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The author conducted studies comparing estimation of parts with pie chart and bar chart visualizations. Students in a college course were given a sheet containing a series of pie charts and were asked to label the parts in each chart. The following week they did the same with a sheet of bar charts. Speed is measured by how many charts the student has completed after 5 minutes in the 13 minute experiment. The time spent on pie charts is very similar to bar charts with pie charts being slightly faster. Pie charts were found to outperform bar charts in terms of accuracy where they had smaller error and fewer large errors (greater than 3 points) than bar charts. The author concludes the pie chart is the superior choice for this task contrary to many cited works describing their inferiority without evidence.
[@eellsRelativeMeritsCircles1926a]
The authors note several limitations to the study done by Eells including that there is no condition including a scale for the bar chart and there are no tests of comparison tasks which they suppose bar charts will perform better at. They conduct a study comparing two bar charts with the equivalent pie charts. Each chart has two segments one set with a ratio of 1:1.5 and the other with ratio 1:4. The users are asked to report their answer in terms of the ratio of part A to part B. In terms of correctness, they find the bar chart outperforms the pie chart in both conditions and in terms of error in one condition.
[@vonhuhnFurtherStudiesGraphic1927]
The authors conducted studies comparing the estimation of parts using pie charts and bar charts in a similar manner to the Eells study but with a larger number of participants. The charts are presented with 2 to 5 segments individually on cards in a determined order and the subjects are asked to give the values for each segment. The authors attempt to characterize the chart with the higher accuracy for the different conditions and find that the pie chart outperforms the bar chart in all cases except for two cases with only two segments.
[@croxtonBarChartsCircle1927]
[@croxtonGraphicComparisonsBars1932a]
[@petersonHowAccuratelyAre1954]
[@culbertsonStudyGraphComprehension1959]
Graphical Perception: Theory, Experimentation, and Application to the Development of Graphical Methods
[@clevelandGraphicalPerceptionTheory1984]
[@clevelandGraphicalPerceptionGraphical1985]
[@clevelandGraphicalPerceptionVisual1987]
The authors conduct studies comparing bar, stacked bar and pie charts with two segments on proportion (the percentage of the segment relative to the whole), comparison (the percentage the smaller segment was of the larger), and discrimination tasks (the larger of the two segments). In the first experiment the subjects were given a 1 or half second viewing time and in the second experiment they answered at their own pace. As expected, the pie chart performed well for the proportion tasks while the bar chart performed well for the comparison and discrimination tasks. They then propose schematic summaries pairing their results with prior work to combine scanning, projection, superimposition, and detection operators to the three tasks and charts in the studies. They propose that the proportion task uses anchoring then scanning, comparison uses projection, then anchoring, then scanning for bar charts but requires superimposition, then anchoring, then scanning for the stacked bar and pie charts. The suppose that anchoring is the key process for the proportion task and pie charts salient 0, 90, 180 degree anchors support this well explaining the advantage. They claim that angles provide the least accurate estimates because of the inferior anchoring when not at perceptually salient angles.
[@simkinInformationProcessingAnalysisGraph1987]
[@lewandowskyPerceptionStatisticalGraphs1989]
[@spenceDisplayingProportionsPercentages1991a]
[@hollandsJudgmentsChangeProportion1992]
[@hollandsJudgingProportionGraphs1998]
[@hollandsBiasProportionJudgments2000]
The author of this blog post describes the flaws of the pie chart and argues that they should not be included in a visualization design program. They state that the primary strength of the pie chart is that the part-whole relationship is built into it in an obvious way and that the only advantage of the chart is that it is superior for understanding the combined proportion of parts in a dataset based on the studies by Spence and Lewandowsky. He claims that a bar chart with a quantitative scale is only slightly less effective than a pie chart for a 25% segment and that pie charts are only effective in judging values at 0, 25, 50, 75, and 100 percent but that these values can be better visualized by a bar graph. He also claims that alignment is a significant aid in reading values from a pie chart. He notes that adding labels and values to a pie chart is equivalent to producing a poorly designed table and that a bar chart is a better visualization than either a table or a pie chart. He also notes that augmentations such as 3D effects, internal divisions, transparency and gloss are harmful to reading the charts. Finally he states that comparisons between pie charts are difficult and this task is much better served by bar, line, and area charts.
[@fewPiesDessert2007]
[@heerCrowdsourcingGraphicalPerception2010]
[@kosaraMechanicalTurksDream2010]
[@spenceNoHumblePie2005]
The authors conducted a study comparing four variations of pie charts to a standard pie chart acting and a control. The variations were an expanded slice, an exploded pie, an elliptical pie and a square pie. They find that all variations cause an increase in error including those that do not distort the central angle. They find no change in response time and are unable to show a difference between models for angle, arc, or area compared with the results. This supports the idea that all three methods are used in estimating values from pie charts.
[@kosaraJudgmentErrorPie2016]
[@kosaraEmpireBuiltSand2016]
The authors conducted a study comparing baseline pie charts to a donut chart, an arc length chart, an angle chart, an angle donut chart and a circular area chart. The goal is to determine which encodings cause an increase in error over the baseline pie chart in order to determine which method is used for interpreting pie charts. The error for the angle only charts was greater than for the other charts. They conclude that angle encodings work well for some people but arc length and area work well for all. They also note possible issues with the angle only encoding of the chart that could call into question this conclusion. They asked participants what they thought they were using to read the charts and show that people who said they used angle performed better on the angle charts than those reporting another method. They note that encodings seem to combine in an additive manner with none of the individual encodings matching all of them combined. Finally they compare 6 donut charts with inner hole of size 0% to 97% of the radius. They show no impact from the donut chart variations except at 97%.
[@skauArcsAnglesAreas2016]
The author conducted a study comparing various angles of 3D projections of pie charts at 90, 60, 30, and 15 degrees with 90 degrees being the equivalent 2D pie chart. They created models for users reading the charts by area, arc length, and angle based on the distortions introduced by each projection and fitted them to the results. The models fit showed area as the best fitting model followed by angle and then arc length. This indicates that area is the likeliest method for reading pie charts but does not rule out other possibilities such as back-projection into 2D and using another method. They are also able to show increased absolute error for the 30 and 15 degree conditions compared with the 2D chart.
[@kosaraEvidenceAreaPrimary2019]
The author conducted a series of studies comparing the performance of pie charts and horizontal stacked bar charts with various visual cues for estimating viewer estimation of part-whole relationships. The charts have two segments each and the viewer must estimate the value of the indicated part in the pie chart or the stacked bar chart. The findings show visual cues in stacked bar charts improve accuracy, pie charts outperform stacked bar charts, and that there is evidence of natural visual anchors in baseline pie charts that subjects are using with pie charts.
[@redmondVisualCuesEstimation2019]
[@kosaraCircularParttoWholeCharts2019]
[@kosaraImpactDistributionChart2019]