  Politano and Pouquet's law, a generalization of Kolmogorov's four-fifths law
to incompressible MHD, makes it possible to measure the energy cascade rate in
incompressible MHD turbulence by means of third-order moments. In
hydrodynamics, accurate measurement of third-order moments requires large
amounts of data because the probability distributions of velocity-differences
are nearly symmetric and the third-order moments are relatively small.
Measurements of the energy cascade rate in solar wind turbulence have recently
been performed for the first time, but without careful consideration of the
accuracy or statistical uncertainty of the required third-order moments. This
paper investigates the statistical convergence of third-order moments as a
function of the sample size N. It is shown that the accuracy of the
third-moment depends on the number of correlation lengths spanned by the data
set and a method of estimating the statistical uncertainty of the third-moment
is developed. The technique is illustrated using both wind tunnel data and
solar wind data.
