# What Makes a UI Simple? Difficulty and Complexity in Tasks Engaging Visual-Spatial Working Memory
## 5 Discussion  
Automation of design and validation of user interfaces for human-computer systems is essential for the development of the internet ecosystem, adoption of smart systems, etc. Effective organization of the interaction necessitates that human needs and limitations, particularly in the cognitive aspects, are expressed quantitatively and are properly accounted for [48]. In our work, we explored different predictors that characterize the difficulty of tasks engaging visual-spatial working memory, which are relatively rarely covered in the currently existing computational models of user behavior, unlike e.g., visual attention [25] or visual complexity [49]. The results of our analysis suggest that Hypothesis 1 has to be rejected in favor of Hypothesis 2, as the compression-based metrics of visual complexity (\(L_{RLE}\), \(L_{DEF}\)), as well as Hick's law information theoretic metric, were inferior to the proximity-based metrics, as demonstrated by the regression equation for \(E_{M}\) (13). The compression-based factors and the Hick's law factor were significant in the regression equation for _Complexity_ (14), which replicated our previous findings [12], even though in that work, we did not test \(F_{N}\) and \(F_{M}\) as the candidate factors for VC. That said, the actual subjective evaluations of VC did have significant positive correlation to the measures of performance in VSWM-related tasks: \(\mathrm{\tau_{4546}}=0.196\) (\(p<0.001\)) for \(E_{M}\) and \(\mathrm{\tau_{4546}}=0.218\) (\(p<0.001\)) for \(T_{M}\). The practicality of collecting the subjective evaluations from users is doubtful though, as the performance can be better predicted with the metrics that can be automatically evaluated from the configurations. Indeed, our study suggests that Hypothesis 3 should be accepted, as the proposed index of difficulty (16) had the highest correlation with the performance in VSWM-related tasks (as operationalized with \(E_{M}\)): \(\mathrm{\tau_{4546}}=0.340\) (\(p<0.001\)). Of the three candidate factors (\(N_{I}\)), the formulation of \(IDM\) that uses the number of von Neumann figures (\(F_{N}\)) as the memorized item showed clear advantage in correlation (see Table 3) and regression analyses (19). It is also aligned with Hypothesis 2, and \(\mathrm{F_{N}}\) showed the best match to the 7 \(\pm\) 2 information chunks limit found by [PERSON] and colleagues for working memory. Hypothesis 4 should also be accepted, as the value of throughput obtained in our experiment, 3.75 bit/s, is consistent with the ones reported in the literature: 2-4 bit/s for human operator tasks relying on working memory [37; 39; 40]. The Fitts' throughput values generally found for computer mouse, which the subjects used in the designation stage of the experiment, are also coherent: 3.7-4.9 bit/s [30]. The significant effect of gender on time that we found, 3.9 bit/s for males and 3.6 bit/s for females, is in line with the general advantage of younger males in both spatial orientation tasks and motor reaction speed, which is well described in the existing works [50; 51]. At the same time, the difference in accuracy between the genders is often non-existent [52], and in our experiment, it was not significant either (\(p=0.09\)). The limitations of our research, first of all, include relatively low values for correlations and R\({}^{2}\) coefficients in the regression analysis for the per-trial data. Indeed, many established user behavior models have higher R\({}^{2}\) values, particularly Fitts' law, for which R\({}^{2}\)s of over 0.9 are generally reported [30]. On the other hand, for models involving Hick's law, the fit is generally lower, e.g., in [34], they reported R\({}^{2}\) = 0.52 for traditional menu selection. The discrepancy in our study is explained in part by the experimental procedure, which included not only memorization, but also motor behavior-based designation stage, i.e., clicking the memorized cells.