Design expert 12

Liposome optimization was performed using a Box–Behnken surface response methodology using Design Expert 12 software (Stat-Ease Inc., Minneapolis, MN, USA). The optimal conditions were predicted by a second-order polynomial model. The general regression equation used was: $Y={\beta }_0+{\beta }_1{X}_1+{\beta }_2{X}_2+{\beta }_3{X}_3+{\beta }_{12}{X}_1{X}_2+{\beta }_{13}{X}_1{X}_3+{\beta }_{23}{X}_2{X}_3+{\beta }_{11}{X}_1^2+{\beta }_{22}{X}_2^2+{\beta }_{33}{X}_3^2$
where Y is the predicted response; β₀ is the model constant; X₁, X₂, and X₃ are independent variables; β₁, β₂, and β₃ are quadratic coefficients; β₁₂, β₁₃, and β₂₃ are cross-product coefficients; and β₁₁, β₂₂, and β₃₃ are quadratic coefficients.
GraphPad Prism 8 (GraphPad Software Inc., San Diego, CA, USA) was used for the cell viability analysis. Experimental data were tested for normality and analyzed by one-way analysis of variance with a Tukey post hoc test. A p-value < 0.5 was considered statistically significant.

The screening of organic substrates using the OFAT method was analyzed by R software. The mathematical modeling was carried out and optimal conditions of the SSF process identified using Reliasoft2020 Weibull⁺⁺ software. Design-Expert 12 software (Stat Ease Inc., Minneapolis, MN, USA) was used to generate the design matrix and analyze the results. The upper limit and lower limit for each independent variable studied were based on our preliminary experiments. The conidia/g and CFU values were log-transformed (base 10) and analyzed by analysis of variance (ANOVA). All means of the treatments were compared using Duncan’s multiple range tests at p ≤ 0.05. Multiple regression analysis methods were used to study second-order polynomial equations of independent variables. To check the statistical significance of these equations, an F-test was applied to evaluate R². The significance of independent variables and their interactions were tested using ANOVA analysis. Standardized effects of the independent variables and their interactions on dependent variables were also investigated by preparing a Pareto chart. Results were assessed with various descriptive statistics, i.e., p-value, F-test, R², R² adj, sum of squares (SS), and mean sum of squares (MSS) test to assess the goodness-of-fit of the developed quadratic mathematical model to the experimental data [46 (link)].

SPSS Software (22.0) was used to perform statistical analysis. The results were expressed as the Mean ± Standard Deviation (SD) of three parallel trials. Comparison of means was realized by one-way analyzes of variance (ANOVA). Moreover, the Principal Component Analysis (PCA) and Pearson correlation test were conducted using R software (v 4.1.0.). The data were considered statistically significant if the p-values were <0.05 and <0.01 for the correlation test.
The response surface methodology (RSM) was used to optimize the wet process of saponins elimination from quinoa seeds. The statistical study was performed by Design-Expert 12 software (Stat-Ease, Minneapolis, MN, USA). It was used for regression and graphical analysis of experimental data of %ES. A Box–Behnken Design (BBD) was used to optimize the number of experiments required to investigate this study which was 15. Wherefore, the experimental sequence was randomized to minimize the effects of the uncontrolled factors. Indeed, the design center point was repeated three times to estimate errors and curvature. After processing, the %ES from the seeds was opted out as the response-dependent term.

CCD-RSM was employed to identify optimal SFE-CO₂ conditions by determining the effect of P (25–45 MPa), T (40–60 °C) and τ (30–90 min) on SFE-CO₂ extract yield and ORAC, selected as the response factors (RF) in the optimization experiments. The face-centered CCD design with 8 factorial, 6 axial and 6 center points (in total, 20 experimental runs), randomized order of experiments, models and the second-order polynomial equations for both RFs were established using the Design-Expert 12 software (Stat–Ease Inc., Minneapolis, MN) as previously described elsewhere by our research group [15 (link),16 (link),17 (link),18 (link),19 (link)]. Student test (p-value) at 5% probability level (p < 0.05), “lack of fit” coefficient and the Fisher test value (F-value) were used to define the statistical significance and adequacy of the model and each variable for both RFs.

Design-Expert 12 software (Stat-Ease Inc., Minneapolis, MN, USA) was utilized for conducting the five-factor, three-level I-optimal design in this study. Additionally, this software was employed for generating response contour plots and performing the relevant analyses.

Design Expert 12 software (Stat-Ease Inc., Minneapolis, MN, USA) was used for statistical analysis to determine the obtained yield (%), while the results of hydration properties and colour analysis were statistically analysed with origin Pro 8.0 (Origin Lab, Northampton, MA, USA). Obtained results were represented as means ± SD, and the data were analysed by employing one-way analysis of variance (ANOVA), followed by LSD test.