Summary:

Determining infrastructural potential of a municipality is possible by measuring a number of diagnostic features describing this potential in the municipality – the number of these variables depends mainly on the purpose of the analysis. 13 variables considered as diagnostic were used in this paper to illustrate diversification of agricultural infrastructure of farms on the municipality level. The set of these variables marks a point in the multidimensional space, which is characteristic for each investigated object but differentiating objects among themselves. The potential was estimated on the basis of synthetic measure of development which is an aggregate of diagnostic features. The computed synthetic index reduces multidimensional data to a single number and replaces the point in the multidirectional space by a point on an axis in one-dimensional space. The goal of the article is to show if the picture of a population of municipalities in their many dimensions and original shape seen through synthetic coefficient is similar to the original and whether the obtained one-dimensional distance properly reflects distances in the initial space of the studied infrastructure potential. In the presented work the information quality provided by the synthetic coefficient computed for the studied districts has been analysed using multidimensional scaling. Computational method of multidimensional scaling involves minimisation of the function called stress function or slightly modified standard stress function, so called coefficient of alienation, where dij are reproduced distances at a given number of coordinates in the space of scaling. In the scaling method no limitation are imposed on the form of expressions defining the distance. In order to facilitate the interpretation and limit the scope of the article, only two dimensions of the space of scaling were assumed. Shepard diagram was used for scaling quality assessment. A method of reduction of dimensions number is approximation of experimentally determined matrix of distance between objects using a lower number of dimensions. In this work we use 13 variables illustrating the potential of agricultural infrastructure of farms and the numerical force of the 1st group (areas with low value of development measure) is 67, the 2nd group (areas with average values of development measure) is 77, 3rd group (areas with high values of development measure) is 19 and the 4th group (areas of very high value of development) is 13. These data sets were used to formulate distance matrices, which have dimensions of following square matrices: the 67x 67 matrix for the first group, the 77 x 77 matrix for the second group, 19 x 19 for the third group and 13 x 13 for the fourth group. The usual Euclidean distance has been used for the analysis conducted. The coordinates were interpreted on the basis of conducted correlation analysis of scaling space coordinates with initial variables. The studies comprised 178 municipalities of the malopolskie province for which it was possible to obtain statistical data and distinguish between agricultural infrastructure and municipal infrastructure of the investigated municipality.