Comparison of Values of Pearson's and Spearman's Correlation Coefficients on the Same Sets of Data
Spearman's rank correlation coefficient is a nonparametric (distribution-free) rank statistic proposed by Charles Spearman as a measure of the strength of an association between two variables. It is a measure of a monotone association that is used when the distribution of data makes Pearson's correlation coefficient undesirable or misleading. Spearman's coefficient is not a measure of the linear relationship between two variables, as some "statisticians" declare. It assesses how well an arbitrary monotonic function can describe a relationship between two variables, without making any assumptions about the frequency distribution of the variables. Unlike Pearson's product-moment correlation coefficient, it does not require the assumption that the relationship between the variables is linear, nor does it require the variables to be measured on interval scales; it can be used for variables measured at the ordinal level. The idea of the paper is to compare the values of Pearson's product-moment correlation coefficient and Spearman's rank correlation coefficient as well as their statistical significance for different sets of data (original - for Pearson's coefficient, and ranked data for Spearman's coefficient) describing regional indices of socio-economic development.
Anderson T.W., 1996. R.A. Fisher and multivariate analysis. Statistical Science 11 (1): 20-34.
Bravais A., 1846. Analyse mathématique sur les probabilités des erreurs de situation d'un point. Mémoires présentés par divers savants à l'Académie Royale des Sciences de l'Institut de France 9: 255-332.
Daniels H.E., 1944. The relation between measures of correlation in the universe of sample permutations. Biometrika 33 (2): 129-135.
Fisher R.A., 1915. Frequency distribution of the values of the correlation coefficient in samples from an indefinitely large population. Biometrika 10: 507-521.
Fisher R.A., 1921. On the "probable error" of a coefficient of correlation deduced from a small sample. Metron 1: 3-32.
Galton F., 1869. Hereditary genius. An inquiry into its laws and consequences. MacMillan, London.
Galton F., 1875. Statistics by intercomparison. Philosophical Magazine 49: 33-46.
Galton F., 1885. Regression towards mediocrity in hereditary stature. Journal of the Anthropological Institute 15: 246-263.
Galton F., 1877. Typical laws of heredity. Proceedings of the Royal Institution 8: 282-301.
Galton F., 1888. Co-relations and their measurement, chiefly from anthropometric data. Proceedings of the Royal Society of London 45: 135-145.
Galton F., 1890. Kinship and correlation. North American Review 150: 419-431.
Griffith D.A., 2003. Spatial autocorrelation and spatial filtering. Springer, Berlin.
Haining R., 1991. Bivariate correlation with spatial data. Geographical Analysis 23 (3): 210-227.
Kendall M.G., 1938. A new measure of rank correlation. Biometrika 30: 81-89.
Pearson K., 1896. Mathematical contributions to the theory of evolution. III. Regression, heredity, and panmixia. Philosophical Transactions of the Royal Society Ser. A 187: 253-318.
Pearson K., 1900. Mathematical contributions to the theory of evolution. VII. On the correlation of characters not quantitatively measurable. Philosophical Transactions of the Royal Society Ser. A 195: 1-47.
Pearson K., 1920. Notes on the history of correlation. Biometrika 13: 25-45.
Piovani J.I., 2008. The historical construction of correlation as a conceptual and operative instrument for empirical research. Quality & Quantity 42: 757-777.
Plata S., 2006. A note on Fisher's correlation coefficient. Applied Mathematical Letters 19: 499-502.
Rodgers J.L. & Nicewander W.A., 1988. Thirteen ways to look at the correlation coefficient. The American Statistician 42 (1): 59-66.
Spearman C.E, 1904a. The proof and measurement of association between two things. American Journal of Psychology 15: 72-101.
Spearman C.E, 1904b. General intelligence, objectively determined and measured. American Journal of Psychology 15: 201-293.
Spearman C.E., 1910. Correlation calculated from faulty data. British Journal of Psychology 3: 271-295.
Stigler S.M., 1988. Francis Galton's account of the invention of correlation. Statistical Science 4 (2): 73-86.
Student, 1908. Probable error of a correlation coefficient. Biometrika 6: 302-310.
Valz P.D. & Thompson M.E., 1994. Exact inference for Kendall's S and Spearman's rho. Journal of Computational and Graphical Statistics 3: 459-472.
Walker H. M., 1928. The relation of Plana and Bravais to theory of correlation. Isis 10 (2): 466-484.
Weida F.M., 1927. On various conceptions of correlation. The Annals of Mathematics, Second Series 29 (1/4): 276-312.