Sixty-two years of daily data from the NCEP / NCAR Reanalysis I project are analyzed. The skewness and kurtosis (third and fourth central statistical moments, respectively) of the data is found at each spatial grid point for the entire time domain. Nine atmospheric variables were chosen for their physical and dynamical relevance in the climate system: geopotential height, relative vorticity, quasi-geostrophic potential vorticity, zonal wind, meridional wind, horizontal wind speed, vertical velocity in pressure coordinates, air temperature, and specific humidity. For each variable, plots of significant global skewness and kurtosis are shown for the DJF and JJA months at a specified pressure level. Additionally, the statistical moments are then zonally-averaged to show the vertical dependence of the non-Gaussian statistics. Thus this is a more comprehensive look at non-Gaussian atmospheric statistics than previous studies in this topic.