Monday, January 14, 2008

Visual meaning readings: statistical graphics

Hi folks,

Here's the set of readings for tomorrow -- last minute I admit. Make sure you read the short first paper, and if you have time, look at the second -- we'll discuss it Thursday if necessary. As I said earlier, reactions are not due until Thursday (while Thursday's reactions are due Wednesday).
  • William Cleveland, Robert McGill. (1985). Graphical perception and graphical methods for analyzing scientific data. Science, 229, 4716, 828-833. Full text available through our library.
  • William Cleveland, Robert McGill. (1987). Graphical Perception: The Visual Decoding of Quantitative Information on Graphical Displays of Data. Journal of the Royal Statistical Society. Series A (General), 150, 3, 192-229. Full text available through our library.
For those who are intrigued and want more, Cleveland has also published a couple of interesting books in the early 90s. Another early paper on visualizing internet data also caught my interest:
  • William Cleveland, Don Sun. (2000). Internet traffic data. Journal of the American Statistical Society, 95, 451, 979-985. Full text available through our library.



Unknown said...

I've read other perception literature (for example some of Julesz's work that the paper mentions) and one thing that struck me at the beginning was the authors' choice of using graphs for their tests. I haven't seen others use them, usually it is figures on a field of other figures. I found using these graphs to be much better representative examples of concepts.

One thing I noted is that they explain slope vs angle judgments in relation to Fig. 2. I'm sure what they are saying is accurate, but they do the reader a disservice in their presentation. By surrounding the near vertical and horizontal lines with such narrow rectangles, they are playing on other parts of our perception that change how the line itself is perceived. Were these graphs presented in this form to the original test subjects?

I thought their other prime example, the distance between curves, to be very enlightening. Besides their comments, it appears to me that on the parts of the curves with large slopes they appear closer because we perceive points to more in a ray-pointing-out-from-center-of-the-curve than strictly vertical. By that I mean, without concentration, you equate points on the curves that are near each other rather than what are mathematically equivalent.

The end of the paper, where they compare graphing methods, seemed a lot less interesting to me and so I didn't get as much out of it.

Unknown said...

My last post was in relation to the 1985 paper, the shorter of the two.

The other paper seems to be a further analysis of some of the ideas in the first. They go back into the vertical versus horizontal observations; is 45 degrees special because it is the midpoint of horizontal and vertical or are there other factors?

These studies appear to have been done on a computer monitor. Back then, these were square so I wonder if there is any difference in perception when using a square monitor vs widescreen vs a widescreen turned vertically.

I also wonder if relative size makes any difference. The authors point out that, when comparing lines, the ratio matters and the actual lengths do not (so 5mm vs 5.1mm is the same comparison as 50mm to 51mm). This makes sense when you have unlimited time to look at something. However, in the study of this paper, participants are given a very short time to look at the lines, does this have any effect on the results? Two small lines in the middle of a screen would be easier to "take in" versus two lines that take up an entire screen. Granted, back then monitors were not very big, so I'm thinking in terms of today's large widescreens.

Stuart Heinrich said...

Response to: Graphical Perception and Graphical Methods for Analyzing Scientific Data
Reviewer: Stuart Heinrich

One of the primary abilities measured by the authors is the subjects ability to estimate ratios between slopes visually. They showed that it is easiest to estimate the ratio between slopes when those two slopes are near to 45 degrees, because this is the angle that maximizes the difference between angle or orientation of two lines having the same ratio between their slope. In the second paper, the authors verified this with more experimental evidence.

However, this should be directly obvious because the difference between angles of two line segments having the same slope ratio approaches 0 at 0 and 90 degrees, and slope is just a mathematical concept that is a function of the orientation, which is actually visible.

In other words, the difficulty in assessing the ratio between slopes as the slopes approach 0 or 90 degrees has nothing to do with the human visual system -- it has to due with a loss of precision due to the nonlinearity of the function. For example, a computerized scanning device that measured the difference between angle slope would be subject to the same principle, although due to the precision of the instrument it would have a higher tolerance than humans.

One of the other major arguments made by the authors was that it was easier to observe the difference in lengths if they are lined up on one side. This also is obvious and intuitive, because it maximizes the distance between the endpoints graphically.

On the same principle, the authors demonstrated a weak optical illusion where the viewer was asked to pick the X value that maximized the Y distance between two vertically stacked parabola. The human eye, having no reason to perceive the X and Y components of distance separately, naturally chooses the peak of the parabola (which is the point where the difference between curves is maximum), even though the Y distance is maximized at a different point. Therefore, one can conclude that if the Y distance between two curves is important, it should be graphed as a separate function of x.

Overally, I did not think that this paper contained enough insight to be worth of publication, because all of their conclusions are either intuitively obvious or straightforward to prove.

In the second paper, the Median-Absolute-Slope Procedure demonstrates a phenomena that is intuively obvious: if the graph is stretched out too much, you can't really tell what it means. Their procedure provides an algorithm that can automatically find a good stretching factor in many situations, which makes it a potentially useful too for computer generated graphs.

Ryan said...

Graphical Perception and Graphical
Methods for Analyzing Scientific Data

To begin, I agree with alex that I definitely got more out of the first half of the paper than the discussion of various graph types at the end. I liked the idea of ranking how our visual perception can analyze various types of information encoding. I assume this was relatively early work in this field; their rankings could use a lot of polish and further experimentation to justify, which to their credit they readily acknowledge.

As we mentioned in the class discussion, I am not a big fan of their comparison of visual perception of slope vs. angle. They seem to want to ignore the non-linearity of slope and how it makes it dramatically more difficult for humans to intuitively compare slopes and slope ratios compared to the linear angle comparisons. My other complaint with the paper is with their use and arrangement of their figures. Being in Science magazine they probably had less control over this, but it is still very annoying. They put multiple charts and figures with no connection between them together which added a lot of confusion.

Graphical Perception: The Visual Decoding of Quantitative Information on
Graphical Displays of Data

I liked the methodology of this paper more, as they looked much more thoroughly into their subject and backed their ideas up with theoretical and experimental support. Unfortunately I'm not nearly as interested in the discussion of the "best" shape parameter for a graph as I am for discussions of how our visual perception handles different forms of data encodings.

Ben Watson said...

Hey everyone, thanks for your comments. I have to agree that the layout in this paper was awful. Given that these papers were about visual clarity, that's particularly ironic!

Like most of you, I'm also troubled by the use of the slope/angle figure as a primary example. While we do compare line segment orientation in real life, as the authors say we intuitively do it in an angular fashion. Even the notion that we'd do this in terms of slope, which range from -inf to inf, strikes me as ridiculous. For example as we pointed out in class, the same angle between two line segments results in different ratios depending on the orientation of both segments in their global setting! It might be 1 sometimes, 0 other times, inf other times, etc.

Can't completely agree with Stu about how "obvious" the paper's insights were, for several reasons. First, this paper is about twenty years, old, so the knowledge they present was quite uncommon. Second, noticing the obvious is often the hard part: it's so obvious we usually go right past it! Third, I'm not sure that the authors' ordering of various visual forms is really obvious at all.

Thanks and best,