Stephen Few acknowledges that pie charts perform better than bar charts when combining adjacent proportions and that’s my starting point. I don’t agree with him when he says that combining proportions is a rare event in the real world. I’m trying to show that combining proportions should always be considered when the user has a large number of categories and a pie chart may be a good option.

In Excel you can grab the slice to explode it. It wouldn’t be very difficult for Microsoft to extend this functionality to allow the user visually reorder the slices. If this option is not available you should know in advance how your audience wants to combine the data or how you want the chart to support your message.

In the end, I agree with you: if you have non-adjacent proportions a bar chart is probably a better option.

1) Dynamic Charts/On-Demand details would be good for any chart when done right, not just pie charts, so I think that part of your post is just a good practice when one has a medium where an interactive chart can be used.

2) Your primary conclusion for pie charts is that “They seem to be more efficient than bar charts in some very specific tasks, like comparing combined proportions.” I would argue that this is only the case if you know ahead of time what categories are going to be combined. That is, if you were using the chart above as support for an article specifically comparing Living Expenditures and Discretionary Expenditures then your argument that one can quickly look at the two groups and see that there is an approximate 60%/40% ratio between the two groups is valid.

One primary deficiency I see in the combining proportions argument is that combining proportions in a pie chart is only easy if the slices being combined are adjacent slices.

Example: from the above pie if I was actually interested in combining food & beverage, transportation and personal finance categories it is not as easy a process. Mentally I step through by saying “Food & beverages” is a little larger than the combined health care and apparel slices, thus when combined with transportation it would make more than 1/4 of the pie so say 30% for those. Then I look at the personal finance and since it falls fairly close to 1/8 of the pie (luckily the right border of the slice is nearly at “12-o’clock” on the pie making the 1/8 estimate easy), but it does look a little larger than 1/8 (12.5%) so I will say it is ~15% and thus in total those groups are ~45%. So, as long as the slices line up to make it easy to estimate 1/2, 1/4, or 1/8 I can probably get by with okay estimates. If I were using a vertical bar chart with horizontal lines at every 5% though this combining proportions would be much simpler, I’d have higher confidence in my combined proportion and my hypothesis is that I’d typically be more accurate in my estimate. (combining sub-portions from the arcs is even more difficult because all you have is the arc)

This brings up two possibilities, one is if you have your dynamic/on-demand chart maybe you could drag the slices around and reorder them so that you will always be combining adjacent slices (dragging bar charts to reorder would/could help too, I haven’t really seen something like this used to address sorting issues, but would be nice if we could easily create interactive charts that allowed sorts or arbitrary ordering of the graphic elements).

Another possibility would be if you had a pie equivalent to the horizontal lines on a vertical bar chart. If I had a dashed light gray line (or something similar) every 5/10% of the pie chart my ability to estimate the size of any individual slice would be improved. Though it would have to be done in a way that would make it clear that these are not the edges of the pie.

So in the end, I think your efforts are interesting, but unless you want to split the pie into two groups that are already adjacent (and hopefully fall close to lines that would be at 1/8’s of the pie) I think it is easier and likely more accurate to have a bar chart to represent the quantities.

I think the racetrack strips are a step too far in cramming detail in, especially as the Census Bureau data sets I can find don’t seem to have those numbers. It’s not clear what value they add, and it just looks like using a doughnut chart to compare series. If you’re going to do that, I think a bar graph would be the way to go instead.

I appreciate the effort, and I may use the technique if my bosses absolutely force me to use a pie, but I’ll still stick with cartesian graphs for almost everything complicated, and tables for anything sufficiently simple, even though I’m an occasional defender of some polar graph types myself.

I like treemaps and have some doubts about waterfall charts. But I’d really like to discuss pie charts/doughnut charts only and not if there are better charts.

@derek: I’ll try do address your comments regarding the chart.