Two cluster of precincts and candidates

I also figured out how to color the clusters by absolute values rather than relative values, which helps to differentiate the candidates. They still fall into two large groups, but now it’s easier to see subgroups. Mayor-council alignments are highly sensitive to the council multiplication factor (4 here), so ignore Kleinschmidt and Czajkowski for candidate clustering.

For the record, low scoring candidates have been eliminated (otherwise they make all precincts look more similar), and absentee and provisional votes have been combined with One Stop precincts.

The precincts present a similar clustering as before, except the under-voters are now distributed into other clusters. The yellow group is fairly neutral. The green group is left leaning. The purple group is left-leaning with a focus on Harrison/Rich/Easthom. The blue group is left-leaning with a focus on Merritt/Kleinschmidt. The red group is right-leaning and includes two of the Durham precincts.

As a bonus, I thought this visual was attractive. It shows a smoothed trend line of the vote percentages (times four for town council candidates) by precinct, where the precincts are ordered by support for Kleinschmidt, the winner of the race for mayor. (Click graph for a larger version.)

The “left-leaning” candidates generally rise with Kleinschmidt while the “right-leaning” candidates (dotted lines) fall. Merritt’s strong showing at Lincoln and Northside is also evident. Unfortunately for him, those precincts had very low turn-out.

Two-way clustering of candidates and precincts

I’ll agree the diagram looks a bit complicated, but if you put in a little work, there’s a few gems to be found. Precincts are listed down the left side, and candidates across the bottom. The square at each precinct-candidate intersection is colored according to the candidate’s relative support at that precinct, red being strong, gray medium and blue weak. That part’s called a cell plot or heat map.

The tree-like parts are dendrograms, which show the results of the hierarchical cluster analyses. Similar items (precincts or candidates) are grouped together in the tree.

For the candidates, along the bottom, there’s a clear pair of clusters, which I’ll call left-leaning and right-leaning candidates. Coincidently, the left-leaning are on the left and the right-leaning are on the right.

The precincts are more interesting, though I have even less knowledge of their actual political orientations. I’ve colored the precincts into five groups. The first (red) and to a greater extent the second (yellow) cluster generally voted in favor of the right-leaning candidates. That is, the left six columns of the heat map are bluish and the right four columns are reddish. The opposite is true for the green and purple clusters; they’re more left-leaning, especially the purple precincts.

What puzzles me is the middle (blue) cluster. Those precincts don’t seem to like anyone. The numbers I used for clustering were percent of ballots cast, and apparently there were more voters in those precincts with incomplete ballots, voting in some but not all races. For instance, the two major mayoral candidates, Kleinschmidt and Czajkowski, only received votes on 28% and 21%, respectively, of the ballots at the Kings Mill precinct.

That leads to looking at votes per ballot for each race by precinct. Here’s a bar chart with the precincts ordered by town council votes per ballot.

Most precincts had near 100% participation in the mayoral race (exactly 100% for Booker Creek and Coker Hills), and most precincts averaged over three (of four available) votes in the town council race. So only the already-identified cluster of three (plus Dogwood Acres to a lesser degree) stand out regarding participation.

I imagine the One Stop (early voting for all precincts) totals reflect a lot of Carrboro voters. What makes the others different? Were people there to vote for a different race, like the school board? Or just voting for a favorite son/daughter candidate?

See anything odd about the numbers? The columns are not aligned vertically because of different digit widths; in particular, the “1″ digit is very narrow. As a result, the Publications and Subscriptions value seems smaller than the Grants value at first glance, since the latter number is wider.

I thought it was a cardinal rule of font design that all digits were the same width. Unicode even has a “Figure Dash” character, which is a dash with the same width as the digit characters.

I set out to find the font in question. First I sampled what I had on my Mac. I didn’t find the font, but I did find several fonts with digits of unequal width. Most of them were artful fonts like Comic Sans, but Georgia was also in that category.

Next I tried Indentifont, a clever idea for identifying a font by asking a series of questions about the characters, such as what kind of bar the “G” has. It returned a few fonts that matched by answers, but none that looked like the report text. The “1″ and the “t” are particularly distinctive.

Finally I realized that with the PDF available I could just examine the file in a text editor. After searching for the word “Font” a few times, I kept seeing the word “Knockout” nearby. Checking the characters on the foundry site the Knockout font family, shows a perfect match for the font called “No. 32 Junior Cruiserweight”.

So my theory about fonts was wrong, but I still hold that tables of numbers should never contains variable-width digits.

In the worse case, though, two completely different scales are carefully transformed to almost line up and suggest correlation. An insidious example from a few years ago was the presidential popularity versus price of gas graphs, about which one writer believes show that there’s “clearly a correlation.”

