The title of each graph of the statistical study indicates the parents variables (R or M & F) to which the correlations are related. These correlations are represented by each point of the coloured lines corresponding to each examined C variable (children).
Likewise, the variables of unknown order, formed by the different groups of 1 to 10 values from the 70 IQ values of each parent and children variables are placed on the left hand side of the graph. The groups of 1 to 10 values located on the right hand side have been previously ordered with the variable mentioned at the bottom of the graph.
Indeed, an almost instantaneous perception of the exactitude of the particular specification of the statistical study is obtained; sixty coefficients of determination (r²) are shown in a way that highlights the global and underlying relations of the involved data set.
STATISTICAL STUDY COMMENTS
1. General statistical significance
The great increase of the correlation for the estimation of homogenous groups 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.
When the model of the statistical study has more freedom with the two intelligence quotients' variables, M and F, either it definitely adjusts better by statistical effect or the statistical data set we have available is a particular case.
In general, the model of genetic evolution of intelligence (Mendelian genetics – Conditional intelligence – Gobal Cognitive Theory) adjusts perfectly, showing an r² superior to 0.9 in several cases. Bearing in mind the tendency to increase the goodness of fit with the size of rearranged groups, we could asume it would be over 0,9 in almost all the cases for groups bigger than 20, of course, it should be needed a bigger sample.
2. Statistical survey with the Social Model and centred variables.
All the eight graphs with centred variables of the Social Model have bigger correlation (general multidimensional correlation index GMCI) than the corresponding graphs with original variables.
With the results of this statistical survey 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.
In particular, the result is coherent with the supposition that these centred 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.
Centred variables, in opposition to original variables, are those variables with some changes in their values; that is to say, one with smoothed tails due to a limitation of a 10% deviance from the average (T1-d) and variables X3 and X6, which are average values of three and six original variables respectively.
The groups located on the right hand side have been previously ordered with the variables mentioned at the bottom of the graphs with an asterisk.(*)
The Social Model of this statistical survey 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 GTCEL. On the other hand with respect directly to the variables Mothers (M) and Fathers (F), estimating the model with the method of the ordinary square minimums and allowing for a comparative analysis between the two formulations.
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. It does, however, make sense that the results are not as good as the X3 and X6 variables.
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.
Regarding the coefficients of determination (r²), in all graphs of this model their values are superior to 0,79
3. Statistical significant figures of this particular graph
As you can clearly see by its form, the three dependent variables of the children, analyzed in the model, behave in a very similar way to the progenitors' explanatory variable R
The is q023 and q024 graphd are especially beautiful because of their form. We can see how the three dependent variables behave practically equal regarding the growth of the correlation with the number of elements of the groups, and especially the saw-tooth form in the even numbers with the only difference in the correlation due to its different degree of aggregation.
The general multidimensional correlation index (ICMG) is 14,98 which is a normal value in the whole EDI study.
However, the biggest determination coefficient r² of this graph is 0,92 which is very high value within this type of statistical studies.