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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At the turn of the 21st century Polish agriculture intensively changed as the consequence of: 1) the socio-economic transformation that started in 1989, 2) the general transition from a centrally-planned economy to a market economy and 3) Poland’s accession in 2004 to the European Union. In this paper, we try to describe, in a synthetic way, the spatial heterogeneity of development of agriculture in Poland. For this purpose we identified the types of contemporary Polish agriculture. We applied the measures of global (Moran 1950) and local (LISA) spatial autocorrelation devised by L. Anselin (1995) and used their calculations in classification methods. Our dataset consists of 69 variables and 3,069 spatial units at the LAU2 level. As the result of the analysis we identified 20 types of agriculture in Poland and presented their characteristic features. We have paid particular attention to a spatial distribution of identified types. We concluded that the distribution is not only a result of natural or socio-economic conditions and local spatial relationships, but also to a greater extent is still affected by historical conditions (mainly partitions and changes of borders after the First and Second World Wars).

We investigated changes in snow cover depth in eastern Europe over a period of about 100 yr, analyzing data for 5 stations located on the territory of the former Soviet Union. First we determined the basic characteristics of snow cover occurrence at each station: mean and extreme values of snow cover depth, standard deviation and variability index. Then, trends of changes in the mean monthly snow cover depth were analysed and turning points were identified using a Mann-Kendall test. Snow cover depth has decreased significantly at the 3 easternmost stations (Orenburg, Kirov, Gorkij), but at Kirov snow cover depth has increased again since 1950. At Vilnjus snow cover depth has decreased rapidly since the early 1980s. KEY WORDS: Eastern Europe · Trend analysis · Snow coverResale or republication not permitted without written consent of the publisher

The study shows the usefulness of the LISA and Kulldorff's spatial analyses in epidemiological studies, including the etiology of congenital malformations. Because the two methods work in different ways, good results can be obtained when they are used together.