Pie charts are a ubiquitous way of showing percentages. But while we can see differences in angles quite well, reading the meaning of the difference is another matter, so for precise data, we still need the numbers. A little known variant of pie charts is not round, but square, and can be read with an accuracy of one percent. We will look at data on women in information technology using this method.

The National Center for Women and Information Technology (NCWIT) publishes a very impressive one-page summary of the under-representation of women in IT (PDF). We all know, of course, how few women there are in IT, especially in leading positions. But seeing the actual numbers is still shocking. The graphics here use parts of that summary to compare numbers and charts.

Square pie charts are a technique that I have so far only seen in the book Diagram Collection, without much description (the image at the very top is a scan from the book). But the principle is really very simple: a square is divided into 10×10 fields, and for each number, as many fields are filled in as there are percent. Consequently, the numbers remain readable by simply counting the number of fields covered by one color. Taking a hint from squarified treemaps, the areas should also be as square as possible for better comparability. Square pies are quite compact, the ones in the images on this page are only 50×50 pixels.

Even to somebody not familiar with the technique, and with visualization in general, the technique should be obvious enough not to need an explanation. Like pie charts, square pies can be sexied up by adding a bit of pseudo-3D – and unlike pie charts, the 3D distortion does not affect the readability of the values, because the lines dividing up the fields are still there, and act as guides. The number of filled-in squares is much more robust than an angle, which changes considerably with any kind of distortion. The rectilinear nature of the display may be less attractive, but it certainly is more readable even under difficult conditions.

There is certainly more to be said about showing more than one value in a square pie chart, about squarifying or not, etc. Percentages over about 50% appear to be larger than they are if the area is squarified. Relative sizes in area are not as easy to judge as relative lengths, but it would be interesting to see how angles compare to both of them. Square pies seem to be most impressive when the percentages are very small.

Is this visualization? Probably not, because it lacks any kind of interaction. It is more a charting technique like pie charts, which can of course be used as a part of a visualization, with added interaction, etc. But it certainly is an interesting variation on existing techniques, and may offer some insight into how to structure visual metaphors for visualization more effectively.

Juice Analytics has picked up the idea of square pie charts and made it into a challenge to implement them in Excel. There are some very interesting submissions and a great screencast explaining two of them.

### 9 Responses to Women in IT – Squaring the Pie?

1. How are they different? They are both 2d representations of one D data, with varying conditions on the way the area is divided up.

I think in most cases (especially when the number of levels are small) side-by-side dotcharts or barcharts are better, as comparing length on a common scale is easier than comparing area (see Cleveland’s paper on the topic)

2. Robert Kosara says:

Sure, they are both 2D and rectilinear, but they show very different data. The square pie chart is for completely flat data that adds up to 100%, whereas the treemap shows structured data: a hierarchy. They may end up looking the same, but the meaning is not. I realize that treemaps are used for all kinds of unstructured data too, and so I guess in that sense they can be similar – but that is only when you considerably abuse the treemap.

The good thing about using area here is that you get a much higher resolution. For 100%, you need at least 100 pixels, and that will not be precisely readable. You would need much longer lines to make it possible for viewers to easily read the values. The square pie chart effectively folds the linear bar into an area that is much faster to understand. I know the perceptual issues, but I wonder if they can be circumvented by using a grid and showing areas as part of larger ones.

I think you need to think more deeply about the treemap. Yes, a treemap displays a hierarchy of data, but square piechart is a subset of the treemap – for datasets with only one level of hierarchy. Thinking about a tree map for a hierarchy with only one level, what does it do? It takes a rectangular area (or, in general, any shape) and divides it up into pieces so that the area of each piece is proportional to some value associated with each piece – this is exactly what the square piechart does. Different variants of the treemap use different principles to divide up the space.

I agree that the small aspect ratio allows you to pack more square pie charts in to a smaller amount of space, but I disagree that this is useful. The perceptual problems associated with assessing area are a considerable disadvantage. Sure you can count up the squares, but that’s not really any different to taking a protracter and measuring the angles on a piechart – it’s the low level processing that’s important.

4. Robert Kosara says:

True, but I maintain that this is an abuse of the treemap. Why use a treemap if your hierarchy is only one level deep? Why not use a square pie chart instead? :p The point here is that there is a difference in what the methods display, even if they end up looking the same. This is a semantic difference, not a visual one. The treemap does not subsume everything that is a partition of a rectangular space, otherwise you could argue that a bar chart is just a treemap that uses a special type of layout.

I don't think you have to count the fields to see them better than in a round pie chart. The grid gives you cues as to how much space is used up by what. I haven't tested this, but I think that if you compared a version with and a version without a grid, the one with the grid would do much better. I know that linear is more accurate than area, but I think that in a visualization context, other factors matter as well.

5. Imagine you have a hierarchy with two levels and you want to display it with a square piechart – is it a square piechart or is it a treemap? What I’m trying to get it is that it’s important to think about the principles that underly a visualisation, not the superficial differences. A square piechart and a treemap are similar at a deep level (and yes, in some ways a barchart is like a treemap).

I’m sure the version with a grid would do better, but I doubt it would do as well as a side-by-side barchart.

6. I just noticed that Naomi Robbins mention these in her book “Creating more effective graphs”, but calls them waffle charts, and cites the first use in a NY Times article in 2001.

7. Robert Kosara says:

The book I found them in is from 1997, but the idea is probably much older. Wolfgang Aigner has suggested that they were in fact invented by Otto Neurath, which would mean some time in the 1920s.

8. It would be great to track down an original reference. Some historical context is always nice.

9. [...] remove gaps and you get this:I’m shamelessly copying the first image in Robert Kosara’s Square Pie Charts (I don’t know how Robert made his). Check his post. He makes some square pie charts like [...]