Large scale surveys usually employ a complex sampling design and as a consequence, no standard methods for estimation of the standard errors associated with the estimates of population means are available. Resampling methods, such as jackknife or bootstrap, are often used, with reference to their properties of robustness and reduction of bias. A method based on variance component models is proposed as an alternative to the jackknife procedure used for calculation of the standard errors for the subpopulation means of proficiency scores in a large scale survey of education in the United States. A simulation study provides evidence that the jackknife estimator for the standard error of the estimate of the mean is substantially less efficient than its variance component counterpart. The ultimate decision to use variance component methods should be based on the predicted (guessed) impact of the features of the data not accounted for by the variance component models. An appendix contains the scoring algorithm. Six tables present analysis results. (Contains seven references.) (Author/SLD)