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我们该如何读饼状图？饼状图和饱受诟病的环状图有什么不同之处吗？把普通的饼状图设计成分离型可以吗？接下来，我们将为读者一一解答这些问题。事实上，饼状图展示的信息远比我们想象的要多得多。
一直以来，饼状图在可视化领域受到不公平的对待。很多人以攻击饼状图及使用饼状图的人为傲。这种现象也确实由来已久。但是在商务汇报和信息图表中，饼状图的确实是十分常用的。
我们写这些文章是基于这样一个疑问：我们知道自己是如何读这些图的吗？是大家通常所说的读角度？还是读弧长或是面积？事实上，无论是哪种说法都没有调查研究的结果来支持其说法。关于论证，我们只找到了一篇写于1926年的文章，这篇文章曾被广泛引用。然而那是90年前写的文章了，而且作者仅仅是询问他人，也并没有给出最终的结论。所以这篇文章也是相当不可靠的。
我们开始针对这一问题进行研究，下面我们将就两项研究进行结果展示。
第一个研究是真正的读图方法。我们解析图表的构造然后去编制成计算机语言即编码。我们用这些编码的变化来评估人们真正使用的方法，无论人们宣称自己怎么读图，我们都可以得到正确的结论。
上图中从左到右分别是饼状图、环状图、弧线图、饼状角图，环状角图，面积图。
测试的结果非常有意思：完整的饼状图和环状图的结果最好的，而只显示角度的图结果最差，弧线图和面积图的结果基本上差不多。让我们感到意外的是，面积图的结果也很好，这是我们之前没有预料到的。
这个测试结果能说明什么呢？这说明读角度并不是我们读饼状图的主要方法，也绝不是唯一方法。这么说不仅是因为弧线图的结果和面积图差不多，还因为饼状图和环状图的结果并没有很大差异——因为环状图没有圆心，人们很难读角度。
第二个研究是环状图的内径对读图的影响。所以我们测试了一组不同内圈大小的环状图（以实心饼状图作为参照）。
结果是这些图的测试结果都是相同的，除了最细的那个比其他的要差一些（我们还不知道原因是什么）。这就说明环状图在结果展示上并没有比饼状图差！对于这个结果，我们之前并没有想到，想必这个结果也和很多人所想大相径庭。
在以上结论的基础上，关于常见的饼状图变形，对于其在商务汇报和信息图表中表现如何，我们做出了预测。相应的我们开始了进一步的研究与测试。
上图中，从左到右分别是：基础饼状图，部分放大饼状图（常用来强调），分离型饼状图，和两个特殊形状饼状图。我们设计了以上这些图形来模拟那些基于饼状图做出的图形，而基于饼状图做出的这些图形一般都是放在一些模型上的（通常是比椭圆和正方形更为复杂的模型）。
如果你依然认为我们是看圆心角读饼状图的话，那么按照这个理论，部分放大图和分离型饼状图并不会妨碍我们看圆心角，所以我们应该能够像看普通饼状图那样准确读图。然而得到的结果却颇让人感到意外。这两种图形都造成了较大的误差。部分放大图明显导致了人们高估其真实值。对比普通的饼状图，变形的图表不出意外的表现更差。
因此，如果你为了追求精确的表达，一定不要把你的饼状图变形了，也一定不要改变它们的形状，同时也不要分解图形或者把其中某一部分放大。
无论你是否喜欢饼状图，我真的一点都不在意。但是可视化要求科学性，所以我们假设的规则要基于证据——而不是谣传、个人观点或者是美学评价。那么还有什么其他的假设是没有根据的呢？在可视化领域，其实还有很多我们自认为了解实际上却没有系统研究的地方。因此，在基础研究这块，确实还有很多机会等待我们发挖掘。
A Pair of Pie Chart Papers
How do we read pie charts? Do they differ from the even more reviled donut charts? What about common pie chart designs like exploded pies? In two papers to be presented at EuroVis next week, Drew Skau and I show that the common wisdom about how we read these charts (by angle) is almost certainly wrong, and that things are much more complicated than we thought.
