Exception to the rule
Transgender trends

Noisy subways

This NYC subway report is impossible to read.

However, it is very difficult to find a good way to show the information.  In fact, the data contained very little of that.  Curiously, the ratings are very dispersed so that each line is graded high on some category and low on others.  Here's one view of it:


I have grouped the subway lines together (A/C/E, 4/5/6, etc.).  The metrics are plotted left to right in the same order as in the original.  Is it all noise and no signal?

(I just realized the vertical axis is reversed: best ratings are at the bottom, worst ratings at the top.  Doesn't matter anyway since I can't see any patterns.)

Source: "No. 1 Train is Rated Highest by Commuter Advocates", New York Times, July 24 2007.

PS. Two contributions from readers.  Still looking for insight from this data...

Trains789fg5_2 Trainspotmatrix_2


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I think some colours and quartiles will help - there's no need to show precise ordering.

How about this


I think that this kind of line up makes it hard to see if any line has high values or low, instead of just fluctuating values. How about coloring the area below the line or something to hint the absolute value at any point?
No pattern is the pattern ;)


Two ideas:

1. Spider chart, either many laid up as small multiples, or overlapped into a few spider charts and individual lines distinguished by color.

2. Whisker-style sparkchart for each subway line. A basic version would have an uptick as an above-average ranking and downtick for below average. A fancier version would scale the tick height according to the rank.

Jon Peltier

Rankings are not very meaningful. If there were ratings of 1-5 or good-to-bad it would be easier to make comparisons. Putting the data for each line in a single row, instead of strewing them up and down the chart, also helps.

With these things in mind, I'd say Dermot's example looks pretty good.

Robert Kosara

The problem here is that the data doesn't make any sense. If they ranked the lines in each of the criteria, why are there gaps? And what were they trying to achieve, anyway? Figure out which line is the best across all/most criteria, or find the biggest problems? Their method doesn't seem to work for either question. The original graph does a good job of hiding that fact, and I don't think you can do much to improve that.


Even the individual values don't make sense. "G" is number one in "Reliability of service" but 22 in "Breakdown rate". Wouldn't breaking down frequently imply unreliableness?

Also, there's no way to tell the spread of values. The clumping in the "Clarity of announcements" column implies that there's not a huge difference between lines -- but is that because they're all really good or all really bad or somewhere in the middle?

Lastly, the middle columns -- "Breakdown rate" and "Seat availability" are the only ones without clumping, and clearly, they're the only data points that could be objectively measured -- either a train breaks down or it doesn't. And either a seat is available or it isn't.

IB a Math Teacher

Not only is Dermot's example clean and simple to understand, but it also brings back good memories of Candy Buttons. Mmmmmmmm!


Following dermot's inspired example, and acknowledging, as Jon says, that "rank" isn't a very good quantitative measure, here is an example of a more "quantitative" way of displaying the values than a traffic light scheme. Something similar can be seen on page 174 of Tufte's Visual Display of Quantitative Information. There, the spots are quite correctly limited to five levels of quality.

One useful transformation that could be performed on this matrix would be to try to re-order the rows and columns to cluster similar patterns of spots (the technique developed by Jacques Bertin). I made an attempt to order the rows to that effect, but my heart shrank at the task of doing it for the columns, so I just stuck to alphanumeric order.

A way of automating the problem to produce as close as possible to a saddle-shaped distribution of spots (dark at top left and bottom right, and light at top right and bottom left) would be higly welcome, but my mathematics and Excel VBA aren't up to the job.


nice job, derek. i like your version a lot. as for the clustering, i think alphanumeric is the way to go since the first thing people would do is look for the subway lines that they take.


Further improvement into Derek's graph would be differentiating subway lines either with horizontal space or by using modest background color in every other column. Now at least my eyes can't easily concentrate into one specific line.


The data are hard to group, but there is some pattern. This graphic isn't suitable for display but it can help to spot pattern.

The numbered lines generally rank higher than the lettered lines. Lines 1 and L have the highest overall ranks; lines C and W are the worst. Lines 4, 5, and 6 are similar in their pattern of strengths and weaknesses (they're clean, not very reliable, and crowded). Line 2 is much worse than the other numbered lines.

Jon Peltier

Robert -

Looks like origami, but you didn't end up with a swan!


Robert, the reason why there are gaps when the data is in rank order is that some of the lines are ranked equally through tied scores: the next following rank must then be lower, hence the gaps. So there is a one rank gap where two lines are tied, a two-rank gap where three lines are tied, and so on. The exception is the J and Z lines, which appear to be treated as one by the Straphangers Campaign.

Kaiser, I noticed that you say you grouped the lines A,C, and E. This sounds like some grouping that is based on the structure of the NYC subway; is there a source us foreigners can consult on the geography, topology, and managerial organization of the network that would tell us why the groupings work well that way?

It would also be nice to have context: which lines have the greatest rush hour passenger load, which ones share a certain cleaning contractor? etc. Perhaps six small thematic maps of New York, each one with the lines shaded or colored according to rank of a single quality, would provide some illumination. Are the dirtiest east-west lines in the north? Are the east-west lines with the greatest delays in the south? This kind of graphic would be beyond most of us simple Excel hackers, but would suit the New York Times' reputation for colorful graphics perfectly

I think we're all finally stalled, in gaining insight into the data, by the basic fact of ranking instead of scoring. If we had access to the scores the Straphangers Campaign used, instead of the ranks the NYT publishes, I believe we'd be able to make progress.


Derek: Yeah, I knew these were ordinal rankings, but I took the problem as one of finding pattern rather than exact quantitative comparison.

Jon: These are star plots aka spider or radar plots. They're definitely not as pretty as the candy buttons, but they have the virtue that they translate the rankings into distances (i.e., the lengths of the rays) rather than colors. The eye has an easier time ranking distances than colors or hues so when searching for pattern in the data it's probably better to use position or length. The stars are ordered in decreasing size rather than by name of the line.

As I said, this display isn't appropriate for presentation but I think it's easier to discern pattern among the lines than with the other alternatives presented.


Sorry, two Roberts in this conversation. I was answering Robert Kosara's question:

"The problem here is that the data doesn't make any sense. If they ranked the lines in each of the criteria, why are there gaps?"


Derek: you can take a look at the NYC subway map here -
NYC Subway


Kaiser, thanks. Version ordered by subway line here. Still no pattern beyond the one you initially spotted, but at least now New Yorkers can compare the spots by scanning for the familiar lines and colours.


Speaking of information graphics and the New York subway, I found this proposed alternative to the MTA map. It certainly gets the thumbs up from this Londoner raised on Harry Beck's classic Underground diagram.


A while ago I said I wished I knew how to sort reorderable tables diagonally. I found out the way to do it via a technique called the "barycenter heuristic". I've described it in my graphics blog here.

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