Comment by sobriquet9
3 days ago
I think if you showed not only the point estimate, but also some measure of uncertainty like standard deviation, it should have given you a passing grade. It's hard to say why an answer like 6.8 +- 5 is wrong.
Even if you don't yet have formal statistical chops, it should be at least possible to show cumulative distribution function of results that will convey the story better than a single answer with overly optimistic implied precision.
This is early high school. We didn't have error bars yet, we just took an average. I just used that as a convenient way to describe how erratic our numbers were. If 6.8 is the average you know we had some low numbers in there. And some nice high ones, too.
You're certainly correct that the true value would have been in our error bars, and one of those good teachers I acknowledge the existence of in my large paragraph, sarcastic as it may be, could conceivably have had us run such a garbage experiment and shown that as bad as it was, our error bars still did contain the correct value for probably all but one student or something like that. There's some valuable truth in that result too. Cutting edge science is often in some sense equivalently the result of bodging together a lot of results that in 30 year's hindsight will also be recognized as garbage methodology and experiments, not because the cutting edge researchers are bad people but because they were the ones pushing the frontier and building the very tools that later people would use to do those precision experiments with later. I always try to remember the context of early experiments when reading about them decades later.
It would also have been interesting to combine all the data together and see what happened. There's a decent chance that would have been at least reasonably close to the real value despite all the garbage data, which again would have been an interesting and vivid lesson.
This is part of the reason this is something that stuck with me. There were so many better things to do than just fail someone for not lying about having gotten the "correct" result. I'm not emotional about anything done to me over 30 years ago, but I'm annoyed in the here and now that this is still endemic to the field and the educational process, and this is some small effort to help push that along to being fixed.
It's honestly kind of bullshit because the bedrock of a lot of my work is being realistic, and if I had such a piece of crap equipment I would have gladly reported the 6.8 meters per second squared and then turned around and identified all of the problems with my setup right down to characterizing the lag time on the stopwatch start.
In fact one of the trickiest problems I had to resolve once was to show that the reason a piece of equipment couldn't accurately accumulate a volume from a very small flow was because of the fixed-point decimal place they chose. And part of how I did that was by optimizing a measurement device for the compliance of a fixed tube until I got really good, consistent results. Because I knew that those numbers were actually really good it came down to how we were doing math in the computer and then I just had to do an analysis of all of the accumulation and other math to determine what the accumulated error was. It turned out to be in really good agreement with what the device was doing.
All of that came from our initial recognition that the measured quantity was wrong for some reason.