly from graphical perception and preattentive processing: every non-data mark competes for the limited attention and the same feature channels the data must use, so decoration is not neutral but a source of clutter that raises search cost and can create spurious pop-out. Szafir's catalog of misleading encodings is the empirical counterpart, identifying which economies genuinely help and which distort (Szafir, 2018). The third demonstration lets a reader remove non-data ink from a cluttered chart and watch the data-ink ratio climb.

The data-ink ratio

The bars — the data-ink — never change; only the decoration does. Turning everything on reproduces the article’s cluttered chart (ratio 0.40); erasing the shading, background, and frame and thinning the gridlines drives the ratio to 0.92. Because the numerator is fixed, every unit of non-data ink removed raises the share of the graphic that actually shows the data.

Worked Example

Tufte's data-ink ratio can be computed exactly, which makes the effect of decluttering precise rather than a matter of taste. The ratio is defined as the ink used to represent data divided by the total ink in the graphic:

data-ink ratio = data-ink ÷ total ink.

Consider a cluttered bar chart whose ink budget, in arbitrary but consistent units, is: the bars themselves (the data-ink) = 60; heavy gridlines = 30; a decorative outer frame = 10; three-dimensional shading on the bars = 35; and a filled background = 15. The non-data ink totals 30 + 10 + 35 + 15 = 90, so the total ink is 60 + 90 = 150. The data-ink ratio is therefore 60 ÷ 150 = 0.40: only 40 percent of the ink carries data, and the other 60 percent is decoration competing for the reader's attention.

Now redesign the chart by erasing non-data ink: remove the three-dimensional shading (−35), drop the background fill (−15), delete the outer frame (−10), and thin the heavy gridlines from 30 units down to 5 (−25). The data-ink is untouched at 60. The remaining non-data ink is just the 5 units of light gridlines, so the total ink falls to 60 + 5 = 65, and the data-ink ratio rises to 60 ÷ 65 = 0.923, which rounds to 0.92. The data are unchanged, yet the share of the graphic devoted to them has more than doubled, from 0.40 to 0.92.

The arithmetic makes Tufte's principle concrete: because the data-ink is held fixed, every unit of decoration removed shrinks the denominator alone, so the ratio rises monotonically toward its ceiling of 1.0 as non-data ink approaches zero. The number is a design heuristic, not a law — some non-data ink (a light reference grid, axis labels) aids comprehension — but it quantifies exactly why stripping chartjunk sharpens a display (Tufte, 2001).

Discussion

A coherent view of data display emerges across these literatures. A display is effective to the degree that it maps the quantities a viewer needs onto the perceptual channels the viewer reads most accurately, presents the target patterns in features that early vision extracts in parallel, and structures the whole so that its spatial form is congruent with the relations to be understood (Cleveland & McGill, 1984; Healey & Enns, 2012; Hegarty, 2011). The recurring theme is that a display's meaning is not printed on the page but reconstructed in the viewer, through perception and prior knowledge, so the same data can inform or mislead depending on how it is drawn (Shah & Carpenter, 1995; Zacks & Tversky, 1999; Xiong et al., 2020).

This reframes display design as applied cognitive psychology rather than aesthetics. The founding demonstrations — Anscombe's quartet, Larkin and Simon's analysis of why a diagram can beat a description — show that displays earn their power by fitting the architecture of vision and cognition (Anscombe, 1973; Larkin & Simon, 1987). The normative traditions of Bertin and Tufte, once read as taste, turn out to encode the same constraints that controlled experiments measure (Tufte, 2001; Cleveland, 1993). Getting a display right is thus a matter of engineering the fit between the encoding and the perceiver, and getting it wrong imposes real cognitive costs on whoever must read it.

Current Directions

Contemporary work has turned the field into a cumulative, experimental science of communication. The 2021 synthesis of what works in visual data communication marks the consolidation of decades of scattered findings into design guidance grounded in attention and perception, signaling that display design now has an evidentiary base rather than only a normative one (Franconeri et al., 2021). A parallel methodological current imports the rigor of vision science directly: Elliott and colleagues map a design space of vision-science methods for visualization research — adapting psychophysical staircases, forced-choice tasks, and modeling from perception experiments to measure display performance precisely (Elliott et al., 2021).

