- Volume 23 Issue 4
DOI QR Code
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
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.
- Chung, Y., Jung, D. and Heo, S. (2009). 2009 Customer satisfaction evaluation survey to the service from Gyeongsangnam-do regional offices of education, Changwon National Univeristy, Gyeongnam.
- Heo. S. and Chang. D. (2010). A sample survey design for service satisfaction evaluation of regional education offices. Journal of the Korean Data & Information Science Society, 21, 671-678.
- Holt, D., Scott, A. J. and Ewings, P. D. (1980). Chi-squared tests with survey data. Journal of the Royal Statistical Society A, 143, 302-320.
- Heo, S. (2006). Power analysis of the Rao-Scott first-order adjustment to the Pearson test for homogeneity. Proceedings of Joint Statistical Meeting, Seattle, U.S.A., 3126-3129.
- Kim, D. H., Cho, K. H., Hwang, J. S. and Jung, K. H. (2009). A sample design for life and attitude survey of Gyeongbuk people. Journal of the Korean Data & Information Science Society, 20, 1165-1167.
- Kim, D. H., Hwang, J. S. and Kwak, S. G. (2010). A sample design for the survey on actual state of SMEs. Journal of the Korean Data & Information Science Society, 21, 1021-1029.
- Lee, C., Kang, H. and Sim, S. (2012). An implementation of the sample size and the power for testing mean and proportion. Journal of the Korean Data & Information Science Society, 23, 53-61. https://doi.org/10.7465/jkdi.2012.23.1.053
- Lavrakas, P. J. (2008). Encyclopedia of survey research methods, Vol.2, SAGE Publication, Inc., London.
- Rao, J. N. K. and Scott, A. J. (1981). The analysis of categorical data from complex sample surveys: Chi-squared tests for goodness of fit the independence in two-way tables. Journal of the American Statistical Association, 76, 221-230. https://doi.org/10.1080/01621459.1981.10477633
- Rao, J. N. K. and Scott, A. J. (1984). On chi-squared test for multiway contingency tables with cell proportions estimated from survey data. The Annals of Statistics, 12, 46-60. https://doi.org/10.1214/aos/1176346391
- Rao, J. N. K. and Scott, A. J. (1987). On simple adjustments to chi-square tests with sample survey data. The Annals of Statistics, 15, 385-397. https://doi.org/10.1214/aos/1176350273
- Shao, J. (1996). Resampling methods in sample surveys (with discussion). Statistics, 27, 203-254. https://doi.org/10.1080/02331889708802523
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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 vol.7, pp.3, 2014, https://doi.org/10.13160/ricns.2014.7.3.208