This paper presents an application of a jackknifing approach to variance estimation of ability inferences for groups of students, using a multidimensional discrete model for item response data. The data utilized to demonstrate the approach come from the National Assessment of Educational Progress (NAEP). In contrast to the operational approach used in NAEP, where plausible values are used to make ability inferences, the approach presented in this paper reestimates all parameters of the model, and makes ability inferences based on replicate samples of the jackknife without using plausible values. Results of the standard errors are presented for estimates of group means, total means, and other statistics used in official reporting by NAEP. Differences in results between this approach and the operational approach are discussed.