## 3 Results
### Results for the Screening of the Factors
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Response: Deflection (mm)** & \multicolumn{3}{c}{**Response: Deflection Ratio**} \\ \hline
**Term** & \(p\)**-Value** & **Term** & \(p\)**-Value** \\ \hline Pallet Stiffness & \textless{}0.0001 & Pallet Friction & \textless{}0.0001 \\ Pallet Friction & \textless{}0.0001 & Columns & \textless{}0.0001 \\ Weight & 0.0001 & Height \textless{} Pallet Friction & \textless{}0.0001 \\ Pallet Stiffness \(\times\) Weight & 0.0001 & Height & \textless{}0.0001 \textasci{} \\ Box Friction & 0.0002 & Columns \(\times\) Height & 0.0001 \\ Height & 0.0002 & Box Friction & 0.0001 \\ Box Friction \(\times\) Pallet Stiffness & 0.0009 & Height \textless{} Box Friction & 0.0006 \\ Columns & 0.0010 & Columns \(\times\) Pallet Friction & 0.0309 \\ Pallet Friction \(\times\) Pallet Stiffness & 0.0015 & Pallet Friction \(\times\) Box Friction & 0.0693 \\ Columns \(\times\) Height & 0.0017 & Box Friction \(\times\) Pallet Stiffness & 0.1511 \\ Height \(\times\) Pallet Friction & 0.0023 & Layers \(\times\) Box Friction & 0.2088 \\ Columns \(\times\) Pallet Stiffness & 0.0104 & Columns \(\times\) Box Friction & 0.2088 \\ Height \(\times\) Box Friction & 0.0134 & Weight & 0.2789 \\ Pallet Friction \(\times\) Weight & 0.0328 & Columns \(\times\) Layers & 0.3396 \\ Pallet Friction \(\times\) Box Friction & 0.0397 & Layers & 0.3489 \textasci{} \\ Height \(\times\) Pallet Stiffness & 0.0432 & Height \(\times\) Weight & 0.4402 \\ Columns \(\times\) Weight & 0.0695 & Layers \(\times\) Pallet Friction & 0.4586 \\ Box Friction \(\times\) Weight & 0.1127 & Height \(\times\) Pallet Stiffness & 0.4966 \\ Layers \(\times\) Pallet Friction & 0.1460 & Pallet Stiffness \(\times\) Weight & 0.6204 \\ Columns \(\times\) Box Friction & 0.2057 & Layers \(\times\) Pallet Stiffness & 0.6424 \\ Columns \(\times\) Pallet Friction & 0.2075 & Layers \(\times\) Height & 0.7101 \\ Height \(\times\) Weight & 0.5336 & Pallet Friction \(\times\) Weight & 0.8768 \\ Layers \(\times\) Pallet Stiffness & 0.6632 & Layers \(\times\) Weight & 0.9013 \\ Layers \(\times\) Height & 0.7221 & Box Friction \(\times\) Weight & 0.9013 \\ Layers \(\times\) Weight & 0.8300 & Pallet Stiffness & 0.9714 \textasci{} \\ Layers \(\times\) Box Friction & 0.8668 & Columns \(\times\) Pallet Stiffness & 0.9753 \\ Columns \(\times\) Layers & 0.9477 & Columns \(\times\) Weight & 1.0000 \\ Layers & 0.9577 \textasci{} & Pallet Friction \(\times\) Pallet Stiffness & 1.0000 \\ \hline \hline \end{tabular} \({}^{\sim}\) denotes effects with containing effects above them.  
\end{table} 
Table 5: Fractional factorial \(p\)-values for the factors and 2 nd-interactions of the initial screening design by board deflection (mm) and deflection ratio as main response. Factors below divider were considered non-significant (\(p\)-value > 0.10). carrying a lighter load do not experience significant load bridging. There is a complete absence of a measurable bending response of the pallet. Besides pallet stiffness and payload weight, it is worth noting that the number of layers in the unit load does not seem to influence the pallet segment's bending results, either as a main effect or as part of an interaction of higher order for either of the two analyses. The other four effects that were analyzed were considered significant regardless of the response variable studied. Multiple interactions were also identified as significant, supporting this study's hypothesis that interactions between multiple factors are significant and have not been properly studied before. A 24 full factorial design analysis was conducted using the model results from the screening design. This took advantage of the projection properties of the fractional designs. Deflection ratios were considered the main model response. The main factors were number of columns, payload height, pallet friction, and box friction. According to the screening design results, pallet stiffness, payload weight, and number of layers do not significantly affect the pallet bending ratio and therefore were excluded.