Variance Estimation within a Nested Two-Stage Sample Design

• Activity Number: 405
• Type: Contributed
• Date/Time: Thursday, August 15, 2002 : 10:30 AM to 12:20 PM
• Sponsor: Section on Survey Research Methods*
• Author(s): Steven Kaufman*+
• Affiliation(s): National Center for Education Statistics
• Keywords: Replication ; Bootstrap ; Complex Sample Design

Abstract

Replication variance estimation for a two-stage nested sample design is usually implemented by generating replicates that replicate the original first-stage sample selection. Since the second-stage is nested, the second-stage variance can be reflected by associating each second-stage unit with its respective first-stage unit (i.e., the second stage sampling is not directly incorporated into the replicates). As long as the first-stage sampling rates are not too high or sampling is done with replacement, this should provide a reasonable variance approximation. This paper investigates whether generating replicates that directly reflect both the first and second stage sampling provide any advantages over replicates that directly reflect only the first-stage sampling. A simulation is performed using a stratified randomized PPS systematic selection procedure to select the first-stage sample, while the second-stage sample is selected using a without-replacement simple random sample. With the development of the appropriate two variance estimators, relative errors, relative mean-square errors, and coverage rates are computed to measure any differences between estimators.