Applied Statistics

Graph of the week

Brendan Nyhan links to this hilariously bad graph from the Wall Street Journal:

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It’s cute how they scale the black line to go right between the red and blue lines, huh? I’m not quite sure how $7.25 can be 39% of something, while $5.15 is 10%, but I’m sure there’s a perfectly good explanation . . .

Follow the above link for more details. As Brendan notes, the graph says essentially nothing about the relation between minimum wage laws and unemployment (“Any variable that trended in one direction during the current economic downturn will be correlated with the unemployment rate among teens or any other group.”) and he also helpfully graphs the unemployment trends among the general population, which has a similar upward trend.

This is not to say that increases in the minimum wage are necessarily a good idea–that’s not my area of expertise. I’m talkin here about a horrible graph–all the worse, I fear, because of its professionalism. The above graph looks legit–it has many of the visual signifiers of seriousness, looking similar to a newsy graph you might see in the Economist, rather than like a joke graph of the sort identified with USA Today and parodied so well by the Onion.

P.S. I have no problem with the use of a crisp graph to make a political point; see for example here or here.

Comments

  1. #1 Curlyjim
    March 8, 2010

    It’s pretty classy that they made the wage graph steps, as if you tried to fit a line to that, it’s clear that the rate of wage increase is higher than the rate of unemployment increase, which I suspect was not the intention.
    Does this also mean to imply that $4.45 is the minimum that a minimum wage can be, and that $13.45 is a maximum?

  2. #2 Eric Johnson
    March 8, 2010

    First of all I love your blog – thanks!

    Second, how would you represent this differently? I’m not disagreeing that it’s not very well done, but this is something I need to do fairly regularly in my work, i.e., juxtapose two data series where the only thing linking the two sets is time. This is a useful way (in my opinion) to find targets for deeper analysis. (I work in the pharma industry)

    If I had been asked to do this graph, I think the only thing I would have done differently is to add a separate y-axis to the right for the minimum wage series.

    I guess my real question is whether you don’t like this as a visualization technique (and if so, can you suggest a better one), or whether it’s the underlying analysis (or lack thereof) that you think is shoddy.

    Thanks in advance,
    Eric Johnson

  3. #3 Toivo Maki
    March 8, 2010

    Eric,
    I’d like to help because I think there’s a very important lesson to be learned here, that I don’t think you’re getting. When you ask, “I guess my real question is whether you don’t like this as a visualization technique (and if so, can you suggest a better one), or whether it’s the underlying analysis (or lack thereof) that you think is shoddy.” here’s what I would say:

    Obviously, the analysis they’ve done is terrible. You can look at some of the criticisms Brendan Nyhan made of it for starters that just destroy major arguments being made. To that I would add they’re cherry picking their data. If you had a larger dataset time-wise, and put wages in real, vs. nominal, dollars, you would immediately see that the minimum wage hadn’t been raised in ten years, and that $5.15 in 2007 was historically low. I’m talking the lowest it’s been since the 50′s. During the late 70′s the minimum wage went up every year and teen unemployment went down. Their analysis is garbage. So I guess what I’m trying to say first is that “visualization technique” is not independent of the analysis. It’s not just a matter of selecting the correct graph type in Excel and making it look the way you want it to look. Good visualization technique should be “honest”. The values you select for your axes are not arbitrary. The data series you choose to include are not arbitrary. The choices in this example were made to support a misleading argument, and so the “visualization technique” used here is, quite frankly, a lie. I hope this helps.

    I would recommend reading Stephen Few if you want to learn good visualization technique. He is, IMO, excellent.

  4. #4 Eric Johnson
    March 8, 2010

    Thanks Toivo. I guess my question did come across as pretty naive. I have Few’s Now You See It… and a couple of Tufte’s books next to my desk and peruse them for ideas fairly frequently, along with Prof. Gelman’s textbook on Data Analysis & Regression.

    I read Nyhan’s article, so I was aware that there really wasn’t any honest analysis behind it and that it was basically a fabrication, but I was more interested in the fact that Prof. Gelman didn’t seem to like this particular method of visualization, apart from the fact that the data it’s representing is a lie (neither of the links he listed use that particular method of juxtaposing data series that way). Looking back at my question, it was pretty vague and naive sounding though, and you’re points are good ones.

    I wasn’t trained as a statistician (my background is physics), and I don’t really have any statisticians around me (strange, considering the industry I’m in), so I’m acutely aware that some of the things I do might cause real statisticians to cringe.

    Thanks again,
    Eric Johnson

  5. #5 Eric Johnson
    March 8, 2010

    Oops, :s/you’re/your
    I should use the preview feature before posting…

  6. #6 Andrew Gelman
    March 9, 2010

    Eric: What Toivo said. Also, in this particular case, besides extending the x-axis and also plotting the aggregate unemployment rate, what I’d start with is to pull out the minimum wage line and show it on a separate graph below the first one. Also I think I’d show two minimum wage lines: one that’s inflation-adjusted, and one that’s adjusted by dividing by average income.

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