Based on the Delfino and Salas hypothesis, Medina asked himself: Is there anything in the pro-Chavez versus anti-Chavez votes from each election or the recall vote that can reveal that if there is any difference between them? The answer is yes, you can look at the symmetry of the distributions and they will tell you whether there is one ir two random variables.
Suppose you have to variables, let’s say the 1998 anti-Chavez vote and the 2000 anti-Chavez vote at each voting center. You plot one versus the other such as the automated 2000 anti-Chavez vote versus the 1998 automated anti-Chavez vote, you get a plot that looks like this:
Fig. 1 Plot of anti-Chavez votes in 2000 versus anti-Chavez votes in 1998 at automated centers.
You now will measure what is called the vertical and transversal deviations of a graph like this. Let me explain this a little better:
For the graph above you would have an “expected value” which comes from doing a least squares fit to the line y=ax that best fits the data. Now, for each point in the voting data you measure the “vertical” deviation, that is how far is the point vertically from the “expected” or mean line y=ax and the “transverse” deviation, that is how far is each point from the mean line in the direction perpendicular to the line. (See Figure 3)
You now plot these two deviations in a histogram, where as you go away from deviation “zero” you will have fewer points in both the positive and negative directions. For the graph above from the anti-Chavez in the automated centers in 2000 and 1998 you get something that looks like this:
Fig. 2 Distriburion of transverse deviations for the automated votes of the RR
Now, the interesting thing is that there is a mathematical test to determine whether the two variables are random or not. If the two variables were random, which is what you expect from two consecutive elections at the same automated centers, then you get schematically, asymmetric distribution from the fertical deviations and an assymetric one from the transverse deviations.
Fig3. Only one variable is random. The other depends on it.
But, if one only one of the variables is random, i.e. in our case, if the two elections are not “independent” of each other but one set of results was obtained from each other then you expect the opposite, an assymetric distribution from the vertical deviatiosn and a symmetrical one form the transverse:
Fig4. Both variables are random
Well what Medina did was to plot this distributions for the RR versus the signatures and also the manual and automated centers and what he finds is that EXCEPT for the case of the data from the automated centers of the RR versus the signatures, everything else follows what you expect from two random variables. That is, in all cases but the RR, the vertical deviations show a positive asymmetry, while the transverse deviations are symmetrical. This suggests that both variables were independently random.
In contrast, the data for he automated centers of the recall vote versus the signatures shows the opposite, the vertical deviations are symmetrical, while the transverse ones are asymmetrical.
Now, for those of you that are not too mathematical inclined, this means that there is a mathematical test that shows exactly the positive behavior between the two cases.
In fact, Medina performed three mathematical calculations that showed that in the following cases there was only single random variable:
–The total number of votes versus voters in the RR
–The total number of signatures versus voters in the RR
–The total number of automated votes versus the signatures in the R
While he performed four others that showed in othere cases there were two independent variables:
–Total votes at the RR versus signatures.
–Manual votes un 2000 versus manual votes in 1998R
–Automated votes 2000 versus 1998
–Manual Votes RR versus signatures.
Mathematically, there is no other conclusion that the SI votes at the automated centers of the RR were obtained from the number of people who signed the petition to recall Chavez using some form of equation with a distribution
How about that!