  We unify two approaches that have been taken to explain the non-Gaussian
probability distribution functions (PDFs) obtained in measurements of
longitudinal velocity differences in turbulence, and we apply our approach to
Couette-Taylor turbulence data. The first approach we consider was developed by
Castaing and coworkers, who obtained the non-Gaussian velocity difference PDF
from a superposition of Gaussian distributions for subsystems that have a
particular energy dissipation rate at a fixed length scale [Castaing et al.,
{\it Physica D} {\bf 46}, 177 (1990)]. Another approach was proposed by Beck
and Cohen, who showed that the observed PDFs can be obtained from a
superposition of Gaussian velocity difference PDFs in subsystems conditioned on
the value of an intensive variable (inverse ``effective temperature'') in each
subsystem [Beck and Cohen, {\it Physica A} {\bf 322}, 267 (2003)]. The
intensive variable was defined for subsystems assuming local thermodynamic
equilibrium, but no method was proposed for determining the size of a
subsystem. We show that the Castaing and Beck-Cohen methods are related, and we
present a way to determine subsystem size in the Beck-Cohen method. The
application of our approach to Couette-Taylor turbulence (Reynolds number
$540~000$) yields a log-normal distribution of the intensive parameter, and the
resultant velocity difference PDF agrees well the observed non-Gaussian
velocity difference PDFs.
