An estimation of the design effect for the two-stage stratified cluster sampling design

Most large-scale educational surveys utilize a multi-stage stratified cluster sampling design. Past findings revealed that the standard errors of Taiwan students' mean performances were slightly larger than other countries'. In response to the request by the institute in charge of TIMSS sampling, this study was launched to derive a formula that could estimate the standard error of population mean prior to conducting a two-stage stratified cluster sampling design. This formula could then be used to select an optimal stratification framework that could reduce the size of standard error to an acceptable level. Its validity was investigated in three subsequent studies. In the first study, standard errors for 30 TIMSS 2007 participating countries were estimated according to the newly derived formula as well as by the jackknife replication. The correlation between the two sets of standard errors amounted to 0.98. The second study investigated the practicality of using the new formula in addition to auxiliary variables for predicting standard errors on the data of 29 countries that participated in both TIMSS 2003 and 2007. The third study explored the relationship between the number of stratum and the standard errors under a two-stage stratified cluster sampling design when the auxiliary variables for stratification were continuous. This paper closed by suggesting a four-step procedure to facilitate researchers in estimating standard errors of means during the planning stage of sampling design.