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Re: [Phys-L] points don't have error bars (distributions do)


I was thinking of a slightly different issue, I suspect. I have no problems with your additional comments about errors associated with a specific measurement made under a specific set of circumstance. I would even say it is a hallmark of an "expert" to naturally think about uncertainty and to be able to estimate the magnitude of that uncertainty in common situations (without needing to collect 1000 data points to estimate the true distribution).

However, the graphs you link to have changed. The first time I looked at the figures you linked to, there was a curve being fit to a set of data points, with error bands on the curved fit to the set of points. (From my interpretation of your post) you were comparing the spread of the *curve* to the spread of the *points*. The existence of a curve being fit implies that the data points were a function of some "x" as well as having their own internal variability. Now the graphs are horizontal with completely horizontal error bars, so you have removed "x" from consideration. You currently seem to be focusing on the "internal variability". I was addressing the curve you seemed to be fitting, which is a different issue.

So for instance, if I am trying to see how the resistance of a light bulb depends on the voltage, I have the first question of how well do I know an individual resistance measurement, and then how well do I know the curve. Furthermore, I could try to fit several different curves to the R vs V data, and each would have different error bands (mostly) independent of the error bars of the individual resistance measurements.


PS In industrial settings, this is part of a process called "Gage R&R" or "Gauge R&R" (repeatability and reliability). There they are concerned about different people with different instruments being able to measure different parts in a consistent, accurate manner.

John D said
I've been thinking some more about this. I now have a concrete, quantitative, objective,
pedagogical example that illustrates why it is a bad idea to associate error bars with the individual
reading. By "bad" I mean wrong in principle and demonstrably problematic in practice....