The other active front is the social and cognitive psychology of how displays are actually read. Decision-focused frameworks now model the full path from a mark on a screen to a choice, including where prior belief and working-memory load introduce error (Padilla et al., 2018), and communication-focused work documents systematic biases such as the curse of knowledge that afflict even expert designers (Xiong et al., 2020). Together these currents move data display from a craft judged by principles toward a discipline in which encoding choices are tested for their measurable effect on what people perceive, understand, and decide.

Common Misconceptions

A prettier chart is a better chart.

Decoration competes for the same attention and feature channels the data must use. What makes a display better is matching the encoding to how vision reads quantities, not visual embellishment (Cleveland & McGill, 1984; Tufte, 2001).

Any chart type will do if the numbers are right.

Encoding channels differ sharply in accuracy: position on a common scale is read far more precisely than angle or area, so a bar or dot plot supports better value extraction than a pie chart of the same data (Cleveland & McGill, 1985; Heer & Bostock, 2010).

Summary statistics capture everything a plot would show.

Anscombe's quartet has near-identical means, variances, and correlations yet utterly different shapes; only the display reveals the curve, the outlier, and the true pattern (Anscombe, 1973).

A well-drawn display means the same thing to everyone.

Comprehension is top-down: the chart's form cues which relations are noticed, and a designer's own knowledge can make a message seem more obvious than it is to a naive viewer (Zacks & Tversky, 1999; Xiong et al., 2020).

Glossary

Anscombe's quartet.

Four datasets with nearly identical summary statistics but visibly different shapes, used to show that a display reveals structure summaries conceal.

Chartjunk.

Non-data decoration — heavy frames, gridlines, shading, ornament — that adds ink without adding information and competes with the data for attention.

Conjunction search.

Looking for a target defined by a combination of features (e.g., red and round); has no preattentive signature, so search time grows with the number of items.

Curse of knowledge.

The bias by which someone who knows a chart's intended message overestimates how obvious that message is to a naive viewer.

Data display.

An external visual representation of data — chart, graph, map, or diagram — engineered so that relations can be read off by perception rather than computed symbolically.

Data-ink ratio.

Tufte's measure of the fraction of a graphic's ink that represents data rather than decoration; raising it, by erasing non-data ink, tends to clarify a display.

Elementary perceptual task.

A basic act of extracting a quantity from a graph — judging position, length, angle, area, or color — whose accuracy defines the encoding hierarchy.

Encoding hierarchy.

The ordering of graphical channels by how accurately they are read: position on a common scale first, then length, then angle and area, with color least accurate.

Ensemble coding.

The visual system's rapid extraction of summary statistics, such as the mean of many similar marks, so a group is perceived as a whole rather than as individual items — a channel a display can exploit or fall afoul of.

External cognition.

Using external representations such as displays to offload and support reasoning, letting perceptual processes substitute for effortful mental computation.

Graphical perception.

The study of how accurately and quickly people extract information from graphs, and of which encodings support that extraction best.

Pop-out.

The effortless, parallel detection of a target that differs from every distractor in a single preattentive feature, found in roughly constant time regardless of the number of distractors.

Preattentive feature.

A visual property (hue, orientation, size) detected rapidly and in parallel across the field, so a target defined by it pops out in roughly constant time.

Visual variable.

Bertin's term for a dimension a mark can vary along — position, size, shape, value, hue, orientation, texture — each suited to particular kinds of data.

