Jets are an important element of the global ocean circulation. Since these jets are turbulent, it is important that they are characterized using a statistical framework. A high resolution barotropic channel ocean model is used to study jet statistics over a wide range of forcing and dissipation parameters. The first four moments of the potential vorticity distribution on contours of time-averaged streamfunction are considered: mean, standard deviation, skewness and kurtosis. A self-similar response to forcing is found in the mean and standard deviation for eastward barotropic jets which exhibit strong mixing barriers; this self-similarity is related to the global potential enstrophy of the flow. The skewness and kurtosis give a behaviour which is characteristic of mixing barriers, revealing a bi/trimodal statistical distribution of potential vorticity with homogenized potential vorticity on each side of the barrier. The mixing barrier can be described by a simple statistical model. This behaviour is shown to be lost in westward jets due to an asymmetry in the formation of zonal mixing barriers. Moreover, when the statistical analysis is performed on eastward jets in a streamfunction following frame of reference, the distribution becomes monomodal. In this way we can distinguish between the statistics due to wave-like meandering of the jet and the statistics due to the more diffusive eddies. The statistical signature of mixing barriers can be seen in more realistic representations of the Southern Ocean and is shown to be an useful diagnostic tool for identifying strong jets on isopycnal surfaces. The statistical consequences of the presence, and absence, of mixing barriers are likely to be valuable for the development of stochastic representations of eddies and their dynamics in ocean models.