  Estimates of uncertainty or variance in experimental means are central to
physics. This is especially the case for `world averages' of fundamental
physical parameters in particle physics, which aggregate results from a number
of experiments to express current knowledge about these parameters and where
variance in these world averages reflect uncertainty in that knowledge. The
standard aggregation method used to estimate such parameters is a form of
hierarchical fixed-effect meta-analysis. This method is inherently unsuitable
for estimating these parameters because it ignores sources of random variation
between experiments (that is, variation in experimental accuracy, which becomes
increasingly important as experimental precision rises). This problem is
well-known in the statistical literature, where the typical recommendation is
to use random -- rather than fixed-effect techniques. We illustrate this
problem by applying random-effect meta-analysis to estimates of the W-Boson
mass.
