Choosing a form under constraint: print, screen, slide, phone, wall

Year 3 / Module 33 Data visualisation in practice / Unit 2 / Choosing a form under constraint: print, screen, slide, phone, wall

Choosing a form under constraint: print, screen, slide, phone, wall

HCI3109 · Unit 2 of 10

The form follows the display and the medium as much as the data, because the channel a reader can actually use is limited by size, viewing distance and reproduction, and the perceptual ranking of channels predicts how a chart degrades when the medium changes.

Choosing a form under constraint: print, screen, slide, phone, wall

The first of ten units argued that the first design decision is the question and the reader who holds it. This second of ten units argues that the second decision is bounded before it is made, because a chart is built for a surface. The same data can answer the same question on a printed page, a projected slide, a phone or a wall. The surface a reader can use fixes the sizes it can offer and the reproduction it must survive.

The thesis is that the form follows the display as much as the data. Its complication is that the ranking of the ten elementary perceptual tasks has so far survived one replication on a different reader population. Once the reader can see the marks at all, the form that suits the task wins.

The ranking of channels survives a medium change, and the available tasks do not

Cleveland and McGill (1984) did the measurement that makes prediction possible. They identify ten elementary perceptual tasks and order them by accuracy. Position along a common scale comes first, positions on nonaligned scales next, then length, direction and angle, then area, then volume and curvature, and shading and colour saturation last. The order is a property of the reader, so it can be looked for on other hardware. Heer and Bostock (2010) re-ran the spatial encoding study on Amazon Mechanical Turk twenty-six years later and recovered the same ranking. The order is therefore not an artefact of one laboratory.

A form is a specification, not a picture

Wickham's (2010) layered grammar explains why a change of medium can be a design decision rather than a redraw. A plot is a stack of layers. Each layer combines data, aesthetic mappings, a statistical transformation, a geometric object and a position adjustment. Because scales and the coordinate system are separate components, the surface enters the specification as a layer. Anscombe (1973) built four datasets whose summaries agree, with means of 9.0 and 7.5 and a correlation of 0.816, yet the four scatterplots reveal four different structures. Matejka and Fitzmaurice (2017) turned that result into an algorithm. It generates datasets that are identical over chosen statistical properties and visibly different. A form that cannot be redrawn for its surface is an analysis that will not be delivered.

That algorithm produced a named artefact. Matejka and Fitzmaurice started from the Datasaurus, a seed dataset built by Alberto Cairo that plots as a dinosaur. They moved one point at a time and accepted a move only when the mean, standard deviation and correlation held to two decimal places. Simulated annealing biased the search towards a target shape. The result is the Datasaurus Dozen: twelve datasets that share the original's summary statistics to two decimal places and plot as twelve different pictures. The picture is the channel that carries the structure the summaries cannot.

Size, aspect ratio and separation are medium variables

Heer and Bostock (2010) also put a floor under the argument. The authors compared charts 40, 80 and 160 pixels tall on a 0 to 100 scale. Only the smallest height produced significantly more error. They concluded that there is

little benefit for increasing chart height beyond 80 pixels when using a 0-100 scale.

Aspect ratio is the second variable. Heer and Agrawala (2006) revisited Cleveland's rule, which says a line chart's aspect ratio should bank average segment orientation to 45 degrees, and they extended it into multi-scale banking. One carbon dioxide series shows an accelerating rise at 1.17 and seasonal fluctuation at 7.87. The data did not change. The display did.

Separation is the third variable. Talbot, Setlur and Anand (2014) measured it. Separated bars cost 0.81 percentage points of absolute error against adjacent bars. Divided bars cost 7.38, with an interval of 6.65 to 8.23, above the earlier estimates of 6.6 and 4.7.

Space decides whether series are split or shared

Javed, McDonnel and Elmqvist (2010) tested four ways of drawing several time series on maximum, slope and discrimination tasks. The four ranged from shared-space line graphs to split-space small multiples and horizon graphs. Split-space techniques were generally better for comparisons across a large visual span, while shared-space techniques were faster over small spans. More series reduced correctness and increased time, and less space per chart harmed correctness while barely affecting time. Split-or-share follows the span of the comparison, and a small display pays for its size in accuracy.

