  Least-squares data analysis is based on the assumption that the normal
(Gaussian) distribution appropriately characterizes the likelihood, that is,
the conditional probability of each measurement d, given a measured quantity y,
p(d | y). On the other hand, there is ample evidence in nuclear physics of
significant disagreements among measurements, which are inconsistent with the
normal distribution, given their stated uncertainties. In this study the
histories of 99 measurements of the lifetimes of five elementary particles are
examined to determine what can be inferred about the distribution of their
values relative to their stated uncertainties. Taken as a whole, the variations
in the data are somewhat larger than their quoted uncertainties would indicate.
These data strongly support using a Student t distribution for the likelihood
function instead of a normal. The most probable value for the order of the t
distribution is 2.6 +/- 0.9. It is shown that analyses based on long-tailed
t-distribution likelihoods gracefully cope with outlying data.
