# Increase of _Trichoderma harzianum_ Production Using Mixed-Level Fractional Factorial Design
## 3 Results  
The mixed-level fractional factorial design is shown in Table 7. A total of 48 experiments with the corresponding values for spore production are shown. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Run** & **Air** & **\% Humidity** & **Temperature (°C)** & **pH** & **Substatum** & \
\begin{tabular}{c} **Spore Concentration** \\ \(\times\)**10\$ CFU.g**\({}^{-1}\) \\ \end{tabular} & **\% Viability** &
\begin{tabular}{c} **Spore Production** \\ \(\times\)**10\$ CFU.g**\({}^{-1}\) \\ \end{tabular} \\ \hline  
es & 30 & 23 & 5 & Sesame husk & 1.25 & 93 & 1.162 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Results of the experimental runs. Table 8 shows the ANOVA; we can see that air and substrate factors, as well as their interaction, are statistically significant. On the other hand, it can be noticed that any change in levels of pH, temperature, and humidity has no significant impact on spore production. Table 9 shows a standard deviation of 0.1973 which indicates that our data tends to be distributed very close to the mean. A mean of 3.7424 for spore production was obtained. The coefficient of variation is 5.27, which means that the arithmetic mean is representative of the data set. \(R^{2}\) = 0.9945 and \(R^{2}adj\) = 0.9935 indicate that a high percentage of the variability in the response can be explained by the regressors. \(R^{2}\)_pred_ = 0.9921 indicates that the model has a high predictive capacity. An _Adeq Precision_ = 89.0719 indicates a good signal; based on this information, we conclude that this model can be used to predict and optimize spore production. Figure 1 shows the normal probability plot for residuals and the Box-Cox method. The normal probability plot indicates that the residuals tend to be normal since the data in \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Run** & **Air** & **\% Humidity** & **Temperature** (°C) & **pH** & **Substratum** & \
\begin{tabular}{c} **Spore Concentration** \\ \(\times\) **10\({}^{8}\) CFUg\({}^{-1}\)** \\ \end{tabular} &
\begin{tabular}{c} **\% Viability** \\ \(\times\) **10\({}^{8}\) CFUg\({}^{-1}\)** \\ \end{tabular} \\ \hline  
o & 30 & 27 & 7 & Breadruit seed & 7.76 & 97 & 7.530 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: \(Cont.\) \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Source** & **Sum of Squares** & **Df** & **Mean Square** & **F-Value** & **\(p\)-Value** \\ \hline Model & 281.59 & 10 & 40.19 & 823.7 & \textless{}0.0001 & Significant \\ Air (A) & 5.76 & 1 & 5.76 & 144.15 & \textless{}0.0001 & \\ Humidity (B) & 0.2140 & 1 & 0.2140 & 6.26 & 0.0769 & \\ Temperature (C) & 0.0305 & 1 & 0.0305 & 0.8912 & 0.3513 & \\ Ph (D) & 0.1792 & 1 & 0.1792 & 5.24 & 0.0678 & \\ Substratum (E) & 274.94 & 3 & 91.40 & 2673.55 & \textless{}0.0001 & \\ Air–Substratum (A–E) & 0.4758 & 3 & 0.1586 & 4.64 & 0.004 & \\ Residual & 1.26 & 37 & 0.0342 & & \\ Cor Total & 282.85 & 47 & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 8: ANOVA for spore production maximization. Background color in the table is to indicates the significant factors in the ANOVA. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Std. Dev** & **0.1973** & **\(R^{2}\)** & **0.9945** \\ \hline Mean & 3.7424 & \(R^{2}adj\) & 0.9935 \\ C.V.\% & 5.27 & \(R^{2}pred\) & 0.9921 \\ _Adeq Precision_ & 89.0719 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Fit Statistics. the left tail are very similar to those in the right tail. The _Box-Cox_ method indicates that the distribution would be more normal with a square root transformation. Since no outliers are found, and there is no skew in the distribution, it is not necessary to carry out the transformation, the distribution is not perfectly normal, but it is normal enough to perform the analysis. In addition, we must remember that the least squares method is robust to the assumption of normality. Figure 1: Normal probability plots of the residuals (**a**) and Box–Cox plot (**b**).