## 3 Materials and Methods
### Experimental Design and Optimisation  
The effect of the tested independent factors on the response within the studied range was evaluated by performing a fractional factorial design (FFD) (i.e., a 2\({}^{5-2}\) (quarter fraction) with two central points of analysis). The extraction factors included in the design were amount of the sample (\(x^{1}\), 0.5-2.5 g), volume of water (\(x_{2}\), 0-5 mL), adsorption temperature (\(x_{3}\), 40-100 \({}^{\circ}\)C), pre-incubation time (\(x_{4}\), 5-15 min), and adsorption time (\(x_{5}\), 10-50 min). Since the variables have different units and ranges, each of the variables was first normalised and forced to range from \(-\)1 to +1 in order to obtain a more even response. Therefore, the factor levels were denoted as \(-\)1 (low), 0 (central point) and +1 (high) according to the following equation:  
\[x_{\rm i}=\frac{x_{\rm i}-x_{0}}{\Delta x}, \tag{1}\]  
where \(x_{\rm i}\) is the coded value of the factor \(x_{\rm i}\), \(x_{0}\) is the value of \(x\) at the centre point, and \(\Delta x\) is the increment of \(x_{\rm i}\) corresponding to a variation per unit of \(x_{\rm i}\). The factors included in the design are shown in Table 3 along with their respective levels.  
The design of experiment (DOE) matrix was established with resolution (R) of III, wherein every main effect is confounded (aliased) with at least one first-order interaction. The \(2^{5-2}_{III}\) fractional factorial design allowed the first three variables (\(x_{1}\) to \(x_{3}\)) to be set and thus the DOE was obtained by establishing the full \(2^{3}\) factorials as the basic design (with the three factors \(x_{1}\), \(x_{2}\) and \(x_{3}\)) and factors \(x_{4}\) and \(x_{5}\) were subsequently equated to the \(x_{1}x_{2}\) and \(x_{1}x_{3}\) interactions, respectively. This particular design produced the following defining relationships: I = \(x_{1}\)\(x_{2}\)\(x_{4}\) = \(x_{1}\)\(x_{3}\)\(x_{5}\) = \(x_{2}\)\(x_{3}\)\(x_{4}\)\(x_{5}\). The linear model for this fractional factorial design is:  
\[y=\beta_{0}+\sum_{\text{i=1}}^{\text{k}}\beta_{\text{i}}x_{\text{i}}+\sum_{ \text{j<i}}\beta_{\text{ij}}x_{\text{i}}x_{\text{j}}+\varepsilon, \tag{2}\]  
where \(\beta_{\text{i}}\) (i = 1, 2,..., 5) is the parameter estimated for the factor i, \(\beta_{\text{ij}}\) (i = 1, 2,..., 5; j = 1, 2,..., 5) is the parameter estimated for the interaction between variables i and j; \(x_{\text{i}}\) is the coded form of factor i that influences the response \(y\), and \(x_{\text{i}}\) is the coded form of factor i that influences the response y. The whole design consisted of 11 runs carried out in random order and these are presented in Table 3.  
Principal component analysis (PCA) and multi-response optimisation (MRO) were performed with the trial version of STATGRAPHICS Centurion XVI (Statopoint Technologies, Inc., Warrenton, VA, USA) to define and optimise the key-marker compounds of aromatic rice grains. The experimental results in single factor experiments were analysed using Gnumeric 1.12.17. The analysis of variance (ANOVA) and least significant difference (LSD) test were used to determine the significance of differences between the means.