Density decides whether length or area wins

Kong, Heer and Agrawala (2010) studied area encoding in treemaps. Accuracy was worst for two squares or two extreme ratios such as nine to two, and best for moderate non-square ratios. That agrees with Heer and Bostock's (2010) finding that an aspect ratio of one performed worst for rectangular area. Luminance had no effect on area judgements. The paper locates the density at which the form changes. Bar charts were more accurate for leaf nodes in sparse data, and treemaps became faster as density rose. Length or area depends on how much data the display must hold.

The wall and the phone are physical objects

Ball and North (2005) observed five people using a nine-monitor tiled display of 3,840 by 3,072 pixels. Users adapted to the bezels to separate applications, but the mouse proved inadequate and users lost the cursor. Chittaro (2006) listed the constraints that make a desktop visualisation fail on a phone, including screen size, resolution, weaker hardware, unfamiliar input and a distracting context. He concluded that desktop visualisations do not port. A thumb on a phone, often the reader's only device on a metered connection, and a lost cursor on a wall are one class of fact: the surface decides which actions are cheap.

A chart is worth the knowledge it yields, less the cost of getting it

van Wijk (2005) supplies the accounting. He models a visualisation as a specification that turns data into an image and the image into knowledge. He writes the profit of a method as the value of the knowledge it yields, multiplied by users and sessions, less development, per-user and exploration cost. His summary is blunt:

a great visualization method is used by many people, who use it routinely to obtain highly valuable knowledge, without having to spend time and money on hardware, software, and effort.

Re-forming a chart for the wall as well as the phone multiplies development and per-user cost.

The form speaks as well as encodes

Zacks and Tversky (1999) add a constraint the rankings do not cover. Across three experiments, they found that readers associate bars with discrete comparisons and lines with trends. Bars are discrete entities that support point estimates, while lines connect them and represent slope. The association did not depend on taught rules. The authors attribute it to the graphs' perceptual properties and to the communicative situation. A reader reads the form before the numbers, so a medium that forces bars into a line changes the sentence as well as the legibility.

The contested question: does more display always help?

The literature disagrees about the shape of the medium's constraint. One position treats display as a resource whose return keeps rising. Ball and North's (2005) users almost unanimously preferred the multi-monitor desktop to a single monitor, and the difficulties they reported were of too much space rather than too little. A second holds that the return has been measured to stop. Heer and Bostock (2010) found no significant accuracy difference between a chart 80 pixels tall and one twice that. Javed and colleagues (2010) found correctness falling as series shared space. A third comes from van Wijk's (2005) cost model, in which a larger display that raises exploration cost lowers a method's profit. The positions reconcile only if the measure is stated, since the groups measure preference, perceptual error and cost.

An experiment would settle it. Take one task, one encoding and one dataset, and vary the display in steps from phone to projection to wall. Measure decision error, completion time and the navigation the reader performs. Hold the number of series and the data density constant, so that the split-or-share and density thresholds are not confounded with size. The prediction from the ranking of channels would be stated in advance and reported against.

The three positions rest on different evidence. The growth position rests on one six-month observation of five people (Ball and North, 2005), a case study of preference. The stopping position rests on a controlled experiment replicated on a crowdsourced sample (Heer and Bostock, 2010). The cost position is an economic model, not a measurement (van Wijk, 2005). While the dispute is open, a designer should state which measure is at stake, take the smallest surface that clears the perceptual floor, and buy more space only where a task needs it. The strongest objection is that the channel ranking has survived a single replication, so the claim that form follows the medium as much as the data outruns its evidence.

Where this is heading

The direction of travel is from one ranking towards thresholds. Kong and colleagues (2010) give the transition points at which one form overtakes another as density changes. Heer and Bostock (2010) give the chart height below which accuracy suffers. Javed and colleagues (2010) make split-or-share a function of the comparison span. Ball and North (2005) and Chittaro (2006) pull towards the physical costs no chart specification contains, so the next step is guidance stated as conditions rather than one ordering.

The sources this unit rests on

Each note states what the cited work did and found and what it adds to the argument. Identifiers and metadata were checked on 2 November 2026.

