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On 10/21/2012 02:23 PM, Folkerts, Timothy J wrote:
But in many (all?) cases, the individual data point itself can be
considered to have been drawn from a random distribution. For
example, suppose I measure a voltage as 8.00 V using a specific
voltmeter. The manufacturer tells me that the accuracy of the meter
is 1 digit ± 0.5%. In effect, the manufacturer is telling me that if
I measured the SAME voltage with a set of their instruments, then the
readings of those meters would not all be the same and they should
range within 0.05 V of the "correct voltage". That single point is a
single instance of a value drawn from a random distribution.
I think I agree with all of that except for the first word.
At this point in the message, I don't see what the "but" is.
We agree that a point can be considered as being drawn from
a distribution. The distinction is important, but apparently
well understood. So far so good.
such, the error bars are telling us about the distribution of values
for that specific point, whereas the parameters of the curve itself
relate to a different random distribution.
I wouldn't have said that. It's not the alleged error bars
on the measured point that tell you the form of the distribution.
You knew the form of the distribution before you took the first
*) You knew the /distribution/ based on the voltmeter user's
manual and/or calibration certificate.
*) You learned the /point/ when you made the measurement.
The distinction between /point/ and /distribution/ is important.
I find this figure helpful:
-- I can draw the /distribution/ without reference to the points.
-- I can then decorate it with as many (or as few) points as I like.
-- There is nothing to gain and much to lose by drawing error bars
on the points. The width of the distribution is a property of the
distribution, not a property of whatever points (if any) I have
drawn from the distribution.
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