## 5 Dynamical Results of the Stimulus Response Model (SRM)
Once the samples of parameter values are obtained, the \(p\)-value of the Anderson-Darling test is applied to each sample to determine whether they are distributed as a N(\(m\), \(sd\)), i.e., a normal distribution of \(m\) mean and \(sd\) standard deviation corresponding to each parameter. Note that the \(H_{0}\) hypothesis is that the samples follow a normal distribution. Subsequently, if the \(H_{0}\) hypothesis holds, the confidence intervals are computed in the usual way. In addition, the results of the fitting process obtained through the genetic algorithm are evaluated by the determination coefficient values (\(R^{2}\)), which measures the fitting degree between the experimental scores and the corresponding values provided by the SRM. Note that the SRM values here considered are those computed by the averages of the 40 size parameter samples, i.e., by the mean value of their confidence intervals. In addition, the \(R^{2}\) measures the relation between the square covariance of both sets of data and the product of both variances, and it varies from 0 to 1, i.e., \(0\leq R^{2}\leq 1\), such that the closer to the unit the better the fitting degree. The determination coefficient values are provided jointly with the \(p\)-value of the Anderson-Darling test with which the residuals are checked for being noise, i.e., a N(0, \(sd\)) or a normal distribution of zero mean and \(sd\) standard deviation between the experimental scores and the corresponding values given by the model. Note again that the \(H_{0}\) hypothesis is that the residuals follow a normal distribution. It is important to emphasize the joint meaning of \(R^{2}\) and the Anderson-Darling test: the \(R^{2}\) value represents the part of scores' dynamics explained by the SRM, and if, in addition, the residuals are demonstrated to be random by the Anderson-Darling test then it can be asserted that no other significant dynamical pattern is also assumed by the scores' dynamics. Moreover, if a high \(R^{2}\) value is associated with a low residual dispersion (do not confuse with the statistical dispersion of Section 3) and vice versa, then, in this case, the individual feels the drug effect accurately, and in the contrary case (low \(R^{2}\) value that is associated with a high dynamical dispersion) the individual feels the drug effect not clearly. Moreover, the production of the SRM numerical solutions as well as the above-described genetic algorithm is stated in a C++ program. The corresponding figures and Anderson-Darling test \(p\)-values have been obtained by the software MATHEMATICA 14.0. Figure 2 (for Participant 1) and Figure 3 (for Participant 2) show the scores in low stimuli conditions for both participants in the experimental design in Phase A (base line), in both happiness scales. Note that both figures are far from seeming to represent noise. In fact, the Anderson-Darling test provides for both participants a \(p\)-value lesser than 0.01, i.e., it is not an orthodox noise N(\(m\), \(sd\)), being \(m\) the average score. Therefore, either the outcomes follow a dynamical pattern produced by boring or the noise follows an unknown distribution. However, the dynamical patterns of happiness produced in Phase B and Phase C by alcohol and caffeine, respectively, are radically different, as it can be observed in the subsequent figures. Figure 4 presents the scores with uncertainty along time of the ES and SFS for Phase B of the experimental design of Participant 1, jointly with the curves predicted by the SRM because of 26.51 mL of alcohol dose. Note that for the ES response \(R^{2}=0.87\) and for the SFS response \(R^{2}=0.88\), being the corresponding Anderson-Darling test of the residuals, respectively, 0.71 and 0.95, which provide us a conclusion: the SRM explains almost fully the scores' dynamics of Participant 1, in other words, the prediction of the SRM for this participant is excellent, which implies that Participant 1 feels accurately the happiness response to the alcohol stimulus.