## 3 Results  
The pine stands under analysis had different densities, ranging from 1800 trees\(\cdot\)ha\({}^{-1}\) to 3900 trees\(\cdot\)ha\({}^{-1}\) (a difference of 46%). The diameter at breast height ranged between 5 and 27 cm. The analysis of the percentage share of the bark damage instances in the investigated tree stands revealed that the stripping in all the experimental sites was a mass phenomenon. The bark stripped pines constituted 65-96 % of the analysed single-species pine stands. The instances of bark damage were located at a height between 1.0 and 2.6 m from the ground and their lengths ranged from 40 to 70 cm. [PERSON]'s correlation coefficient between the trees' density on the plot and the number of bark stripping trees is r = 0.92 (\(p<p_{cr}\)). On the other hand, the correlation coefficient between the density of trees on the plot and the NBDI is r = 0.81 (\(p<p_{cr}\)). The bark damage observed on the trees did not exceed four instances. The Poisson distribution with \(\lambda\) = 1.38 was used for the description of the observed NBDI (Figure 1). The Kolmogorov-Smirnov test was applied to verify the coherence of the theoretical and empirical distributions. The calculated \(p\)-value was bigger than the critical \(p_{cr}\), confirming the consistency of both distributions. The distribution of DBH is unimodal and approximately symmetric. The contour of the distribution indicates normal distribution of the data. Figure 2 shows the histogram of DBH distribution and a curve representing the density of the normal distribution (for a mean = 13.7 and SD = 3.9). Figure 1: Tree numbers observed (black bars) and calculated from the Poisson distribution (grey bars, \(\lambda\) = 1.38) with \(\{0..4\}\) damage instances. A line representing the density of the normal distribution seems to adequately describe the histogram of the DBH observations. Shapiro-Francia, Anderson-Darling, and Cramer-von Mises tests were used for the evaluation of DBH distribution normality. The calculated \(p\)-values were orders of magnitude lower than the critical \(p_{cr}\). Rejection of the null hypothesis regarding the DBH distribution normality was clear. Uniformity of NBDI and DBH distribution with respect to the 25 sampling areas identified with factor variable ID was evaluated. The generalised linear model (GLM) with Poisson error distribution was used for testing NBDI dependence on ID [63; 64]. The model formula was:  
\[\text{NBDI}\sim\text{ID}\]  
i.e., NBDI depends linearly on ID. The \(p\)-values of the structural parameters corresponding to the individual IDs were bigger than the \(p_{cr}\). No evidence for the influence of the area ID on average NBDI was found. The distribution of DBH was non-normal. An ANOVA model DBH-ID for the comparison of means produced non-normal residuals impairing \(p\)-value interpretation. The pairwise Wilcoxon rank sum test was used for testing the homogeneity in location parameters of the DBH observations in the different areas. The observation results collected in the areas under analysis were compared with one another. The Benjamini and Hochberg method was used for \(p\)-value adjustment with respect to multiple comparisons [65]. No significant shift in DBH distributions for pairs of areas was identified. To evaluate an effect of both ID and DBH on NBDI models, NBDI-ID + DBH with Poisson and binomial error distribution were assessed. In both models the \(p\)-values corresponding to DBH structural parameters were lower than \(p_{cr}\). Conversely, for all levels of ID the related \(p\)-values were higher than \(p_{cr}\). The analysis of the data concerning the observed areas indicates homogenous distribution of the basic statistical properties. The influence of ID on the variables can be ignored. Only 16.8% of the trees at all the sites were undamaged. The majority of the damage to the trees was limited to one (43.5%) or two (24.9%) instances. Trees with three instances of bark damage made up 12.7% of the total, and sporadically, some trees had four instances (1.1%).