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 productmoment 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.

1When fitting spatial regression models by maximum likelihood us- Where maximum likelihood methods are chosen for fitting spatial regres-3 sion models, problems can arise when data sets become large because it is 4 necessary to compute the determinant of an n × n matrix when optimizing the 5 log-likelihood function, where n is the number of observations. As Bayesian 6 methods for spatial regression may also require the handling of the same ma-7 trix, they may face the same technical issues of memory management and 8 algorithm choice. We have chosen here to term the problem we are considering 9 the "Jacobian", although the expression of interest is ln |I − λW|, where | · | 10 here denotes the determinant of matrix ·, I is the identity matrix, λ is a spatial 11 coefficient, and W is an n × n matrix of fixed spatial weights, so the problem 12 perhaps ought to be termed finding the logarithm of the determinant of the 13 Jacobian. In order to optimize the log-likelihood function with respect to λ, 14successive new values of this calculation are required. 15The often sparse matrix of spatial weights W represents a graph of rela- Although it may seem that the computation of the Jacobian is an unimpor-34 tant technical detail in comparison with the substantive concerns of analysts, 35we feel that this review may provide helpful insight for practical research using 36 spatial regression with spatial weights matrices representing spatial processes. 26We continue by defining spatial regression models to be treated here, the 27 data sets to be used for this comparison, and how we, following Higham (2002),

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