# A New Measure for Serious Games Evaluation: Gaming Educational Balanced (GEB) Model
## 3 Results
### Statistical and Machine-Learning Validation of the Games Evaluation  
Finally, a statistical and machine-learning validation was performed on the results of the games evaluation to assure that those concepts are clearly explained in the GEBs metric questions and users are able to distinguish them (doing a proper evaluation). This evaluation included a violins plot analysis, a Pearson's correlation analysis, a Principal Components Analysis and an evaluation of the information and hidden patterns contained in the survey results by means of machine learning classifiers. Firstly, a violins plot analysis was done for each game. Figure 7 shows this analysis. The violin plot shows the distribution of the users' answers for each variable. If two concepts were misunderstood or badly expressed in the GEBs metric questions, the answers might show almost the same distribution for both concept/variables. Therefore, if two concepts were misunderstood, their graphs should be very similar, game-by-game (e.g., a long one for Aesthetics and for Realism for Neverending Nightmares, a violin shape for Aesthetics and for Realism for Actual Sunlight and a round one for Aesthetics and for Realism for Sym); although they can be different if one game is compared with another (e.g., a long one for Neverending Nightmares and a violin shape for Sym). Figure 7 shows very different shapes in most of the cases. Only Technology and UE with MD, Realism and Instructional Strategies with MD, Backstory and Production show the same similarities for the three games together. In the first case, both features evaluate audiovisual representation, but Technology and UE focuses on ease of control and mastery, and MD Realism on fidelity of representation and customization. In the second case, Instructional Strategies and Backstory and Production evaluate the integration of educational content into the game, but the former assesses the gameplay as a whole and the latter the plot. Like these, similarities are far from being significant, the violin analysis points to a clear difference between the proposed metric variables. Secondly, to reinforce the result of the violins analysis, a Pearson's correlation analysis between the different model variables for each game was performed. This analysis can determine if there is a statistical association between a couple of variables. Table 2 summarizes this analysis by collecting the \(p\)-values. The first value in each cell refers to Neverending Nightmares, the second to Actual Sunlight and the third to Sym. Statistical correlation between the two variables is found if the \(p\)-value is lower than 0.05. Therefore, \(p\)-values lower than this threshold are outlined in bold. The intention of this table is to show, from a first glance, that there are no cases where the three values are simultaneously in bold; a fact that would conclude that there is correlation between those two variables for the three games. An expanded version of this table can be found in the Excel supplementary File. There are some six correlations between two games: Backstory and Production (MD: B and P) and Feedback and Debriefing (MD: F and D) with AI and Adaptivity (MD: AI and A) and with Interaction (MD: I), and Instructional Strategies (IS) with Interaction (MD: I) and Aesthetics (A) with AI and Adaptivity (MD: AI and A). These results might be expected due to the nature of the datasets and the small sample size; users can evaluate two variables for one game in the same way (e.g., aesthetics and dynamics for Neverending Nightmares). However, this result does not imply a correlation between both variables in the metric; this correlation is only true if it appears for the three games at the same time (e.g., aesthetics and dynamics for the three games), because the diversity of the three evaluated games makes it impossible to find this correlation if its origin is not a badly defined metric (e.g., aesthetics and dynamics cannot be correlated for the three games, because they are not equally considered in the design of the three games).