Fundamentals of Statistics contains material of various lectures and courses of H. Lohninger on statistics, data analysis and chemometrics......click here for more. 
Home Bivariate Data Correlation Spearman's Rank Correlation  
See also: correlation coefficient  
Spearman's Rank CorrelationCalculating Pearson's correlation coefficient requires the two samples to be linearly related and the scale of measurement has to be at the interval level. In the case of nonlinear relations, Pearson's correlation coefficient will lead to wrong results. A remedy to this situation may be the use of Spearman's rank correlation r_{s} (), which can be applied to ordinal data as well. The relation may be even nonlinear as long as it is monotonic. Basically, r_{s} differs from Pearson's correlation only in that the values are converted to ranks before computing the coefficient (the numerical equivalence is only true for untied data, in the case of tied data Pearson's and Spearman's coefficient will be slightly different). When replacing the observation values with the rank numbers the equation of the correlation coefficient may be simplified, resulting in the following formula: with D_{i} being the differences of the rank numbers. The equation is valid when n is greater than 4. In the case of tied observations one has to take the arithmetic average of the rank numbers associated with the ties.


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