## 2 Materials and Methods
### Experimental Design  
#### 2.4.1 Statistical Analysis  
Before selecting the orthogonal array for the Taguchi design, the variables' interactions were investigated. Figure 1a shows the interaction plot for 5 primary printing settings (alginate ratio (%), temperature (\({}^{\circ}\)C), extrusion speed (mm/s), tip diameter (mm), layer H = height (mm)) of DIW 3D printer, while Figure 1b-d display the interaction of the parameters that were considered as significant (extrusion speed \(\times\) tip diameter (\(p\) = 0.00) interaction plot (Figure 1b), temperature \(\times\) extrusion speed (\(p\) = 0.00) interaction plot (Figure 1b), temperature \(\times\) tip diameter (\(p\) = 0.00) interaction plot (Figure 1c)), though from a qualitative interpretation, as observed in Figure 1a. Driven by the interaction plot, two-way non-parametric Kruskal-Wallis tests (ANOVA equivalent) were then run to confirm the significant interactions that should be included in the Taguchi design. According to the \(p\)-Value (<0.05) (Table 3) the interactions that are statistically significant are extrusion speed \(\times\) tip diameter, temperature \(\times\) extrusion speed, and temperature \(\times\) tip diameter.  
\begin{table}
\begin{tabular}{p{28.5 pt} p{28.5 pt} p{28.5 pt} p{28.5 pt} p{28.5 pt} p{28.5 pt} p{28.5 pt} p{28.5 pt} p{28.5 pt} p{28.5 pt}} \hline \hline \multirow{2}{*}{\begin{tabular}{c} **Printing** \\ **Parameters** \\ **(\%)** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Alginate** \\ **Ratio** \\ **(\%)** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Temperature** \\ **Speed** \\ **(mm/s)** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Extrusion** \\ **Speed** \\ **(mm/s)** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Nozzle** \\ **Diameter** \\ **(mm)** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Layer** \\ **Height** \\ **(mm)** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Perimeter** \\ **Weight** \\ **(mm/s)** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Infill** \\ **Speed** \\ **(mm/s)** \\ \end{tabular} } & \multirow{2}{*}{\
\begin{tabular}{c} **Retract** \\ **Speed** \\ **(mm/s)** \\ \end{tabular} } & \multirow{2}{*}{
\begin{tabular}{c} **Travel** \\ **Speed** \\ **(mm/s)** \\ \end{tabular} } \\ \hline Printability Window & [0–8] & [20–28] & [20–28] & [1–23] & [0.25–0.58] & [0.25–0.58] & [1–23] & [1–23] & [1–23] & [30–30–40] & [30–50] & [30–50] \\ \hline \hline \end{tabular}
\end{table}
Table 2: Suggested printability window for 9 selected printing settings.  
Figure 1: (**a**) Interaction plot for 5 primary printing settings (alginate ratio (%), temperature (\({}^{\circ}\)C), extrusion speed (mm/s), tip diameter (mm), layer height (mm) of DIW 3D printer; (**b**) extrusion speed \(\times\) tip diameter (\(p\) = 0.00) interaction plot; (**c**) temperature \(\times\) extrusion speed (\(p\) = 0.00) interaction plot; (**d**) temperature \(\times\) tip diameter (\(p\) = 0.00) interaction plot.  
For a more precise parametrization of printability, four secondary parameters (perimeter speed, infill speed, retract speed, and travel speed) were also assessed. The results shown in their interaction plot (Figure 2) indicate that those variables highly interact, and their interactions should be considered when designing the orthogonal array for the Taguchi design. The qualitative results were also verified by two-way Kruskal-Wallis tests (\(p<0.05\)).