Statistical Analysis of Fuel Economy Claims
I’m subtitling this post “don’t believe all the data you
read.”
There’s a lot of stock put in fuel economy tests to verify
changes in drag. Someone makes an aerodynamic change to their car and runs an “A-B”
test, one run (sometimes more) in each of opposing directions measuring
fuel economy, to “prove” that drag has been reduced. These results are then
posted online uncritically; I’ve done it myself in the past.
There are a couple of things wrong with these tests.
The Normal Distribution
Statistics help us evaluate the truth of real-world claims.
One of the foundations of this branch of mathematics is the “normal
distribution”: the discovery that natural systems follow the same pattern of
variability, with a certain percentage of measured results falling within a
certain deviation of the simple average. For example, over the years I’ve owned
my Prius, I have kept track of the fuel economy displayed on the factory gauge
and the calculated MPG from the pump and miles driven. Last year, I put the
difference between displayed and calculated economy by tank in a spreadsheet and plotted
it:
You can see that the data form a nice curve. Most of the
results are in the middle, close to the mean. As you get further from the mean,
above and below, there are fewer data. This is the normal distribution, and it
is characteristic of just about every kind of measurement of, well, anything.
The mean was 3.0 MPG, right at the top of the curve. |
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Yes, anything. |
H1: μwithout < μwith
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