Anscombe, F. J. (1973). Graphs in statistical analysis. The American Statistician, 27(1), 17-21. doi:10.1080/00031305.1973.10478966 Built four datasets agreeing on their summaries, with means of 9.0 and 7.5 and a correlation of 0.816, yet four different scatterplots. Graphing belongs inside analysis, so the form carries the finding.
Ball, R. and North, C. (2005). Analysis of user behaviour on high-resolution tiled displays. Lecture Notes in Computer Science, 3585, 350-363. doi:10.1007/11555261_30 Six months observing five people on a nine-monitor display of 3,840 by 3,072 pixels; users adapted to the bezels to separate tasks but lost the cursor across the distance. The wall is a workspace, not a screen.
Chittaro, L. (2006). Visualising information on mobile devices. Computer, 39(3), 40-45. doi:10.1109/mc.2006.109 Surveys the constraints separating mobile from desktop visualisation, including screen size, resolution, weaker hardware, unfamiliar input and a distracting context. Concludes that desktop visualisations do not scale well to mobile devices, so a medium brings its own constraints.
Cleveland, W. S. and McGill, R. (1984). Graphical perception: theory, experimentation, and application to the development of graphical methods. Journal of the American Statistical Association, 79(387), 531-554. doi:10.1080/01621459.1984.10478080 Identifies ten elementary perceptual tasks and orders them by accuracy, from position along a common scale to shading and colour saturation last. It grounds the prediction of degradation.
Heer, J. and Agrawala, M. (2006). Multi-scale banking to 45 degrees. IEEE Transactions on Visualization and Computer Graphics, 12(5), 701-708. doi:10.1109/tvcg.2006.163 Revisits Cleveland's rule that a line chart's aspect ratio should bank average segment orientation to 45 degrees, and adds multi-scale banking for each frequency scale. One carbon dioxide series yields different findings at 1.17 and 7.87. Aspect ratio is a medium variable.
Heer, J. and Bostock, M. (2010). Crowdsourcing graphical perception: using Mechanical Turk to assess visualization design. Proceedings of the SIGCHI Conference on Human Factors in Computing Systems, 203-212. doi:10.1145/1753326.1753357 Replicates Cleveland and McGill's spatial encoding study with crowdsourced participants and recovers the ranking. Found more error only at 40 pixels of chart height and little benefit above 80. The surface has a floor.
Javed, W., McDonnel, B. and Elmqvist, N. (2010). Graphical perception of multiple time series. IEEE Transactions on Visualization and Computer Graphics, 16(6), 927-934. doi:10.1109/tvcg.2010.162 Compared shared-space line graphs with split-space small multiples and horizon graphs on maximum, slope and discrimination tasks. Split-space techniques were generally better across a large visual span and shared-space techniques over small spans; more series with less space reduced correctness. Space decides the form.
Kong, N., Heer, J. and Agrawala, M. (2010). Perceptual guidelines for creating rectangular treemaps. IEEE Transactions on Visualization and Computer Graphics, 16(6), 990-998. doi:10.1109/tvcg.2010.186 Found no evidence that luminance affects area judgement, while aspect ratio does: squares and extreme ratios performed worst and moderate non-square ratios best. Bar charts were more accurate at low density and treemaps faster as density rose. Density decides the form.
Matejka, J. and Fitzmaurice, G. (2017). Same stats, different graphs: generating datasets with varied appearance and identical statistics through simulated annealing. Proceedings of the 2017 CHI Conference on Human Factors in Computing Systems, 1290-1294. doi:10.1145/3025453.3025912 Perturbs a seed dataset under simulated annealing to produce datasets identical over chosen statistical properties yet visibly different. The form carries the finding.
Talbot, J., Setlur, V. and Anand, A. (2014). Four experiments on the perception of bar charts. IEEE Transactions on Visualization and Computer Graphics, 20(12), 2152-2160. doi:10.1109/tvcg.2014.2346320 Ran four experiments to explain why bar chart configurations differ in accuracy. Estimated the total separation effect at 0.81 percentage points and the absolute error of divided bar comparisons at 7.38 percentage points, the last above earlier estimates of 6.6 and 4.7. Spacing carries a measurable cost.
van Wijk, J. J. (2005). The value of visualization. VIS 05: IEEE Visualization, 2005, 79-86. doi:10.1109/visual.2005.1532781 Sets out an economic model in which a method's profit is the value of the knowledge it conveys, multiplied by users and sessions, less development, per-user, per-session and exploration costs. Cost belongs beside accuracy.
Wickham, H. (2010). A layered grammar of graphics. Journal of Computational and Graphical Statistics, 19(1), 3-28. doi:10.1198/jcgs.2009.07098 Describes a grammar assembling a plot from layers, each combining data, aesthetic mappings, a statistical transformation, a geometric object and a position adjustment, with scales, a coordinate system and facets. The surface is a design layer, not a rendering detail.
Zacks, J. and Tversky, B. (1999). Bars and lines: a study of graphic communication. Memory and Cognition, 27(6), 1073-1079. doi:10.3758/bf03201236 Three experiments, two on comprehension and one on production, tested whether readers associate bars with discrete comparisons and lines with trends. The associations appeared as predicted. The form carries meaning as well as numbers.

