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From a car, I get a value every second for accelerator pedal, from 0 to 100%. When you don't touch it, it reports 0%, and when you kick it to the max, that is 100%.

I want to calculate how much change there is in this value. It will be one of many indicators of how you drive (how aggressively).

The best I have so far, is to calculate the average absolute value of the change from one reading to the next.

I am sure statistics offer something better, but I don't know what.

My reasoning is that variance is not relevant. What I want is more like the total work you do on the pedal divided by how long the trip is.

When posting this, I have to specify tags. When writing "change", autofill suggest "change scores". Is that something I should look into?

Terje Kolderup
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Average absolute value from one reading to the next is potentially a very good measure of volatility. You might consider whether a 1 second interval is optimal, vs. computing successive changes after averaging over, say, 3s intervals. Other useful summaries might include the maximum acceleration over a long time period, and the 0.9 quantile of the 0-100 acceleration measurements. But it would be nice to have data on break usage, depending on what your real unstated goal is.

Frank Harrell
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  • "Acceleration" is ambiguous here! When the pedal is at a constant unchanging setting, the car's own acceleration can be zero. The rate of change of the pedal involves the third derivative of the car's position (mediated by the response of the drive train, of course), aka the jerk, and the acceleration of the pedal's position involves the fourth derivative of the car's position, aka the jounce or snap. Arguably, positive acceleration of the pedal is most closely related to aggressiveness. – whuber Jun 24 '16 at 14:09
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There are two analogous areas in which you may be able to find pre-existing formulae.

Water level measurements over time: it seems you are truly seeking a measurement similar to the most common water level over a given time period. Farming and geological sites will have loads of equations related to that for you to convert easily.

The second one is network bandwidth billing. A common billing measure is to take the 90th %ile of of average usage as the billable amount. This allows for the exclusion of brief spikes throughout a given time period.

Asking the web about water levels over time, or bandwidth utilization measurements should yield you a lot of substantial results.

MGMead
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