In this age of data visualization, it is important to understand our perception of the symbols that are used. For example, does the perceived size of a disc correspond most closely to its area, diameter, circumference, or some other measure? When multiple items are present, this becomes a question of ensemble perception. Here, we compare observers’ performance across three different tasks: judgments of (i) the mean diameter, (ii) the total diameter, or (iii) the total area of (N = 1, 2, 3, or 7) test circles compared with a single reference circle. We draw a parallel between Anne Treisman’s feature integration theory and Daniel Kahneman’s cognitive systems, comparing the preattentive stage to System 1, and the focused attention stage to System 2. In accordance with Kahneman’s prediction, average size (diameter) of the geometric figures can be judged with considerable accuracy, but the total diameter of the same figures cannot. Like the total length, the cumulative area covered by circles was also judged considerably less accurately than the mean diameter. Differences in efficiency between these three tasks illustrate powerful constraints upon visual processing: The visual system is well adapted for the perception of the mean size while there are no analogous mechanisms for the accurate perception of the total length or cumulative area. Thus, in visualizing data, using bubble charts proportional to area may be misleading as our visual system seems better adapted to perceive disc size by the radius rather than the area.

中文翻译：

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均值，总和和面积的感知。

在这个数据可视化时代，了解我们对所使用符号的理解非常重要。例如，光盘的感知尺寸是否最接近其面积，直径，周长或其他度量？当存在多个项目时，这成为整体感知的问题。在这里，我们比较观察者在三个不同任务上的表现：（i）平均直径，（ii）总直径或（iii）总面积（N= 1、2、3或7）测试圈与单个参考圈的比较。我们将安妮·特赖斯曼（Anne Treisman）的特征整合理论与丹尼尔·卡尼曼（Daniel Kahneman）的认知系统进行了比较，比较了系统1的注意阶段和系统2的注意力集中阶段。根据卡尼曼的预测，几何图形的平均大小（直径）可以为判断精度相当高，但相同图形的总直径无法。像总长度一样，圆圈所覆盖的累积面积也被判断为比平均直径准确度低得多。这三个任务之间的效率差异说明了视觉处理的强大约束：视觉系统非常适合平均大小的感知，而没有类似的机制可以精确感知总长度或累积面积。因此，在可视化数据时，使用与面积成比例的气泡图可能会产生误导，因为我们的视觉系统似乎更适合通过半径而不是面积来感知圆盘大小。