Comparison of Pearson’s and Spearman’s correlation coefficients for selected traits of Pinus sylvestris L.

Abstract

Summary The Spearman rank correlation coefficient is a non-parametric (distribution-free) rank statistic proposed by Charles Spearman as a measure of the strength of the relationship between two variables. It is a measure of a monotonic relationship that is used when the distribution of the data makes Pearson’s correlation coefficient undesirable or misleading. The Spearman coefficient is not a measure of the linear relationship between two variables. It assesses how well an arbitrary monotonic function can describe the relationship between two variables, without making any assumptions about the frequency distribution of the variables. Unlike Pearson’s product-moment (linear) correlation coefficient, it does not require the assumption that the relationship between variables is linear, nor does it require that the variables be measured on interval scales; it can be applied to variables measured at the ordinal level. The purpose of this study is to compare the values of Pearson’s product-moment correlation coefficient and Spearman’s rank correlation coefficient and their statistical significance for six morpho-anatomical traits of Pinus sylvestris L. (original – for Pearson’s coefficient, and ranked – for Spearman’s coefficient) estimated from all observations, object means (for trees), and medians. The results show that the linear and rank correlation coefficients are consistent (as to direction and strength). In cases of divergence in the direction of correlation, the correlation coefficients were not statistically significant, which does not imply consistency in decision-making. Estimation of correlation coefficients based on medians is robust to outlier observations and factors that linear correlation is then very similar to rank correlation.