## 3 Results
### Mechanical Properties
#### 3.1.3 Modulus of Rupture  
The descriptive statistics of the MOR are presented in Table 9. The MOR had a strong correlation with air-dry density (0.720 and 0.770) and a very strong correlation with the MOE (0.919 and 0.900) in spruce and pine, respectively. Therefore, the MOR in each group mainly followed the MOE. Although the MOR in heartwood in the burned butt logs of spruce was the smallest of all groups, the relative difference from the other groups was smaller than in the case of the MOE. \begin{table}
\begin{tabular}{l r r r r r r r r} \hline \hline  & \multicolumn{4}{c}{**Norway Spruce**} & \multicolumn{4}{c}{**Scots Pine**} \\ \hline
**Source** & **F** & **df1** & **df2** & **Sig.** & **F** & **df1** & **df2** & **Sig.** \\ \hline Fire damage class & 2.782 & 2 & 120 & 0.066 & 0.760 & 2 & 119 & 0.470 \\ Height class & 10.522 & 2 & 120 & \textless{}0.001 & 5.644 & 2 & 119 & 0.005 \\ Radial position & 0.062 & 1 & 120 & 0.804 & 7.100 & 1 & 119 & 0.009 \\ Air-dry density & 17.392 & 1 & 120 & \textless{}0.001 & 66.026 & 1 & 119 & \textless{}0.001 \\ Radial position * air-dry density & 0.287 & 1 & 120 & 0.593 & 14.004 & 1 & 119 & \textless{}0.001 \\ \hline
**Random effect** & **Variance** & \multicolumn{4}{c}{**Variance**} \\ \hline Stand & 6.866 & \multicolumn{4}{c}{0.068} \\ Tree & 0.269 & \multicolumn{4}{c}{0.983} \\ Residual & 1.135 & \multicolumn{4}{c}{1.130} \\ \hline
**Fitting statistics** & \multicolumn{4}{c}{} \\ \hline R\({}^{2}\) & 36.7\% & \multicolumn{4}{c}{64.5\%} \\ Bias & \multicolumn{2}{c}{–1.01} & \multicolumn{2}{c}{0.00 (0.0\%)} \\ RMSE & \multicolumn{2}{c}{2.14 (25.4\%)} & \multicolumn{2}{c}{1.47 (15.0\%)} \\ \hline \hline \end{tabular} \({}^{*}\) refers to interaction.  
\end{table} 
Table 7: Fixed effects in the linear mixed model (Equation (9)) for the modulus of elasticity (MOE) and the variation in random effects. \begin{table}
\begin{tabular}{l r r r r r r r} \hline \hline  & \multicolumn{4}{c}{**Norway Spruce**} & \multicolumn{4}{c}{**Scots Pine**} \\ \hline
**Variable** & **Estimate** & \multicolumn{2}{c}{**Std. Error**} & \multicolumn{2}{c}{**95\% CI**} & \multicolumn{2}{c}{**Estimate**} & \multicolumn{2}{c}{**Std. Error**} & \multicolumn{2}{c}{**95\% CI**} \\ \hline  & & **Lower** & **Upper** & & & **Lower** & **Upper** \\ \hline Intercept & 1.717 & 2.866 & –3.956 & 7.391 & 1.314 & 1.375 & –1.408 & 4.036 \\ Fire damage class (ref: no damage) & & & & & & & \\  More damaged side & 0.869 & 0.442 & –0.007 & 1.745 & –0.020 & 0.443 & –0.897 & 0.857 \\  Less damaged side & 1.056 & 0.450 & 0.165 & 1.947 & –0.206 & 0.442 & –1.082 & 0.669 \\  Height class (ref: top log) & & & & & & & \\  Butt log & 0.034 & 0.313 & –0.586 & 0.654 & 0.729 & 0.401 & –0.065 & 1.524 \\  Middle log & 0.938 & 0.311 & 0.323 & 1.552 & 0.864 & 0.415 & 0.042 & 1.686 \\  Radial position (ref: heartwood) & & –0.584 & 2.353 & –5.243 & 4.074 & –4.899 & 1.764 & –8.391 & –1.407 \\  Air-dry density & 0.015 & 0.005 & 0.005 & 0.025 & 0.013 & 0.003 & 0.008 & 0.019 \\  Interaction of radial position with air-dry density (ref: heartwood * density) & & & & & & & \\  Sapwood * density & 0.003 & 0.005 & –0.007 & 0.013 & 0.012 & 0.003 & 0.005 & 0.019 \\ \hline \hline \end{tabular} \({}^{*}\) refers to interaction.  
\end{table} 
Table 8: Fixed coefficients in the linear mixed model (Equation (9)) for the modulus of elasticity (MOE). No significant differences were observed in the MOR of the spruce sapwood of the butt or middle logs, but the MOR of the sapwood of the burned trees in the top logs was lower than in the reference trees (Table 10). As for the MOE, density was the most significant factor affecting the MOR of spruce and pine (\(p<0.001\)). The radial position was a very significant factor in pine (\(p<0.001\)) but did not have any significance in spruce. Height class was a significant factor in spruce (\(p<0.05\)), but it did not have any significance in pine. In contrast to the MOE, fire damage class was a significant factor in pine (\(<\)0.05).