While an auxiliary information in double sampling increases the
precision of an estimate and solves the problem of bias caused by non-response
in sample survey, the question is that, does the level of correlation between
the auxiliary information x and
the study variable y ease in the accomplishment of the objectives of using double sampling? In this
research, investigation was conducted through empirical study to ascertain the
importance of correlation level between the auxiliary variable and the study
variable to maximally accomplish the importance of auxiliary variable(s) in
double sampling. Based on the Statistics criteria employed, which are minimum
variance, coefficient of variation and relative efficiency, it was established that
the higher the correlation level between the study and auxiliary variable(s)
is, the better the estimator is.
Cite this paper
D. Agunbiade and P. Ogunyinka, "Effect of Correlation Level on the Use of Auxiliary Variable in Double Sampling for Regression Estimation," Open Journal of Statistics
, Vol. 3 No. 5, 2013, pp. 312-318. doi: 10.4236/ojs.2013.35037
 W. G. Cochran, “Sampling Technique,” 3rd Edition, John Willey and Sons Inc., New York, 1977.
 L. S. Lohr, “Sampling Design and Analysis,” 2nd Edition, Brooks/Cole Cengage Learning, 2010, p. 596.
 F. C. Okafor and H. Lee, “Double Sampling for Ratio and Regression Estimation with Sub-Sampling the Non-Res- pondents,” Survey Methodology, Vol. 26, No. 2, 2000, pp. 183-188.
 B. K. Pradhan, “A Chain Regression Estimator in Two- Pahse Sampling Using Multi-Auxiliary Information,” Bul- letin of the Malaysian Mathematical Sciences Society, Vol. 28, No. 1, 2005, pp. 81-86.
 A. A. Sodipo and K. O. Obisesan, “Estimation of the Po- pulation Mean Using Difference Cum Ratio Estimator with Full Response on the Auxiliary Character,” Research Journal of Applied Sciences, Vol. 2, No. 6, 2007, pp. 769- 772.
 P. Mukhopadhyay, “Survey Sampling,” Narosa Publishing House Pvt. Ltd., 2007, p. 256.
 F. C. Okafor, “Sample Survey Theory with Applications,” Afro-Orbis Publication Ltd., 2002.
 A. Koutsoyiannis, “Theory of Econometrics,” 2nd Edition, Palgrave Publishers Ltd. (Formerly Macmillan Press Ltd.), 1977.
 M. G. Kendall, “A New Measure of Rank Correlation,” Bi- ometrika, Vol. 30, No. 1, 1938, pp. 81-89.
 M. G. Kendall, “Rank Correlation Methods,” 4th Edition, Griffin, London, 1948.
 T. Kossowski and J. Kauke, “Comparison of Values of Pearson’s and Spearman’s Correlation Coefficients on the Same Set of Data,” Quaestiones Geographicae, Vol. 30, No. 2, 2011, pp. 87-93.
 R. Haining, “Bivariate Correlation with Spatial Data,” Ge- ographical Analysis, Vol. 23, No. 3, 1991, pp. 210-227.
 D. A. Griffith, “Spatial Autocorrelation and Sptial Filter- ing” Springer, Berlin, 2003.
 W. A. Nicewander and J. L. Rodgers, “Thirteen Ways to Look at Correlation Coefficient,” The American Statisti- cian, Vol. 42, No. 1, 1988, pp. 59-66.
 F. M. Lord and M. R. Novick, “Statistical Theories of Men- tal Test Scores,” Addison-Wesley, Reading, 1968.
 M. A. Lang Tom, “Common Statistical Errors Even You Can Find! Part 4: Errors in Correlation and Regression Analyses,” AMWA Journal, Vol. 20, No. 1, 2005, pp. 10- 11.
 N. Shaban, “Analysis of Correlation and Regression Co- efficients of the Interaction between Yildans Come Para- meters of Snap Bears Plants,” Trakia Journal of Science, Vol. 3, No. 6, 2005, pp. 27-31.
 D. J. Ozer, “Correlation and Coefficient of Determination,” Psychological Bullentin, Vol. 97, No. 2, 1985, pp. 307- 315. http://dx.doi.org/10.1037/0033-2909.97.2.307
 M. M. Mukaka, “A Guide to Appropriate Use of Corre- lation Coefficient in Medical Research,” MMJ, Vol. 24, No. 3, 2012, pp. 69-71.