*2.2. Methods*

The study primarily employed two methods.

The first was to normalise the diagnostic attributes and present them as averaged values (the Perkal index) [27,28]. This entailed a synthetic approach to environmental determinants and selected agricultural characteristics. Calculations were made according to the formula:

$$Z\_{ji} = \frac{(X\_{ji} - av \text{g.} X\_i)}{\delta\_i} \,\tag{1}$$

where: *Zji*—normalised value of diagnostic feature "*i*" in spatial unit "*j*"; *Xji*—value of diagnostic feature "*i*" in spatial unit "*j*"; *avg*.*Xi*—mean value of diagnostic feature "*i*"; *δi* —standard deviation of diagnostic feature "*i*".

The baseline values (national averages) of the indices so constructed were used as the basis for the spatial delimitation of values. In the cartographic presentation—assuming a threshold of ±0.5 of a standard deviation (*δ*)—four classes were distinguished, while in the statistical analyses (see tables), the indices for spatial units were generalised into two groups: above the national average (↑) and below (↓).

The second method was the D'Hondt method [29], which allows any structure to be objectively examined [30,31]. The method is practically applied, among others, to distributing seats in the electoral systems of many countries [32]. In this case, it consists, in essence, of dividing each absolute value or percentage assigned to O, E and H by the integers 1 to 6, producing a set of 18 quotients. Then, the six largest quotients are selected from this set. Next, each tested element (O, E and H) is assigned a weighting corresponding directly numerically to how many of these six largest quotients belong to it (i.e., if one of the six largest quotients belongs to O, O is weighted as 1, etc.). The analysed distributions were spatially delimited based on this weighting, conventionally reflecting the share of a given element as: 1—very low, 2—low, 3—significant, 4—high, 5—very high, 6—total dominance in the distribution. The predominant number of quotients was adopted as the criterion, and the number of quotients was aggregated into two groups (of 1, 2, 3, 4 quotients, and of 5 and 6 quotients), and this was used as the basis of the spatial typology of the breakdown of subsidised land by type of pro-environmental payments. This division into two groups of quotient numbers highlighted areas with the highest shares of a given type of support. Attempts to use a larger number of quotient groups (e.g., first group—1 and 2 quotients; second group—3 and 4 quotients; third group—5 and 6 quotients) significantly increased the number of sub-types, thereby worsening the readability and making spatial interpretation difficult.

The discussed method was used mainly for its modifiability (aggregation into a system of two groups) and the clarity of interpretation of results, i.e., the identification and characterisation of individual types. The typology was based on an a posterioriapproach that consists of distinguishing typological classes and identifying types [33].

The research also used Pearson's linear correlation coefficient (*r*). This made it possible to assess the strength and direction of the relationship between the structure and the level of support for the researched measures and the determinants of the green development of agriculture in Poland.

### *2.3. Identification of Determinants: Planes for the Evaluation of Pro-Environmental Payments*

To more fully interpret the spatial differentiation of farmland covered by pro-environmental payments, diagnostic attributes were distinguished that were expressed as average normalised values and then used as the basis for assessing the environmental determinants and the level of selected characteristics of farms.

Environmental determinants were analysed using three diagnostic attributes, i.e.,


In addition to environmental determinants, the research also attempted to assess the impact of selected non-environmental characteristics. Despite the numerous determinants featured in the literature (level of socio-economic development, state agropolitics, sales markets, level of urbanisation) [34], this was done using only the following three diagnostic farm characteristics:


Furthermore, it should be emphasised that the spatial differentiation of the characteristics taken into account is a result of economic history and dates back to the 18th century [35]. At that time, Poland underwent what is referred to as the three 'Partitions', which involved the loss of rule to Russia, Prussia and Austria, as a result of which the area of Poland was shrinking gradually until the Polish state ceased to exist altogether after the third Partition. The more than 120 years of foreign rule resulted in the socio-economic polarisation of Polish territory. The divides between the eastern, western and southern parts of the Polish territory were so deep, strong and conspicuous that they are still perceivable today, such as in the structure of agriculture and agricultural practices [36].
