*2.3. Experimental Design*

The synthesized materials were evaluated by analysis of variance (ANOVA) using Minitab 19 Statistical Software. The parameters studied in this experimental design were as follows: free-radical initiator (APS) (mol%), cross-linking agent (MBA) (mol%), and amount of CNF (wt%). Each parameter was considered with respect to the amount of ClAETA monomer. For this study, two test levels were used (minimum and maximum), as shown in Table 1. For the preparation, all possible combinations of the three factors were analyzed.

**Table 1.** Factors to be studied and their respective levels, where −, +, and 0 indicate the minimum, maximum, and control levels respectively.


The combinations of the factors provide a design matrix of the type 2 × 2 × 3→12, thus assigning 12 treatments to be evaluated, as shown in Table 2. This method of experimental design is known as "Full Factorial Design (FFD)" [31]. An experiment is defined in which all possible combinations of factor configurations are tested and all possible interactions are determined. Full factorial designs are large compared to screening designs. Generally, a FFD is used when you have a small number of factors and levels, and you search for information on all possible interactions. In a FFD, an experimental run is performed for each combination of factor levels. The sample size is the product of the number of factor levels. FFDs are the most conservative of all design types.

**Table 2.** Experimental design matrix (2 × 2 × 3→ 12) for the synthesis of ion exchange hydrogels. Treatment "c" indicates that the lowest level of testing has been completed.


The factorial experimental design for three factors (A, B, and C) facilitated the investigation of the individual and combined effects of A, B, C, AB, AC, BC, and ABC, based on two levels for each factor. Hence, seven effects were analyzed using ANOVA. In this test, it was assumed that the data followed a trend represented by the F statistic (Ronald

Fisher). To ensure that the uncontrolled factors did not affect the results, the experiments were performed randomly. In addition, we analyzed whether the values found (yield of the reaction, cross-linking degree, and water absorption capacity) generated statistically significant effects, through standardized Pareto charts using the same software.
