In terms of designing a study for examining whether or not there is any validity to houses, I see five particular challenges to be overcome. I'll itemize these below, along with recommendations for how to solve the problem.
First: Data quality. Birth time is far more critical for a house examination than for anything else we can study. At present, our best shot is likely the Gauquelin data, since everything is birth certificate derived and we can pull groups of hundreds-to-thousands in size.
Second: Characteristic selection. This is pretty much what we would do for the sign studies. We either need a well-defined characteristic that hundreds-to-thousands in our data have in common (such as the same career, to pick the most commonly used) or another well-defined commonality such as a character trait. (In the Gauquelin studies, this was accomplished by using traits that others had attributed to the individual in writing, as in magazine articles and biographical collections, and then increasing the number available for a given trait by using a thesaurus model to aggregate several near-synonyms or related traits into blocks).
Third: House model selection. There are over five dozen different domification (house calculation) models. At this stage, a study would ideally test several models independently to see whether any of them produced significant results and, if so, which ones. Probably at least half a dozen particular ones should be used (I could produce a priority list if we ever got to that point). - As a variation (Issue #3B), the first large study should address the question of whether a twelving of the mundane circle is valid at all, using a technique similar to what Bradley developed in Profession & Birth Date for sign studies; and, if a twelving were indeed valid, this also would tell us how it is distributed, e.g., beginning with a cusp, centered on a cusp, skewed from a cusp, etc.
Fourth: Probabilities calculation. This is the most difficult task in theory, though perhaps handled easily with existing techniques provided we have enough computer power. The issue is that the likelihood that a given planet will be in a given house at a given latitude for a given diurnal orientation is easy enough to calculate case-by-case, but abominably hard to calculate overall - and the variance is extreme (e.g., it isn't even odds or anything close). Prior studies focusing on angularity have overcome this difficulty by superposing quadrants, since that superposition normalizes the probability inequities.
This problem is minimized, by the way, for various "even house" methods, which includes whole-sign methods. Latitude-dependent factors are minimized but not removed, e.g., there is still unevenness in what sign is rising, but something closer to even twelfths per sign, especially when these are randomized by "spinning the wheel" of possible Ascendants. Some pilots or modeling would be needed to confirm this, but the problem, at least, is less derailing. The problem is that I highly doubt that, if houses exist at all, it would be one of the equal house systems that would show the effects.
With sufficient computing and programming power, and with very large data samples, the matter can be likely addressed by using the approach Tom Shanks created for Michel & Francoise Gauquelin. The root principle is that, rather an a priori estimation of odds (which potentially excludes a number of unknown or under-known factors), one can look within the data sample or its source to calculate probabilities. For the present purpose, the form this takes is as follows: For your whole data sample, break down the various parts of the birth data into separate records of month, day of month, year, hour, minute, longitude, and latitude. Next, randomize these factors and recombine them into fake birth records to use as a matching size control group. The synthetic control group has the same number of people with equal distribution across years, parts of years, parts of months, parts of the day, and part of an hour, as well as the critical geographic latitude distribution.
Q&A and discussion on Houses including house models and domification systems.
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