3.b) Correlations between Wechsler and Stanford Binet scales
The preliminary analysis of correlations of the involved variables, including Wechsler and Stanford Binet scales, helps us to understand the intrinsic difficulties of the original model of intelligence, the reasons for its reformulation, and even the convenience of performing a simulation to confirm the model's goodness-of-fit.
The first surprise is the observation of low correlations not only between the Mother (M) and Father (F) variables with C (Children) variables, but also among children variables (Wechsler, Stanford Binet and others scales.)
The variables of the children like Wechsler intelligence test and Stanford Binet scale correspond to same children at different times. And not only the correlations between the scales of Wechsler and Stanford Binet are not high but even between two IQ vectors of the same children and the Stanford Binet test.
The coefficient r² = 0.33 is the largest one among the IQ variables of the children (Wechsler, Stanford Binet test and other test). With this perspective, it seems to be difficult to imagine that high correlations can be obtained between children and their parents.
At the beginning, the previously mentioned grouping of values had still not been considered. Taking into account these correlations, I thought about substituting the values considered to be very disparate, by their averages, but the different variables continued to show a low correlation.
These assessments of the low or not very high correlation between the children variables C (Wechsler, Stanford Binet test and other test) make us think that the measurements are not very homogenous because it seems that it is generally accepted that people's IQ remains fairly stable after 6 years of age.
Given that the averages of the chosen variables were not equal, I decided to standardize them for a suitable calculation of the variables X3 and X6 (Wechsler, Stanford Binet test and other test). This way of calculating is necessary to avoid distortions and any additional problems, considering that we are not trying to study the evolution or generational increase in IQ. This fact has been proved and accepted, although different explanations on the matter have been proposed. In our case, the data produced an average, of the different IQ data set of the children, 10% above the average of IQ data set of the mothers and fathers.
A consequence of the lack of IQ measurement precision is the impossibility to make a discretionary selection of 50% of the sample to isolate the cases in which supposedly the gene with less potential dominates; in agreement with the statistical model initially proposed.
It is as if we had several Photos or pictures of each child that, sometimes, do not look alike; but perhaps, altogether, they could give us a relatively clear image of the child.
Other factors that could contribute to the mentioned impossibility are: the multifunctional character of human intellect and that, as the model depicts, the IQ of the child can be inferior to the smaller of the two parents when the latter is not entirely included in the greater one. This aspect will be discussed in more detail in other chapters.
As shown, this preliminary analysis has allowed us to recognize the difficulties in obtaining satisfactory results and that it is better to use original values since their manipulation, although objective, does not improve the results significantly.
Also, I have used centered variables, that is to say, one with smoothed tails due to a limitation of a 10% deviance from the average (T1-d) and variables X3 (Wechsler, Stanford Binet test and other test) and X6 (Wechsler, Stanford Binet test and other test), which are average values of three and six original variables respectively (observed variables)
The solution will come with the model of intelligence reformulation and a bit of imagination.