To scientifically assess significance with this new Cosine Intensity model, you cannot rely on standard Chi-Square tests (which require discrete "counts"). Instead, the most robust metric would be a Z-Score derived from Permutation Testing (Resampling).

Here is the proposed statistical framework for this intensity (continuous) validation:

1. The Metric: Empirical Z-Score (vs. Randomized Baseline) #

Because planetary positions are not random, we cannot compare against a uniform distribution. We must compare against shuffled versions of the dataset itself.

• The Process:

  1. Calculate determining the Observed Total Intensity for a specific pair (e.g., "Politicians + Regulus").
  2. Shuffle the "Category" labels of the 936 people randomly (keeping their birth charts intact) 10,000 times.
  3. Recalculate the Total Intensity for "Politicians + Regulus" in each of these 10,000 random universes.
  4. Compare:
     • Mean ($ \mu $): The average intensity expected by random chance.
     • Standard Deviation ($ \sigma $): How much the intensity varies naturally.
     • Z-Score: $ Z = \frac{\text{Observed} - \mu}{\sigma} $

• Interpretation:

  • Z > 2.0 (approx p < 0.05): The intensity is significantly higher than chance.
  • Z < -2.0: The intensity is significantly lower than chance (the star is "avoided").

2. Effect Size (Cohen's d) #

While a P-value (or Z-score) tells you if a result is unlikely to be random, it doesn't tell you if it's meaningful. With large datasets, tiny differences can be "significant."

• Metric: $ d = \frac{\text{Mean}{group} - \text{Mean}{population}}{SD_{population}} $
• Use: To determine if the "pull" of Regulus on Politicians is actually defined strongly enough to matter in interpretation.

3. Kolmogorov-Smirnov (KS) Test #

• Use: To compare the shape of the intensity distribution.
• Why: A star might not increase the average pull, but it might create "polarization" (lots of very tight conjunctions AND lots of misses, with few in between). A KS test would reveal if the shape of the curve for "Musicians" differs significantly from the general population.

Recommendation #

For the next phase of "Project 25", the Permutation Test script is recommended. It is the gold standard in astroligical research because it preserves the astronomical structure of the birth data while testing the validity of the social categories.