The weak adjustment obtained in the previous section was foreseeable; I have already commented in the initial specifications of the model about the nature of intelligence, that the proposed estimator would be centered, but that its variance would be very large due to the random character of the Mendelian inheritance.
Also we have indicated the impossibility of correcting this problem of the statistical data by selecting 50% of the sample where the deviations would have to be minimum. Lack of precision in measurements and temporary and functional deviations of the intelligence expression due to its nature are the main causes. The problem with the statistical data and the correlational study regarding the nature of intelligence is greater than expected.
To avoid this tendency of the statistical data in this correlational study, different groups are obtained depending on the various orders into which the initial seventy values can be arranged. Consequently, the analysis by groups seemed the only way to surpass the mentioned limitations of the available statistical data.
The aggregation, by itself, would not be satisfactory since the values of all the variables would tend to equal the average as the group's elements increase.
If we rearrange the initial sample with criteria such as M1F1 or (M+F)/2 in order to design new correlational study, it will be possible to achieve homogenous groups in which:
The effectiveness of the previously mentioned compensations will be optimum.
The groups divided in stratums will allow for a suitable adjustment of the tendency or relation between the variables of the model.
For each variable, a hundred and ten different variables have been generated based on the diverse number of elements and criterion to rearrangement of the groups; I have used ten group sizes and eleven criteria of arrangement, including the initial order (unknown).
The graph contains the number of elements of the sample that will exist for each group size.
The model about the nature of intelligence has been examined in its double formulation, on one hand, calculating the correlation with respect to the objective function R, determined in accordance with the General Theory of Conditional Evolution of Life (GTCEL). On the other hand with respect directly to the variables of the statistical data M and F, it allows for a comparative analysis between the two formulations.
The variables used in the correlational study to rearranged the groups were M, F, R, M1F1, (M+F)/2, 2F2M, C1, C2, C3 and W. Variable 2F2M will be opposed conceptually to M1F1; C variables correspond to those children who have been studied in a particular analysis and W variables are generated artificially in the model simulation.
The final effect is that the statistical data evaluated by the model about the nature of intelligence has been multiplied several times over and random variations have been compensated. Consequently, its power to detect the correction of its specifications has improved significantly. At the same time, the model of evolution of intelligence has become very sensitive and can compare between close configurations of the statistical data.
Due to the great amount of data generated with the quantitative approach to the nature of intelligence, and to facilitate its analysis, in addition to the results in tables, it appears in graphs. (See statistical annex).
Indeed, an almost instantaneous perception of the exactitude of the particular specification is obtained with the quantitative approach; sixty coefficients of determination (r²) are shown in a way that highlights the global and underlying relations of the involved statistical data.
The results of the quantitative approach are surprising regarding the nature of intelligence, which can be observed both in the graphs of the statistical annex and in the following tables. An aspect that will especially allow us to reach some important conclusions is the model sensitivity of the arrangement criterion.
The great increase of the correlation for the estimation of homogenous groups of the statistical data cannot be imputed to the reduction of 68 to 5 or 4 degrees of freedom, since the estimation with non-homogenous groups, without previous rearrangement, has the same degrees of freedom and the correlation even lowers with respect to the sample without grouping.
The model on evolution of intelligence adjusts perfectly, showing a determination coefficient r² superior to 0.9 in several cases.
Also, it is interesting to verify the fact that the objective function R is almost as powerful as mothers' variables M and fathers F together.
If we estimate with respect to mothers' variables M and F, we obtain an r² of 0.99 for variable WB (Wechsler intelligence test) when the rearrangement variable is the same WB variable. This good adjustment is possible because, in their configuration, the children variables C not only incorporate criterion M1F1 but the real information of the power of all the genes and their correct Mendelian inheritance combination, in agreement with the GTCEL.
Variables M1F1 and R only incorporate, so far, a partial effect which is the Mendelian inheritance and, therefore, variable WB (Wechsler intelligence test) is a better order criterion.
Nevertheless, this does not take place in all cases; it is definitely a consequence of the incorporation of the differences due to the expression and measurement of the IQ in C variables, which does not happen with variables M1F1 and R.
The table shows the G-MCI and the maximum r² of the correlations between the IQ of the parents or the objective function R, and the children's IQ, rearranged in four criteria. The C variables are original ones and no change has been made in any of their values.
In addition, when the model has more freedom with the two variables, M and F, it definitely adjusts better by statistical effect, or, the data we have available are a particular case.
This table helps us to understand the irregular relation that exists between the maximum r² and the G-MCI.
Now, if we paid attention to the graphs of the centered variables, T1-d, X3 and X6, in the first place, we would be able to see that the z23 graph has a singular beauty because of its shape and content
This graph shows an increase of correlation with the R objective function variable proposed by the General Theory of Conditional Evolution of Life (GTCEL) regarding the nature of intelligence, until it surpasses 0,9 (GMCI = 14.98), as the other correlation variables involved move to more centered values.
After all, the variables are not as off as they seemed in the beginning. In particular, the result of the quantitative approach is coherent with the supposition that these centered variables should have less problems with the variability in the expression of the intellectual ability and in the measurement of the intelligence quotients, since, by their definition, they imply a compensation of those deviations.
On other hand, bearing in mind the parallelism between the variables T1-d, X3 and X6 and the good correlations that they provide, we may conclude that it was a reasonable assumption to generate variable T1-d with a 10% maximum margin of variation with respect to the average in variable T1 (Stanford Binet IQ test) . It does, however, make sense that the results are not as good as the X3 and X6 variables.
Another element to point out is the design effectiveness of the multidimensional analysis that we are employing. It allows us to easily draw some conclusions while maintaining a high degree of coherence and security in the reasoning.
Actually, it seems that there is not much margin left to deny the hereditary nature of intelligence, not even to try to reduce it to less than 80%. You have to consider that we are referring to groups with a maximum of ten elements and that, due to the observed tendency; the correlation should be greater with groups of 20 elements.
It is a good idea to point out that objective function R with criterion X6 achieves a greater determination coefficient r² than variables M & F together. The same objective function R is also superior when using M1F1 instead of X6 as rearrangement criterion.