When we talk about accuracy of visual channels, we also have to talk about experiments in graphical perception. What are these experiments? Well, over the years visualization researchers have been running lots of experiments to understand effectiveness of visual channels. And in particular, we have to talk about the work of Cleveland and McGill. So what does these researchers do? Well, they run very seminal study trying to understand how effectively certain number of channels can represent quantitative information. How did they do that? Well, they did it through a very interesting experiment. In the experiment, they have shown different types of charts, like the one that you see in front of you here, a simple bar chart. And then, marking the elements of this chart with a little dot and asking the subjects to estimate how much bigger one was compared to the other. So imagine that I'm showing this chart to you, and I ask you how much bigger is B compared to A. And then, you give me an estimate, say, 50% bigger, 40% bigger, and so on. So what they did was to run this experiment with different types of visual tasks, and using different types of charts. In this case, you see that we have five different types. And they always ask for different types and different information, different data to estimate how much bigger is one compare to the other. But if you look carefully, these different types actually introduce, use slightly different ways of representing information, representing quantities. So in the first one, Type 1, we have the length of the bar is used as a way to represent information. And these bars are one next to another, okay? In Type 2, it's exactly the same thing, but the bars are wider. In Type 3, it's exactly the same, but the bars are much more far apart. In Type 4, you see that the dots are only on the segments that are on top. So what is important here to note is that even though in these two bars we are representing quantity by the length of the bars, these bars are actually not aligned. And because of that, we expect the estimate to be worse, to be harder to make. And the same is true four Type 5, with the difference these two segments of bars are actually not separated, but were at one on top of the others. So the main question of the experimenters here was is there a difference between these types? If I ask my subjects, a sufficiently large number of subjects, to make estimates about how much larger is one element compared to the other, do I get different estimates? And it turns out that, yes, it does lead to different estimates. So this is the chart that you see below represents the result of the study. And the dots represent the average amount of error across all the participants. And as you can see, Type 1 is the one that leads to the best estimate. Followed by Type 2, then Type 3, then Type 4, and Type 5. And as you can see, Type 4 and Type 5, which are those in which the estimate is due to the length of bars that are not aligned, perform much worse than the rest. So why is this important and useful? Well, it's important and useful because it gives you a first guideline on what to do when you are encoding information with different channels. In this case, we can say that if we are representing quantitative information with the length of a bar, the encoding is more effective when the bars are aligned than when they are not aligned. The same type of experiments has been performed with different channels. There is another one that Cleveland and McGill performed that includes a different channel. So in this experiment, they have been comparing the length of the aligned bars to the angles or areas represented in pie charts. So think about how the same information is encoded in a pie chart and a bar chart. In bar charts, we're using the length of the bar to represent quantity. Whereas in a pie-chart, we're using the angle and the area. Okay, so they perform exactly the same type of experiments. And the results showed that representing information with the length of aligned bars is much, much more effective than representing information with the angle and area of a pie chart. So what does this mean for visualization? Well, that you have another useful guideline. If you want to represent quantitative information, it's in general preferable, if possible, to use length and position of a bar rather than the area and angle of a segment of a pie chart.