Speaker
Description
The statistical significance that characterizes a discrepancy
between a measurement and theoretical prediction is usually
calculated assuming that the statistical and systematic
uncertainties are known. Many types of systematic uncertainties
are, however, estimated on the basis of approximate procedures and
thus the values of the assigned errors are themselves uncertain.
Here the impact of the uncertainty {\it on the assigned uncertainty}
is investigated in the context of the muon $g-2$ anomaly. The
significance of the observed discrepancy between the Standard Model
prediction of the muon's anomalous magnetic moment and measured
values are shown to decrease substantially if the relative
uncertainty in the uncertainty assigned to the Standard Model
prediction exceeds around 30\%. The reduction in sensitivity
increases for higher significance, so that establishing a $5\sigma$
effect will require not only small uncertainties but the
uncertainties themselves must be estimated accurately to correspond
to one standard deviation.