Key Researchers

Jacques Bertin (1918-2010). French cartographer and theorist; his Sémiologie graphique systematized the visual variables that underlie every graphical encoding. Wikipedia - Wikidata

William S. Cleveland (1943-2026). Statistician at Bell Labs and Purdue University; with Robert McGill he established the elementary-perceptual-task hierarchy that ranks graphical encodings by accuracy. Google Scholar - Faculty Page - Wikipedia - Wikidata

Steven L. Franconeri (contemporary). Psychologist at Northwestern University; he leads work on the visual cognition of data displays and the 2021 synthesis of what works in visual data communication. ORCID - Google Scholar - Faculty Page - Wikidata

Jeffrey Heer (contemporary). Computer scientist at the University of Washington; he pioneered crowdsourced graphical-perception experiments and the declarative visualization grammars that operationalize encoding theory. ORCID - Google Scholar - Faculty Page - Wikipedia - Wikidata

Mary Hegarty (contemporary). Psychologist at the University of California, Santa Barbara studying visual-spatial displays; she argues a display is effective when its spatial structure is congruent with the concept and inferences it must support. Google Scholar - Faculty Page - Wikipedia - Wikidata

Lace M. Padilla (contemporary). Cognitive scientist at Northeastern University; she built the cross-disciplinary framework for decision making with visualizations and studies uncertainty visualization. ORCID - Google Scholar - Faculty Page

Priti Shah (contemporary). Psychologist at the University of Michigan; she demonstrated the conceptual limits of graph comprehension — how a display's format constrains the relations viewers can read from it. Google Scholar - Faculty Page

Danielle Albers Szafir (contemporary). Computer scientist at the University of North Carolina at Chapel Hill; she studies the perceptual science of visualization design, including color and ensemble coding. ORCID - Google Scholar

Edward R. Tufte (b. 1942). Statistician and design theorist at Yale University; he articulated the design principles of statistical graphics — the data-ink ratio, chartjunk, and graphical integrity. Faculty Page - Wikipedia - Wikidata

Barbara Tversky (b. 1941). Psychologist at Stanford University and Columbia Teachers College; she investigated how graphic conventions such as bars and lines carry meaning and how spatial cognition shapes diagram comprehension. Google Scholar - Faculty Page - Wikipedia - Wikidata

Frequently Asked Questions

What is a data display in cognitive psychology?
It is an external visual representation of data (a chart, graph, map, or diagram) engineered so that quantitative relations can be read off by the visual system rather than computed in the head. Cognitive psychology studies displays as instruments of external cognition that offload reasoning onto fast, parallel perception (Larkin & Simon, 1987).

Why is a bar chart usually more accurate to read than a pie chart?
Because bars encode quantities as aligned position and length, which the visual system reads most accurately, while pies force judgments of angle and area, which sit lower in the encoding hierarchy and yield larger errors (Cleveland & McGill, 1984).

What is graphical perception?
It is the study of how accurately and quickly people extract information from graphs, and of which encodings support that extraction best. Its central finding is that encoding channels form an accuracy hierarchy topped by position on a common scale (Cleveland & McGill, 1985).

What does it mean for a visual feature to be preattentive?
A preattentive feature such as hue or orientation is detected rapidly and in parallel across the whole field, so a target defined by it pops out in roughly constant time; a target defined by a conjunction of features must instead be searched serially (Healey & Enns, 2012).

Why can plotting data reveal things that summary statistics hide?
Because very different datasets can share nearly identical means, variances, and correlations. Anscombe's quartet shows four such datasets whose curves, outliers, and shapes are visible only when displayed (Anscombe, 1973).

Do bar graphs and line graphs of the same data say the same thing?
No. Bars cue discrete comparisons while lines cue trends and continuity, so switching the form changes the relation viewers infer even when the underlying numbers are identical (Zacks & Tversky, 1999).

What is the data-ink ratio?
It is the fraction of a graphic's ink that represents data rather than frames, gridlines, and decoration. Erasing non-data ink raises the ratio and, within reason, clarifies the display (Tufte, 2001).

Can a data display mislead even when it is accurate?
Yes. Comprehension is top-down, so format, prior knowledge, and biases such as the curse of knowledge shape what a viewer takes away, and predictable perceptual distortions can misrepresent the data (Xiong et al., 2020; Szafir, 2018).

References