Abstract
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.
Highlights
IntroductionCorrelations between variables can be measured with the use of different indices (coefficients)
Historical backgroundCorrelations between variables can be measured with the use of different indices
Spearman’s rank correlation coefficient is a nonparametric rank statistic proposed by Charles Spearman as a measure of the strength of an association between two variables
Summary
Correlations between variables can be measured with the use of different indices (coefficients). Kendall’s tau, introduced by Kendall (1938), is a correlation coefficient that can be used as an alternative to Spearman’s rho for data in the form of ranks. In 1904 Spearman adopted Pearson’s correlation coefficient as a measure of the strength of the relationship between two variables that cannot be measured quantitatively. Spearman’s rank correlation coefficient is a nonparametric (distribution-free) rank statistic proposed as a measure of the strength of the 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. The data used in the analysis represent regional indices of socio-economic development
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