Empirical Analysis on Rao-Scott First Order Adjustment for Two Population Homogeneity test Based on Stratified Three-Stage Cluster Sampling with PPS

다국어 초록 (Multilingual Abstract)

National-wide and/or large scale sample surveys generally use complex sample design. Traditional Pearson chi-square test isnot appropriate for the categorical complex sample data. Rao-Scott suggested an adjustment method for Pearson chi-square test,which uses the average of eigenvalues of design matrix of cell probabilities. This study is to compare the efficiency of Rao-Scottfirst order adjusted test to Wald test for homogeneity between two populations using 2009 Gyeongnam regional educationoffices's customer satisfaction survey (2009 GREOCSS) data. The 2009 GREOCSS data were collected based on stratifiedthree-stage cluster sampling with probability proportional to size. The empirical results show that the Rao-Scott adjusted teststatistic using only the variances of cell probabilities is very close to the Wald test statistic, which uses the covariance matrix ofcell probabilities, under the 2009 GREOCSS data based. However it is necessary to be cautious to use the Rao-Scott first orderadjusted test statistic in the place of Wald test because its efficiency is decreasing as the relative variance of eigenvalues of thedesign matrix of cell probabilities is increasing, specially more when the number of degrees of freedom is small.

참고문헌 (Reference)

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