Pie charts are generally looked down on in visualization, and many people pride themselves on saying mean things about them and the people who use them. This is not a new phenomenon, either. Yet they are incredibly common in business settings and information graphics.
The main reason for these papers was the question: do we even know how we read these charts? Is it actually angle, as is usually claimed, or is it really arc length or maybe area? It turns out that there is no actual research to back up the claims that it’s angle. The only paper we could find, and which gets cited over and over again, is from 1926. That’s ninety years ago. And the author just asked people what they thought they used, which is quite unreliable.
So we set out to do some science around this. The full paper reports on two studies to assess the mechanism for pie and donut charts. and look at the effect inner diameter has on donuts. For the short paper, we then took some of the things we had found and tested common pie chart variations. Yes, this is the full-plus-short paper package I mentioned a while ago.
Arcs, Angles, or Areas: Individual Data Encodings in Pie and Donut Charts
Skau-EuroVis-2016-pagesThe full paper reports on two studies. One presented participants with deconstructed charts that were designed to test encodings independently from each other. Measuring their accuracy when using any of these variations, we could assess which of them was actually being used, no matter what people claimed.
From left to right, they are: pie, donut, arc-only, angle-only based on pie, angle-only based on donut, and area-only.
The results are quite interesting: the complete pie and donut charts do the best, while the angle-only conditions are the worst. People were surprisingly good with the area-only condition (far right), which was completely unexpected. Arc-only is virtually identical with area-only.
What does this mean? Angle is not likely the main, and certainly not the only, way we read pie charts. This is not only based on the arc-only results, but also the fact that pie and donut charts did not differ in a significant way – donut charts lack the center, so they should make judging angle harder.
We also wanted to see if there was an effect from the inner diameter in donut charts. So we tested a set of donuts with varying hole sizes (with the “no-hole” pie chart serving as a baseline).
There is no difference between them, other than the thinnest donut being worse than the rest (we’re not sure exactly why). Donut charts no worse than pie charts! Who knew!?
The paper has a lot more information about the studies and detailed analyses of the results: Drew Skau, Robert Kosara, Arcs, Angles, or Areas: Individual Data Encodings in Pie and Donut Charts, EuroVis 2016.
Code and data are also available, for both the arcs-angles-areas study and for the donut radii study
Judgment Error in Pie Chart Variations
Kosara-EuroVis-2016-pagesBased on the full paper, we had some predictions for what should happen for specific pie chart variations that we often see in business presentations and information graphics. We ran a further study to test some of those.
Left to right, there’s a basic pie chart, a pie chart with a larger slice (often used for emphasis), an exploded pie chart, and two pies with unusual shapes. We designed those to mimic the sort of icon-based pie charts that are fairly common in infographics, where segments are drawn on top of some shape (usually much more complex than the ellipse and square).
The results are quite surprising, certainly if you still think that central angle is how we read pie charts. The larger slice and exploded pie chart don’t distort the angle, so we should be able to read them just as accurately as the base pie chart.
And yet, they both led to more error. The larger slice in particular led to a clear and systematic overestimation of the value. The distorted charts, unsurprisingly, did even worse.
If you’re after precision, don’t distort your pie charts. Certainly don’t change their shapes, but also don’t explode them or make a slice larger.
Again, the paper has quite a bit more detail and depth: Robert Kosara, Drew Skau, Judgment Error in Pie Chart Variations, EuroVis Short Papers 2016. Code and data are also available on github.
I don’t care if you like or dislike pie charts. I really don’t. But visualization wants to be a science, so our supposed rules need to be based on evidence – not hearsay, opinion, or aesthetic judgments.
If we can’t trust the common wisdom on pie charts, what can we trust? What other assumptions are unfounded? There are many other areas in visualization where we think we know what’s going on, but it hasn’t been systematically studied at all. That’s still lots of opportunity for truly fundamental research.
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