APPENDIX B. AN INTRODUCTION TO ERROR ANALYSIS
measured quantity
a
is given by
δf
a
=
±
∂f
∂a
²
δa,
with similar expressions for the uncertainty due to
b
,
c
, etc. The second premise is that if
the measured values
a
,
b
,
c
, etc. are
uncorrelated
the uncertainty in
f
from each adds
in
quadrature
as follows
(
δf
)
2
= (
δf
a
)
2
+ (
δf
b
)
2
+ (
δf
c
)
2
+
...
Uncertainties are uncorrelated when they are completely independent of each other. For
example if you measure the mass and acceleration of an object to determine the force on
it, your measurement of mass should have an uncertainty that has nothing to do with the
uncertainty in your measurement on acceleration. An example of correlated uncertainties
would be if you measured the radius of a circle and then doubled that to get a value of
diameter that you consider a “measured” value  any error in the measurement of the radius
would then produce the same relative error in the recorded value for the diameter, so these
uncertainties are
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 Fall '08
 Staff
 Physics, uncertainties, δfa, correlated uncertainties

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