Averaging in the presence of sliding errors Page: 4 of 37
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AVERAGING IN THE PRESENCE OF
"SLIDING" ERRORS
G. P. Yost
Physics Research Division
SSC Laboratoryt*
2550 Beckleymeade Ave.,
Dallas, TX 75237
and
Department of Physics, University of California,f
Berkeley, CA 94720
and
Lawrence Berkeley Laboratorytt
1 Cyclotron Road, Berkeley, CA 94720
Abstract
In many cases the precision with which an experiment can measure a physical quantity
depends on the value of that quantity. Not having access to the true value, experimental groups are
forced to assign their errors based on their own measured value. Procedures which attempt to
derive an improved estimate of the true value by a suitable average of such measurements usually
weight each experiment's measurement according to the reported variance. However, one is in a
position to derive improved error estimates for each experiment from the average itself, provided
an approximate idea of the functional dependence of the error on the central value is known.
Failing to do so can lead to substantial biases. Techniques which avoid these biases without loss of
precision are proposed and their performance is analyzed with examples. These techniques are
quite general and can bring about an improvement even when the behavior of the errors is not well
understood. Perhaps the most important application of the technique is in fitting curves to
histograms.
t Operated by the Universities Research Association, Inc., for the U.S. Department of Energy under Contract No.
DE-AC35-89ER40486.
* Present Address.
t Partially supported by the U.S. National Science Foundation under grants NSF PHY-8907526, PHY-8811054, and
85-07153.
tt Operated by the Universities Research Association, Inc., for the U.S. Department of Energy under Contract No.
DE-AC03-76SF00098.
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Yost, G.P. Averaging in the presence of sliding errors, report, August 1, 1991; Dallas, Texas. (https://digital.library.unt.edu/ark:/67531/metadc733368/m1/4/: accessed April 18, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.