Due to the strong nonlinear dependence of plasma turbulence on drive and dissipation mechanisms, uncertainties in experimental inputs can be greatly magnified in simulations of this turbulence. Thus, careful uncertainty quantification (UQ) and its inclusion within validation metrics is an integral part of plasma turbulence validation studies. To minimize the number of simulations required for UQ, we investigate the use of the rapidly converging nonintrusive probabilistic collocation method (PCM) for efficient plasma turbulence UQ. This approach is shown to yield more realistic uncertainty estimates than simple uniform sampling methods for a practical number of nonlinear simulations. The inclusion of UQ above and near critical gradients is discussed. To demonstrate its utility, the advantages of PCM are first illustrated using a simple model of critical gradient turbulence. It is then used on simulations from a validation study of drift-wave turbulence in the CSDX linear plasma device experiment. The advantage of more advanced methods for selecting samples from the uncertainties in the plasma turbulence simulations is also discussed.