## 3 Results
The influence of NBDI on DBH was investigated. Table 1 shows the statistical parameters of DBH for different NBDI. Figure 2: Distribution of all the tree diameters at breast height. Similar means and medians for the NBDI: {0..4}, indicate no outlying observations. This assertion is supported by similar SD and MAD values. The general tendency shows a decrease in the parameter values corresponding with an increase in NBDI. Figure 3 depicts density plots illustrating distributions of DBH for respective NBDI. The distributions are unimodal, with decreasing positions of maximum and variability along with increasing NBDI. Figure 4 shows positions of the ranges that limit 90% of the most frequent DBH values. Five percent tails of the lowest and highest values were cut to illustrate the most common values of DBH. A shift of the ranges toward lower DBH values and a decrease in their length along with an increase in NBDI were observed. A clear exception is the range for NBDI = 4. Low numbers of observations used in the calculations may be the cause of the range that is wider than expected. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**NBDI [–]**} & \multicolumn{5}{c}{**DBH [cm]**} & \multicolumn{2}{c}{**Number of Trees [pcs]**} \\  & **Min** & **Mean** & **Median** & **Max** & **SD** & **MAD** & \\ \hline
0 & 8 & 16.8 & 17 & 26 & 3.6 & 3.0 & 106 \\
1 & 10 & 15.7 & 15 & 27 & 2.8 & 3.0 & 274 \\
2 & 8 & 11.1 & 11 & 14 & 1.5 & 1.5 & 163 \\
3 & 6 & 8.9 & 9 & 12 & 1.5 & 1.5 & 80 \\
4 & 5 & 6.4 & 7 & 8 & 1.1 & 1.5 & 7 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The values of minimum, arithmetic mean, median, maximum, standard deviation (SD) and median absolute deviation (MAD) were calculated from DBH for different NBDI. Figure 3: Density of diameter breast height (DBH) distribution in relation to the number of bark damage instances (NBDI) on the tree. The influence of NBDI on DBH changes was studied. Figure 5 contains boxplots representing DBH distribution for different NBDI. The positions of boxes in the plot suggest a monotonical decrease in DBH along with increasing NBDI. Because distributions of both variables were different, the Spearman correlation coefficient \(\rho\) and its \(p\)-value were calculated for co-variability assessment. The calculated \(\rho=-0.748\) (\(p\)-value \(<<p_{cr}\)) indicated a decrease in DBH along with increasing NBDI. A linear model was applied for DBH description using the NBDI parameter. The calculated slope was \(-2.98\) and the intercept was \(17.8\). The corresponding \(p\)-values for both coefficients were orders of magnitude lower than \(p_{cr}\). The conclusion from the subsequent analysis of the model is that it can be regarded only as a rough estimation of the real DBH dependence on the NBDI. The model does not accomplish homoskedasticity (verified with the Breusch-Pagan test against heteroskedasticity, \(p\)-value \(<<p_{cr}\)) and normal distribution of the model residuals (tests for normality, \(p\)-value \(<<p_{cr}\)). Figure 4: The 95% confidence intervals for the DBH means for trees with {0.4} instances of bark stripping damage. Figure 5: Median (horizontal line in box), the 25 th percentile to the 75 th percentile (box spans) and a ’whisker’ ranging to maximum and minimum but no more than 1.5 times of the interquartile range (IQR) from the box top and bottom, respectively.