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Effect of complex sample design on Pearson test statistic for homogeneity

복합표본자료에서 동질성검정을 위한 피어슨 검정통계량의 효과

  • Heo, Sun-Yeong (Department of Statistics, Changwon National University) ;
  • Chung, Young-Ae (Department of Childhood Education, Changwon National University)
  • Received : 2012.06.25
  • Accepted : 2012.07.19
  • Published : 2012.07.31

Abstract

This research is for comparison of test statistics for homogeneity when the data is collected based on complex sample design. The survey data based on complex sample design does not satisfy the condition of independency which is required for the standard Pearson multinomial-based chi-squared test. Today, lots of data sets ara collected by complex sample designs, but the tests for categorical data are conducted using the standard Pearson chi-squared test. In this study, we compared the performance of three test statistics for homogeneity between two populations using data from the 2009 customer satisfaction evaluation survey to the service from Gyeongsangnam-do regional offices of education: the standard Pearson test, the unbiasedWald test, and the Pearsontype test with survey-based point estimates. Through empirical analyses, we fist showed that the standard Pearson test inflates the values of test statistics very much and the results are not reliable. Second, in the comparison of Wald test and Pearson-type test, we find that the test results are affected by the number of categories, the mean and standard deviation of the eigenvalues of design matrix.

References

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