6. Conclusions
Yan Lu
In this research, we extend Wald’s (1943) test and Rao-Scott first-order and second-order corrected tests (Rao and Scott 1981) from a single survey to a dual frame survey and derive the asymptotic distributions. A limited simulation study suggests that second order corrected tests almost reach the nominal level. Although the results in this paper are for dual frame surveys, the methods are general and could be extended to more than two surveys. Our research is done in the context of survey sampling; it also applies to other settings in which data could be combined from two independent sources.
Acknowledgements
The author thanks Dr. Sharon Lohr for her valuable advisement and comments on the manuscript. The author also wants to thank the referees and the associate editor for their very helpful comments and constructive suggestions.
References
Bedrick, E.J. (1983). Adjusted chi-squared tests for cross-classified tables of survey data. Biometrika, 70, 591-595.
Fay, R.E. (1979). On adjusting the Pearson chi-square statistic for clustered sampling. In ASA Proceedings of the Social Statistics Section, 402-406. American Statistical Association.
Fay, R.E. (1985). A jackknifed chi-squared test for complex samples. Journal of the American Statistical Association, 80, 148-157.
Fuller, W.A. and Burmeister, L.F. (1972). Estimators for samples selected from two overlapping frames. In ASA Proceedings of the Social Statistics Section, 245-249. American Statistical Association.
Hartley, H.O. (1962). Multiple frame surveys. In ASA Proceedings of the Social Statistics Section, 203-206. American Statistical Association.
Hartley, H.O. (1974). Multiple frame methodology and selected applications. Sankhyā, Series C, 36 (3), 99-118.
Isaki, C.T. and Fuller, W.A. (1982). Survey design under the regression superpopulation model. Journal of the American Statistical Association, 77, 89-96.
Lohr, S.L. and Rao, J.N.K. (2000). Inference from dual frame surveys. Journal of the American Statistical Association, 95, 271-280.
Lohr, S.L. and Rao, J.N.K. (2006). Estimation in multiple-frame surveys. Journal of the American Statistical Association, 101, 1019-1030.
Lu, Y. and Lohr, S. (2010). Gross flow estimation in dual frame surveys. Survey Methodology, vol. 36, 13-22.
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 and independence in two-way tables. Journal of the American Statistical Association, 76, 221-230.
Rao, J.N.K. and Scott, A.J. (1984). On chi-squared tests for multiway contingency tables with cell proportions estimated from survey data. The Annals of Statistics, 12, 46-60.
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.
Rao, J.N.K. and Thomas, D.R. (1988). The analysis of cross-classified categorical data from complex sample surveys. Sociological Methodology, 18, 213-269.
Skinner, C.J. (1991). On the efficiency of raking ratio estimation for multiple frame surveys. Journal of the American Statistical Association, 86, 779-784.
Skinner, C.J. and Rao, J.N.K. (1996). Estimation in dual frame surveys with complex designs. Journal of the American Statistical Association, 91, 349-356.
Thomas, D.R., Singh, A. and Roberts, G. (1996). Tests of independence on two-way tables under cluster sampling: An evaluation. International Statistical Review, 64(3), 295-311.
Wald, A. (1943). Tests of statistical hypotheses concerning several parameters when the number of observations is large. Transactions of the American Mathematical Society, 54, 426-482.
- Date modified: