Wednesday, 24 September 2008

Reorderable tables II: Bertin versus the Spiders

Chandoo at Pointy Haired Dilbert has a post about the inadequacies of radar, or spider, charts; using a sample of four (software?) options to be selected, and six scores by various criteria, he presents them as a radar chart:
Not very informative. So he tries it as a "petal chart"
Still not showing much. The circular formats of radar and petal charts don't really add value in this case, since we expect to be able to sort best from worst, and we don't really care if the best comes round to meet the worst, like the worm Ouroboros chomping on its own tail.

Bertin says every graph is just a table really: this is the table in question:
So why not just show it as a table?
I've re-ordered the criteria and options to show a rough diagonal trend. The criteria are obviously re-orderable categories, and I assume the options are, even though they're numbered 1-4. I take it that's just anonymising. Clearly Option 1 is the package for you if performance and scalability are what you're looking for, while you should consider option 2 if you really care about usability and flexibility. Sometimes the options in the middle excel at some crieria in the middle, but in this case options 3 and 4 don't really have anything to offer against the all-round competence of option 1.

The spot matrix is a favourite of mine, and does appear in Semiologie graphique, but Bertin more frequently shows his tables as a stacked bar chart:
Finally, has re-ordering helped the spider?
Sadly, no.

Tuesday, 23 September 2008

Giving in to data loss aversion

D. Kelly O'Day, of the Process Trends web site, has a new Charts & Graphs blog, and his first post comments on the US Census Bureau's Current Population Reports data discussed by Jorge Camoes, and Andreas Lipphardt at, as an example of a confusing data set with too much detail, or is it just detail in need of sensitive presentation?

(as reader michael rightly points out in comments on the XLCubed post, this can't be showing the rise of income disparity, because it's percentage of households against fixed income level, not percentage of income against fixed household quantiles. Also, the series tops out at $100k, which is peanuts compared to the super-rich levels where the income transfer of the last few decades has really been most spectacular.)

Kelly abandons the time series approach to present the two end points in a dot plot:

However, I think that reducing the curves to a pair of points, one in 1967 and one in 2007, loses a lot of information that the full time series has to tell. So, in the spirit of defending loss aversion, I wondered if a readable time series graph could be constructed that would give real insights into the census table.

First, I made it a cumulative graph, so each income bracket now goes from zero to n(i), not n(i-1) to n(i). This means the lines can't cross any more, which should help:

I eliminated the >$100k line, as this is now by definition 100% of the households, cumulatively. As we see, the percentage of households making under $100k in constant dollars falls steadily from 1967 to 2005, which is just what we would expect from economic growth, and a desirable result. You want more people getting richer. However, this does not carry through to all income levels, which fall by less and less.

Perhaps this is an artifact of the linear scale, as written about by Jon Peltier and Nicolas Bissantz recently. So I tried it with a log scale instead:

(fully accepting Jon's comment that log scales do an equal injustice to the upper values, when the data is values equally distributed within an upper limit instead of proportionally distributed to infinity)

The surprising result is that the <$5k income level contains almost as many households in 2005 as in 1967, and significantly more than in the 70s, after a fall in the 60s. After a modest fall in the 90s, it rises again after 2000, as do all the other income levels below $100k. If we have said a fall is a good thing, then a rise must be bad. So the full time series data do contain a shocking insight, but it's to be found not at the upper levels but the lower ones, and not just by comparing 1967 to 2005, but following the trend down, then up. The dot plot can only tell a story of average improvement between 1967-2007, which masks a story of advance and retreat.

Thursday, 4 September 2008

Reorderable Tables

I've been interested in the idea of reorderable tables since I read about Jacques Bertin coming up with the idea in his 1967 book Semiologie graphique. The idea is that if you don't have a preferred order for your rows and columns, why not order them so the values in the cells make a rough diagonal across the grid? This makes the patterns much more straightforward to detect.

But I didn't know how to implement it in a spreadsheet until I googled on the word "reorderable", which turns out to be used for Bertin's tables, and almost nothing else. Some of the hits describe something called the "barycenter heuristic", which is really quite simple. It's based on the idea that each row or column has a "centre of gravity" that you can calculate, and then sort by. Take for example this table from Juice Analytics review, 5 Options for Embedding Charts in a Web Page

I added formulae for calculating the barycentre of the rows and columns, of the following form:


Then, because Excel sort up/down is temperamental without well-defined headers, and left/right is even more so, I recorded macros like this:

Application.Goto Reference:="SORT_COLS"
Selection.Sort Key1:=Range("SORT_COLS"), Order1:=xlDescending, Header:=xlNo,

Application.Goto Reference:="SORT_ROWS"
Selection.Sort Key1:=Range("SORT_ROWS"),
Order1:=xlAscending, Header:=xlNo,

These use the pre-created named ranges SORT_ROWS and SORT_COLS shown in red and blue here:

Now when I run the two macros, the table sorts itself into this:

I linked the macros to the shorcut keys Ctrl-m and Ctrl-M, and depending on the structure of the data, they either converge quickly and stop responding to key presses, or sort the reverse of whatever they sorted the last time. This last behaviour is handy because it makes the table cycle though the four possible orientations. You may prefer the table in another orientation than the one it converges to initially.

This is a simple example, and could have been done by hand, but you can do it with more complicated tables too. This example is from the Junk Charts article Noisy subways:

It's not a perfect diagonal, and wouldn't be even if it was the optimal solution, and I'm not convinced this technique does find the optimal solution. But it's not bad for something so simple.