## 4 Application and Results
### Phase 5-Discovering Similarities of the Methodologies  
In this phase, ERSA builds the matrix \(Y=\left[y_{ij}\right]\) with dimension \(174\times 16\). The elements of \(Y\) are obtained by assembling the row vectors \(X_{1},X_{2},\ldots,X_{172}\) as rows of the matrix \(Y\) with \(y_{ij}=x_{ij}\), where \(y_{ij}\) represents the element in the i-th row and j-th column of \(Y\), and \(x_{ij}\) represent the j-th element of the \(i\)-th row vector \(X_{i}\). The k-means algorithm, utilizing the elbow method, was chosen among different clustering processes in ERSA for the application to the matrix \(Y=\left[y_{ij}\right]\) where \(a_{ij}\in\{u,f,t\}\). In this paper, we will consider the results for \(a_{ij}=t\), which yields findings that are particularly pertinent and insightful. Fifteen clusters were found, represented in Figure 6. The clusters 1, 3, 5, 7, 9, 11, and 14 are specific to a model, while the clusters 4, 6, 12, 13, and 15 are grouping similar methodologies. Finally, the clusters 8 and 10 only include a limited number of methodologies. * **Cluster 1:** The 1 st cluster is the most populated cluster, with 95 methodologies entering it. It is also one of the simplest ones, since almost all the methodologies have only one  
Figure 5: The first three phases of the ERSA process applied to methodologies for interface design for users in low-income countries. The articles cited in the phase 1 are [PERSON] [34], [PERSON] et al. [35], [PERSON] and [PERSON] [36] and [PERSON] [38; 39; 40]. step, except for one. Most of the articles also studied the conceptual model, except for two that are interested in the experimental model of the physical domain (ExpePhys). * **Cluster 2:** The 2 nd cluster is formed of 2 methodologies that both have around four or five steps, start from the conceptual model of the user domain (ConcUser), and finish on ExpePhys. During the process, both consider aspects of the conceptual models and the user domain, each in a different way. * **Cluster 3:** The 3 rd cluster is composed of 15 methodologies that, except for two, all have one step only, on the experimental model of the user domain (ExpeUser). The two exceptions both end on this step while starting on the physical domain. * **Cluster 4:** The 4 th cluster is made of 5 clusters that all have around four to six steps. The difference between this and the 2 nd cluster is that while both start on conceptual models and end on experiments, the 4 th cluster is considering the computational model of the physical domain (CompPhys). * **Cluster 5:** The 5 th cluster is a simple cluster formed by 21 methodologies, 19 being simple step methodologies over the conceptual model of the functional domain (ConcFunc). The two exceptions are no less than three steps and also take into account ConcFunc. * **Cluster 6:** The 6 th cluster is a cluster of 14 methodologies that all have two or three steps and end on ExpePhys, while starting on different models but mainly on models of the conceptual model. Most of the methodologies also consider CompPhys. * **Cluster 7:** Cluster 7 is only formed of one six-step methodology that starts on ConcUser, ends on ExpePhys, and iterates over this same ExpePhys step. * **Cluster 8:** Cluster 8 is formed by two methodologies that start by ConcUser and the conceptual model of the physical domain (ConcPhys). One stops here, while the other ends with ExpePhys. * **Cluster 9:** Cluster 9 has 5 one-step methodologies that have interest in the mathematical model of the use domain (MathUser). It is the simplest cluster, the only one having all its methodologies being one step. * **Cluster 10:** Cluster 10 has 2 three-step methodologies that both consider CompPhys and ConcFunc, while adding a step in the conceptual model before or after those two steps. * **Cluster 11:** Cluster 11 is only formed of one eight-step methodology that iterates three times over ConcPhys and CompPhys before ending on the mathematical model of the physical domain (MathPhys) and ExpePhys.