## 3 Proposed Method
### Results of Discretization and Grouping
#### 4.2.1 Partitioning for General IQ
Indeed, this partitioning corresponds to two values \(c=7\) and \(c=\log N\) (see Table 3), corresponding to the most important significant parameters of the model. In the first case, for \(c=7\), we obtain a significant F-statistics value for the year and department interaction, allowing to get rid of the variance inhomogeneity revealed during the exploratory analysis. In the second case, with \(c=\log N\), we get the most significant sum of F-statistics (sumF), which characterizes this model with a proportional significance for all effects and their interactions. For the two best partitions by the year selected above, we have two corresponding partitions by the department. For \(c=7\), the algorithm produces four groups of departments in the first partition:  
* Group I--FB, ACEF, PEF;
* Group II--AEF, HEF, MAF;
* Group III--AMCSF. * Group IV--REFE, MTF, PhEF; \begin{table}
\begin{tabular}{c c c c} \hline \hline \multicolumn{2}{c}{**Periods for Year**} & \multicolumn{2}{c}{**Groups for Department**} \\ \hline P1 & 1991–2002 & G1 & FB, REEF, ACEF, MTF, PEF \\ P2 & 2003–2005 & G2 & AEF, HEF, PhEF, MAF \\ P3 & 2006–2013 & G3 & AMCSF \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Final partition by the year and the department obtained for \(BIC\) fitness function. For \(c=\log N\) the algorithm gives three groups of departments in the second partition:  
* Group I--FB, ACEF, PEF, REF, MTF;
* Group II--AEF, HEF, MAF, PhEF;
* Group III--AMCSF. Comparing the resulting partitions, we see that the first three groups I, II, III of the first partition turned out to be stable. The departments included in them remain in the second partition. In contrast, the departments of the unstable IV group were distributed in the second partition into groups I and II. The most stable group turned out to be group III, consisting of one AMCSF in both partitions. This department is associated with serious requirements for mathematical training. The partition into different groups of departments according to the level and dynamics of general IQ is associated to a greater extent with the distribution of students among the faculties of a particular university, which is not entirely interesting from the point of view of global and country changes in the structure of intelligence. Moreover, among groups I, II, and IV, we cannot single out a group of completely humanities or, say, completely engineering specialties. Rather, the group assignment is associated with a passing grade for a particular department, which determines the overall level of enrollment. Therefore, for the convenience of interpretation, we will choose a simpler second partition into three groups, especially since such a partition has a larger sum significance (according to F-statistics) for all effects and interactions of the ANOVA model. Thus, the chosen partitioning by year and department variables is \(3\times 3\), obtained for _BIC_ fitness function (last column of Table 2, \(c=\log N\)). In Table 3, we denote three time periods for the year as P1, P2, P3, and three groups for the department as G1, G2, and G3.