Fun With Graphs: My 91% is Bigger than Your 91%

I found this on Fark.com, and thought it was a bit amusing.

It begs the question: Do they really think folks won’t notice?

Well, it appears that they fly more flights, leading to a greater number of flights arriving on time (if you’ll direct your attention to the scenic x-axis.)

Fantastic! Corporate hoo-ha at its hoo-ha-est.

Actually, this graph, though poorly done, does make sense, at least to me.

What it is showing is the percentage of total flights vs. the total number of flights on time. The graph for US Airways is larger simply because they have a greater number of flights.

For example, if US airways flies 100 flights, and 91 are on time, then it will have a percentage of 91%. If Delta were to fly 50 flights and 46 were on time, it would also be equal to 91%, but the bar would be shorter.

I’m not sure that I described that as well as I could, but another doper will be along who will do much better I’m sure. ( I bet by the time I post this, someone will have already beat me too it. Just watch…)

I must say though, it is an amazingly stupid graph.

Speaking as a professional statistician, this is the sort of plot that earns me a bad name from Mark Twain and Benjamin D’Israeli. (“There are three kinds of lies: lies, damned Lies, and statistics.” Twain attributes it to D’Israeli, but I gather it doesn’t appear in D’Israeli’s writings.)

OTOH, it’s fairer than it needs to be… they could just show that they have more on-time arrivals, and most viewers would never stop and ask what the denominator was.

That was my first thought too…they didn’t have to mention that their rival’s on time percentage was the same as their own.

Observant readers will also notice that Amtrak’s 69% on time performance is of a greater magnitude than American Eagle’s 73! It makes sense, though, for the reasons others have given above.

IANAS (I am not a statistician) but as a scientist I have seen practically all the tricks in this vein. Not lying, mind you. Just presenting data in certain ways in order to lead your audience to certain conclusions. NOT presenting certain data is also a time-honored tradition.

Those interested (especially scientists) are encouraged to read Edward Tufte’s books about graphics. They’re beautiful and interesting. The first and best is called “The visual display of quantitative information”. Highly recommended for all types.

Does that mean I can expect to be late almost one in ten flights when I fly US Airways? Are they bragging or seeking advice?