I have observed that I am almost never the last car through a traffic light. Sometimes I stop (because it is yellow or red), in which case, of course, the car behind me also stops and the car in front of me proves the last car through. And sometimes I go (because it is green or yellow), in which case, usually, the car behind me follows me through.
I long felt that this showed that I am more likely (than other people) to stop at a light; I am relatively cautious. Otherwise, why should I rarely be last through? But this conclusion came with a guilty conscience. Because it seemed obvious that I couldn’t know, from my own experience alone, whether other drivers felt the same way about themselves, apparently making me typical after all.
I’m re-thinking that guilt, and this is to ask your help.
On the one hand, if I observe that I’m late to work 5% of the time, this gives me no information about whether I’m late to work more often that the average person or less often. For that conclusion, I would need to gather data about other people.
But on the other hand, suppose that I observe that in the last 50 cases in which I reached a yellow light, in 40 cases I stopped, in 9 cases I went through followed by another car, and in 1 case I went through alone. I see that I have stopped in (40/50)=80% of the cases while the fellow behind me stopped in only (1/10)=10% of cases. (I think that I'm here ignoring the fact that the driver behind me is reaching this yellow light later than I did, increasing his probability of stopping. Should I?)
Is there some sort of problem of independence here, such that the people behind me when I go through do not represent all drivers?
I realize that if the numbers 9 and 1 were switched -- so that I stopped in (40/50)=80% of cases, I went through alone in 9 cases, and I went through followed by a car in 1 case -- we could not make the opposite inference that I am relatively reckless – could we? Because of the complicated problem of dealing with instances in which I go but there is simply no car behind me, stopping or proceeding? Or for some other reason?
Is there some standard nomenclature for the issue I'm raising, distinguishing the late-to-work analysis from the traffic-light analysis?
Interesting question.
This isn't an answer but it's too long for a comment.
First, your "late to work" is irrelevant. That depends much more on the kind of person you are, whether you leave enough time to get to work, than on your behavior at lights.
If you want to know whether you are last through the light a disproportionate number of times I think you need more data. If you watched a particular light at the same time of day for many days you could count the number of cars that go through the light (green or yellow) and thus estimate the probability that any particular car is last through. Then you could compare that number with the fraction of times you're last through.