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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*.
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.