It does look like a correlation, but that’s only because the scales have been transformed to follow the same long-term path, which could be done to any two generally linear data series. There are a couple related spikes for the September 11 attacks and the Iraq War start which our eyes quickly pick up on, but otherwise the local ups and downs don’t match too well. These graphs disappeared shortly afterwards when the two trends obviously diverged (gas prices got better but Bush ratings didn’t).

What I really don’t understand, though, is this next example on employment data from My Budget 360.

I’ve never seen a dual-scaled graph where both scales were the same units and approximate range. What’s the point? It shifted the intersection point a little, but not enough to affect the thesis of the article. It does exaggerate the climb of the blue line (leisure employment). I can’t tell if this one is intentional distortion or just carelessness.

With only five variables and sixteen observations, my first question is, “What’s wrong with just using a table?” The table in the contest description is even nicely laid out.

My second question is, “Best for whom?” Which illustration is best depends on the audience, which in this case might be doctors, researchers, statisticians or the general public among others.

The data shows Minimum Inhibitory Concentration (MIC, presumably in µg/ml) for each antibiotic and bacteria combination. Lower is better, indicating less antibiotic is needed to treat the bacteria. The MIC values vary widely from 0.001 to 1000, and I applied a logarithm transform for analysis, either on the data or on the graph. Besides nicely spreading out the data values, the log transformation may have a physical interpretation. If an antibiotic culture grows exponentially, then the log of the concentration is the time to grow it.

Exploring the data a little bit, the simplest visualization is a heat map, where every number is represented by a swatch of color. I don’t see much advantage over the table of numbers, except to quickly find extreme values or certain other patterns that the colors help with.

Next, we might think from a researcher/statistician perspective and try to cluster the bacteria that react similarly to the antibiotics. Here’s a heat map and dendrogram resulting from a cluster analysis. The rows are colored by gram staining. It’s like the heat map above, but similar bacteria are grouped together (and the color scale is slightly different). The bacteria that are clustered close together might suggest a commonality for future research.

Since there are only three antibiotics, we can view the data as a 3D scatter plot. Here, the data markers correspond to the clusters.

3D doesn’t work too well in static 2D media like this one since you need to be able to rotate it to see the structure. If you do rotate it, you can see that three of the clusters appear roughly in a straight line, so maybe there are really two different kinds instead of four. Here’s a view looking straight down the line.

A scatter plot matrix shows all the 2D relationships better and is better for static presentation. It can’t show the 3D the alignment of the three clusters, but you can get a hint of it in the neomycin versus penicillin panel.

For my contest entry, I decided to go with the perspective of a 1950s doctor, with the idea that a doctor treating a patient doesn’t know usually know what bacteria is causing the infection and may or may not have the results of a gram staining. With that in mind, my visualization shows the MIC for each antibiotic with the best dose for each scenario called out.

The graph shows that penicillin is best for gram positive bacteria since all purple circles are below 1µg/ml for penicillin. Similarly, neomycin is best for gram negative bacteria and streptomycin is best if gram staining is unknown. A drawback of this graph is that the points are not labeled or connected. I tried a few ways to do that with labels and lines, but the graph just became too messy. If you need that much detail, you probably need the table of numbers.

After doing all that, I found Burtin’s original visualization via a NY Times article.

I hope this isn’t what CHANCE is looking for. It has little communication value except to say “Look how cool I am!” At least all the data is present, so a meticulous reader can get what information he needs. The audience for this must be a hospital administrator who needs to feel like he’s getting his money’s worth with fancy visualizations. I think it is more a work of art than of communication.

Jon Peltier has a write-up of his contest entry. It has all the data of Burtin’s original in a much better rectangular structure.

I started a skeleton outline of some of the issues at the conference wiki, and I’m happy to see others have expanded it.

With so much information it’s hard to pick out too many details. However, it’s easy to see how Ward and Raymond did in each precinct since they’re on the edges and have a stable baseline.

The order of the candidates is by overall finish position, and the order of the precinct is by percent of total Czajkowski/Hill votes that went to Czajkowski. That makes it a little easier to see how those two candidates matched up in the battle for the fourth seat.

Czajkowski got the final spot on the council in a close race, though there is quite a bit of variation among precincts. Not sure if the variation is due to political make-up of the precincts or to targeted campaigning.

I notice my precinct, Estes Hills, was one of the best for my friend Will Raymond. Maybe my yard signs helped!

Update:Here’s another view, highlighting the broad range of results for Czajkowski. Each circle is a precinct.

And a similar one, this time with circle size being proportional to total precinct votes and color being set based on the Czajkowski/Hill ratio. Red precincts went for Czajkowski and blue for Hill. You can see some correlation among the incumbents and among the challengers.