통합자연과학논문집 (Journal of Integrative Natural Science)

조선대학교 기초과학연구원 (The Basic Science Institute Chosun University)
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Empirical Analysis on Rao-Scott First Order Adjustment for Two Population Homogeneity test Based on Stratified Three-Stage Cluster Sampling with PPS

  • Heo, Sunyeong (Department of statistics, Changwon National University)
  • 투고 : 2014.07.30
  • 심사 : 2014.09.25
  • 발행 : 2014.09.30
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초록

National-wide and/or large scale sample surveys generally use complex sample design. Traditional Pearson chi-square test is not 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-Scott first order adjusted test to Wald test for homogeneity between two populations using 2009 Gyeongnam regional education offices's customer satisfaction survey (2009 GREOCSS) data. The 2009 GREOCSS data were collected based on stratified three-stage cluster sampling with probability proportional to size. The empirical results show that the Rao-Scott adjusted test statistic using only the variances of cell probabilities is very close to the Wald test statistic, which uses the covariance matrix of cell probabilities, under the 2009 GREOCSS data based. However it is necessary to be cautious to use the Rao-Scott first order adjusted test statistic in the place of Wald test because its efficiency is decreasing as the relative variance of eigenvalues of the design matrix of cell probabilities is increasing, specially more when the number of degrees of freedom is small.

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참고문헌

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  7. S. Heo and D. Chang, "A sample survey design for service satisfaction evaluation of regional education offices". J. Korean Data Inform. Sci. Soc., Vol 21, pp. 671-678, 2010.
  8. Y. Chung, D, Jung, and S. Heo, "2009 Customer satisfaction evaluation survey to the service from Gyeongsangnam-do regional offices of education", Changwon National University, 2009.

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