Check your understanding & apply it · 4 questions, 1 essay

1A figure must be delivered at a chart height of 40 pixels on a phone, because it sits beneath a news headline. Using the measurements the unit cites, which prediction about accuracy is best supported?

2A reader must compare twelve time series across a full year, and the display draws all twelve on one set of axes. Errors and completion times are both high. Using Javed, McDonnel and Elmqvist (2010), which diagnosis is best supported?

3A team must render the same twelve-region figure on a printed page, a projected slide and a phone, and the editor asks for the three versions to 'look consistent'. Using the unit's sources, which judgement about consistency is defensible?

4A manager argues: 'More pixels means better decisions, so the board should be given the nine-monitor wall.' Which judgement does the unit's reading of the evidence support?

5Essay A publishing team has to deliver the same quarterly figure on four surfaces: a printed column in the annual report, a slide projected behind a speaker, a phone notification card, and a wall of tiled monitors in the lobby. The data are one quarter of regional sales, twelve regions, with an estimate and an interval for each. The editor's brief says only that the figure must 'look consistent across all four'. Using this unit's sources, set out the decision you would make for each surface, identify what you would hold constant and what you would change, say how you would predict the cost of each change before testing it, and state the one measurement you would run to check your decision. Then give the strongest counter-argument to your approach and answer it.

The brief asks for consistency, and the first move is to say what consistency means. I would hold three things constant: the question, the ordering of the twelve regions, and the shared scale, because Wickham's (2010) grammar shows that locally scaled facets are not necessarily comparable across facets, so any surface that forces local scales has already broken consistency in the sense that matters. The form itself I would choose per surface. For print, a set of horizontal dot plots on a common horizontal scale, because Cleveland and McGill (1984) rank position along a common scale as the most accurate elementary task, and Talbot, Setlur and Anand (2014) show that separating the marks raises error, with an estimated separation effect of 0.81 percentage points, so adjacent rows on one axis are worth the space. For the slide, the same dot plot with fewer regions shown at once and the annotation carrying the headline, because a projector is read at distance and the interval is the part most likely to be lost. For the phone, I would test the chart at a height near the floor Heer and Bostock (2010) measured rather than shrinking the print figure, since they found significantly more error at 40 pixels and little benefit above 80 on a 0 to 100 scale, and I would drop the least important regions rather than the interval. For the wall, a scatter of estimate against region with the interval shown, because Ball and North (2005) show that a wall changes the reader's behaviour rather than only the resolution, and Chittaro's (2006) list of mobile constraints is the reminder that a surface brings input, distance and context with it. Before testing, I would predict each change from the channel ranking: converting position to angle or area should cost more than converting one position encoding to another, and shrinking below the measured floor should cost accuracy at a rate the bar chart experiments already bracket. To check the decision I would run one measurement, a value-estimation task on all four surfaces with the same data and the same question, recording error, time and navigation, because van Wijk's (2005) cost model means accuracy alone cannot decide, and Zacks and Tversky (1999) warn that changing bars into lines changes what the reader takes the chart to be saying. The strongest counter-argument is that four bespoke forms multiply development and per-user cost, and van Wijk's (2005) accounting makes the value of a method depend on how widely it is used and how little it costs to use routinely. My answer is that the shared scale and the shared ordering are what make the four versions one figure rather than four, and that the per-surface change is confined to the encoding layer, so the development cost is a parameter change rather than four designs.