# Arcs, Angles, Or Areas: Individual Data Encodings In . - Tableau Software

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Skau & Kosara / Arcs, Angles, or Areas(a)(b)(c)(d)Figure 3: A sampling of pie and donut charts used in infographics, taken from examples found on Visual.ly [Vis15]. (a) exploded pie chart,(b) chart with varying segment radii, (c) pie chart constructed with an icon, and (d) nested donut chart.(a) Pie chart.(b) Donut chart.(c) Arc length chart.(g) Pie chart.(h) Donut chart.(i) Arc length chart.(d) Angle pie chart.(j) Angle pie chart.(e) Angle donut chart.(k) Angle donut chart.(f) Area chart.(l) Area chart.Figure 4: A sampling of charts used in the study of pie and donut chart encodings. The top row all represent 67%, while the bottom row allrepresent 33%.3. Study 1: Arcs, Angles, and Area Study3.1. MaterialsIn order to test the contribution of each visual encoding, we designed new charts that allow us to isolate each retinal variable asmuch as possible (Figures 1 and 4). This allowed us to test the accuracy of arc length, angle, and area independently of their counterpart encodings.The design of the test charts is key to being able to independentlytest the data encodings. Every chart has two segments. Pie charts“in the wild” often have more divisions, but we chose to constrainour stimuli to two parts to avoid complicating the task. In all of thecharts, the blue portion is the segment referenced in the question(Figure 4). The rest of the charts are light gray, so the blue is theonly color (and also darker), providing a clear focus and reducingdistractions.We hypothesized that the baseline charts would be more accurately interpreted than any of the individual encodings, and thebaseline pie chart would be the most accurately interpreted of allchart types. Of the individual encodings, we expected the chart typedisplaying arc length to perform the best because it is most similar to an extremely thin donut chart. We expected the angle chartfor pies to be the next best performer, and then the angle chart fordonuts.However, we did not expect the individual encodings to performmuch worse than the baseline charts. The rationale for this wasthat people presumably use a single cue to read a chart, rather thanaveraging from multiple ones.c 2016 The Author(s)Computer Graphics Forum c 2016 The Eurographics Association and John Wiley & Sons Ltd.The study uses six different chart types (Figure 4): Baseline Pie – a standard pie chart (Figures 4a and g) using allthree visual cues to represent the number. Baseline Donut – a standard donut chart (Figures 4b and h) using area and segment length to encode data. The angle is muchmore difficult to read due to the missing center where the lineswould meet. Arc – a chart showing only arc length (Figures 4c and i), withoutarea or angle.

Skau & Kosara / Arcs, Angles, or AreasPie Chart1008060Before Study1626Donut ChartAfter Study Before Study2420Eells StudyAfter 25AreaFigure 8: At the beginning and end of the study, participants were asked about the encoding they primarily used to interpret pie and donutcharts. These are compared with self-reported answers from an earlier study [Eel26].Distribution of Error Segmented by Visual Variable Preferencemean error4AngleArcLength2Area0Figure 9: The distribution of error segmented by the second self-reported encoding preference for pie charts. People using angle did better inthe angle-only condition than ones who reported using area or arc length. Black lines represent the means for each encoding preference perchart type, error bars show 95% confidence intervals.Taken together, our results allow us to establish an ordering interms of accuracy (with meaning “no different”): baseline donut baseline piearc areaangle pieangle donutEncodings do not seem to combine in an additive manner. Instead, they appear to work together to substitute for the missingencoding when one is absent (as in the donut chart). Angle appearsto contribute the least to the accuracy of the chart’s communication.Arc length has a greater impact on the communicative value of thechart, however it still does not match all three encodings combined.4. Study 2: Donut RadiiThe results of the first study suggest that angle has a minimal contribution to our ability to perceive pie and donut charts. But withindonut charts, does the size of the hole in the center make a difference? It should if angle is important, since any hole removes themost salient portion of the angle encoding: the center where thec 2016 The Author(s)Computer Graphics Forum c 2016 The Eurographics Association and John Wiley & Sons Ltd.lines meet. Arc length is still present, as is area unless the donutgets extremely thin.We therefore ran a study varying the inner radius of the chartsfrom zero (i.e., a pie chart) to the point where only a thin outlinewas left. Our hypothesis was that the different inner radii wouldshow no difference in how accurately they were interpreted. Basedon the previous study’s results, we expected the thinnest donut chartto have somewhat worse performance because of the higher errorfor the pure arc length compared to the donut tested there, but wereunsure at which point accuracy would start to degrade.4.1. MaterialsWe chose a set of six inner radii to ensure good coverage of therange of possible donut designs: 0% – a pie chart (Figure 10a)20% – a small hole in the center (Figure 10b)40% – a medium hole in the center (Figure 10c)60% – a thick circle outline (Figure 10d)80% – a thin circle outline (Figure 10e)97% – a very thin circle outline (Figure 10f)

(g) Pie chart. (h) Donut chart. (i) Arc length chart. (j) Angle pie chart. (k) Angle donut chart. (l) Area chart. Figure 4: A sampling of charts used in the study of pie and donut chart encodings. The top row all represent 67%, while the bottom row all represent 33%. 3. Study 1: Arcs, Angles, and Area Study

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