Before I start this posting, I have to explain a term or two… Whenever you’re doing the type of experiment that I used to do back when I did experiments, you take a thing – for example:
- a pair of loudspeakers
- in a place
- in a room
- playing a 2-second loop of music
- at a known playback level
- to a listening subject
- located at a known location
All of that stuff stays the same. You then make one change to one thing (for example, you increase the bass level, while still making sure that the overall listening level has not changed – therefore you have to turn down the overall volume because you turned up the bass (if the frequency band(s) that are in the region affected by the “bass” controller are present in the 2-second loop of music…)
You then ask the listening subject questions about the difference in the two things they heard – knowing (as the experimenter) that they only heard two things. For example, you ask them to tell you which of the two stimuli they preferred.
In this example, the thing that you (the experimenter) changed is called the “independent variable“. The information that you get from the listening subjects is called the “dependent variable“, since it’s (in theory) dependent on the variable that you’re changing.
As an ex-experimenter, I’m a poor test subject in someone else’s experiment, because I spend most of the time during the test NOT actually doing the test – but trying to reverse-engineer what is being tested. In other words, while I give the experimenter the dependent variables, I’m trying to figure out what the independent variables are…
Cut to the chase…
For the past two weeks, I’ve done more than my usual amount of highway driving here in Denmark. A couple of trips to Copenhagen (a 4-hour drive) and a trip to Aarhus (a 1.5 hour drive). In those many hours of driving, I began to notice a pattern that seemed to involve an independent variable and a dependent variable…
Typically, I drive within 5% of the speed limit. Or, more accurately, the speed displayed on my speedometer when I’m driving is within 5% of the speed limit of the road that I’m on. This is because my car (a 7-year old Honda Civic) has an approximately 5% error in its calculation of my actual speed (with my current wheels and tires at their current air pressure). And, over the past two weeks on the highway, I’ve noticed that almost everyone else is driving almost exactly the same speed as me.
However, I started to notice that there were two exceptions to this. There is a small number of vehicles that are being driven significantly slower than I drive. And there are another small number of vehicles that go significantly faster. So, it appears that we have a dependent variable – the speed at which the vehicles are going… This must be the result of something – the independent variable… So, I was trying to figure out what the independent variables are – trying to reverse-engineer the problem as if I were a subject in an experiment.
It didn’t take long to come up with with a hypothesis – my best guess as to why I could break down the speeds of the vehicles into three different groups… And, once I came up with a hypothesis, I spent the rest of my time watching, to see if the hypothesis could be used to predict a behaviour…
Hypothesis 1: Slower vehicles
So, the first group of vehicles – the ones that go slower than me – almost all fit into a category of being significantly longer than my car. This includes large trucks, busses, and cars towing trailers. So, there appears to be a negative correlation between the vehicle length (over a yet-to-be-determined threshold – see the Appendix 1, below) and the difference in speed relative to the speed limit (which we will assume that I am obeying). Perhaps this is because longer vehicles cannot go as fast because they are heavier. Unfortunately, I have noticed that this conclusion only holds true on the highway. It does not hold true when the speed limit is either 80 km/h or 50 km/h… So, further investigation is required.
Therefore, I can conclude that the independent variable in this case is the vehicle length – with a significant degree of uncertainty.
Hypothesis 2: Faster vehicles
It became quickly apparent that almost all of the vehicles that were travelling faster than me were either a Mercedes, Audi, or BMW. So, assuming that all persons are equal, I can only conclude that the speedometers on German-made cars are poorly calibrated – and all with an error that deviates with the same polarity. The speedometers on German-made cars must be displaying a speed that is lower than the actual value.
Appendix 1: Outlier and Interaction
So, it appears that there are two different independent variables in this experiment. Interestingly, there is also an interaction. This can be seen in the case of German vehicles that are longer than my Honda driving much faster than me. So, it appears that the second independent variable has a heavier weighting than the first. In other words, if a vehicle is longer than mine, AND it’s a German-made car, then it will go faster, not slower. This is true to a yet-to-be-determined-length-difference-threshold, above which it is not true (in other words, German busses go slower than me).
Appendix 2: Outlier without interaction
There was one potential additional independent variable in this experiment that appeared after a little more time on the highway. This was the question of whether the vehicle had a licence plate originating in Germany instead of Denmark. In this case, it appears that the second hypothesis is nulled. In other words, a German-made car with German plates will drive the speed limit.
Appendix 3: Generalisations
It should be said that, after a little research on the Internet, I found that my second hypothesis may be too general. It may, in fact, be concluded that cars made in Southern Germany are the vehicles with the inaccurate speedometers. This nuance is the result of my noticing that most (but not all) Volkswagens are moving at a velocity that is approximately equal to the speed limit.
Counter-intuitively, the larger (and therefore longer) Volkswagens behave more like the Southern German vehicles, which makes me wonder if there is an additional classification that I cannot derive yet…
Speaking as a consumer, and as someone who works in the engineering / development department of a company that makes consumer products, I find it odd that German car manufacturers would intentionally put consistently inaccurate speedometers on the cars destined for their export market. However, based on the observations made in this short “experiment”, it’s the only conclusion I can come up with…
Admittedly, however, my conclusions are based on the reliance on a number of assumptions – some of them quite naive, of course. However, further observations and experimentation are required before submitting a paper to a peer-reviewed journal. This also raises the question of which journal(s) should be chosen for submitting my manuscript. Perhaps the JESC – The European Journal of Spurious Correlations or the GCFC – The George Carlin Fan Club. We’ll see…