Article is devoted to consideration of an indicator - coefficient of correlation of Pearson, to his positive and negative sides of application for the analysis of dynamics and communication between the phenomena, and also the subsequent its modification. Modification of the correlation coefficient is carried out on the basis of replacement of a way of calculation of elements of a formula to be performed on the average values. Approbation of the modified correlation coefficient has been carried out and its merits revealed in more exact assessment of the closeness of links between variation of a studied factor and change of the indicator characterizing stability of the country tax system on empirical data have been shown.