Large-scale surveys often lead to two-stage stratified cluster sampling, which is to select schools first and then select students. The advantages of the two-stage stratified sampling are that the stratified sampling may be more convenient to administer, may results in a lower cost for the survey, and may give more precise estimates for population means. Combine with imputation adjustment for the reject participating schools and nonrespondent students, will reduce the estimates bias. In this study, we will develop a better sampling design, test design, a weighting method and a nonrespondents adjustments method for the Longitudinal Study on Taiwan Assessment of Student Achievement.
