Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 29978
Choosing between the Regression Correlation, the Rank Correlation, and the Correlation Curve

Authors: Roger L Goodwin

Abstract:

This paper presents a rank correlation curve. The traditional correlation coefficient is valid for both continuous variables and for integer variables using rank statistics. Since the correlation coefficient has already been established in rank statistics by Spearman, such a calculation can be extended to the correlation curve. This paper presents two survey questions. The survey collected non-continuous variables. We will show weak to moderate correlation. Obviously, one question has a negative effect on the other. A review of the qualitative literature can answer which question and why. The rank correlation curve shows which collection of responses has a positive slope and which collection of responses has a negative slope. Such information is unavailable from the flat, ”first-glance” correlation statistics.

Keywords: Bayesian estimation, regression model, rank statistics, correlation, correlation curve.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1106889

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF

References:


[1] S. Blyth, ”Karl Pearson and the Correlation Curve,” International Statistical Review / Revue Internationale de Statistique, Vol. 62, No. 3 (Dec., 1994), pp. 393-403.
[2] B. L. Bowerman and R. T. O’Connell, Linear Statistical Models: An Applied Approach, Second Edition, Duxbury Press, Belmont, CA, 1990.
[3] J. B. Forsythe and O. Wilhite, ”Testing Alternative Versions of Agriculture Census Questionnaires,” Proceedings of the Business and Economic Statistics Section, American Statistical Society, 1972, pp 206- 215.
[4] L. D. Goodwin and N. L. Leech, ”Understanding Correlation: Factors That Affect the Size of r,” The Journal of Experimental Education, Vol. 74, No. 3 (Spring, 2006), pp. 251-266.
[5] G. Kalton and H. Schuman, ”The Effect of the Question on Survey Responses: A Review,” Journal of the Royal Statistical Society, Series A (General), Vol. 145, No. 1 (1982), pp.42-73.
[6] E. L. Lehmann and H. J. M. D’Abrera, Nonparametrics: Statistical Methods Based on Ranks, Holden-Day, Inc., Oakland, CA, 1975.
[7] J. C. Liechty, M. W. Liechty and P. Mller, ”Bayesian Correlation Estimation,” Biometrika, Vol. 91, No. 1 (Mar., 2004), pp. 1-14.
[8] N. D. Rothwell and A. M. Rustmeyer, ”Studies of Census Mail Questionnaires,” Journal of Marketing Research, 16, 1979, 401-406.