Control Group Results
The 2.6 million false relationships are derived from 5200 = 2 persons x 2 studies x 1300 relationships as follows:
500 false partners were created for every subject in the study and given a random date of birth in the same year or two years before or after their actual partner’s birth date at the time of the real relationship. The start date used was the start date of the actual relationship. For Elizabeth Taylor, this meant that for her first relationship in the study and for her then partner Richard Burton, 500 false partners were created for each of them with dates of birth in a five-year period centered around 1925 (for Liz) and 1932 (for Richard). The start year for all of these was 1962, the start year of the Burton-Taylor romance. The same was done for all of the partners in all relationships.
This method creates a control of 2.6 million false relationships. The resulting totals were quite close to mathematically expected results. These results were used to calculate expected outcomes throughout this paper.
Calculation of Expected Results:
In the following, we will create an expected value for any synastry aspect based purely on mathematics and astrometry.
Here is the principle of this calculation: There is a factor 2 in both of these calculations since there are 2 aspects to include and for each pair we calculate the direct and also the converse aspect i.e. (Number of relationships/degrees in a circle * total number of degrees included in the orb) * the number of times the aspect can happen in a circle.
This is the calculation used for 1300 relationships at 2° 01”:
Where the planets involved are different (SO-VE, VE-MA, SO-MA)
1,300/360*8.068 for conjunctions/oppositions = 29.13
1,300/360*8.068*2 for other aspects = 58.26
Where the planets involved are the same (SO-SO, VE-VE, MA-MA)
1,300/360*4.034 for conjunctions/oppositions = 14.56
1,300/360*4.034*2 for other aspects = 29.13
Finally, the scaled control is arrived at as follows: (control group result/control group total) * sample group total
Planetary movements seen from the Earth are far from uniform. But in the case of the comparison of two themes, this argument about non-uniformity no longer applies and the simple calculation of the proportionality of the ratio between the sensitive areas as a function of the orbs and the whole zodiacal circle is quite close to the true probability as approximated by the control group.
 Where the control is the number of results in the aspect styles added together (either N-N N-P P-N and P-P for natal and progressed OR N-P P-N and P-P for progressed) and the sample group total is the number of real relationships under scrutiny. For instance for trine aspects of SO-VE in 1300 relationships: N-P SO – VE control result = 115,804 /2,600,000 = .04454 * 1,300 = 57.902 (N-N SO-VE = 58.3835, P-N SO–VE = 58.0405 P-P SO–VE =57.9875) added together equals 232.3135 rounds to an expected number of 232.
With thanks to Kyosti Tarvainen, Vincent Godbout, Robert Currey, and David Cochrane for advice, review and modelling.