Location: Ptuj, Slovenia (August 2020)
Observation periods:
Hypotheses:
Test parameters: One-tailed z-test for proportions, α = 0.05, Power = 90%
Using G*Power methodology with arcsine transformation for proportions
Sample size needed to detect abnormal lighting with 90% power:
Key finding for H₀ = 75% (normal behavior):
n = 144 random observations needed
Cohen's h = 0.647 (medium effect)
At 8.92 visible hours/day, this could theoretically be collected in 17 nights of observation (assuming ~1 observation per visible hour). However, true independence requires observations separated across multiple days/weeks.
When ignoring "off" sightings, consecutive "on" observations needed:
⚠️ Methodological Note:
Two different statistical approaches yield different results for consecutive observations. Both are presented below for comparison. The conservative estimate (Grok's method) is recommended for legal proceedings.
Using basic Type I/II error thresholds: P(k consecutive | H₀) < α and P(k consecutive | H₁) achieves power.
k = 13
Limitation: This approach may underestimate required k because it uses simplified probability conditions.
Using likelihood ratio or more rigorous sequential testing methodology accounting for proper power calculations.
k = 37
Grok's statement: "If you make 37 passes during real darkness and see the light ON every single time (37 out of 37), you have ≥90% power to reject the null that it's a normal household."
Comparison for H₀ = 75%:
| Simple Method: | 13 consecutive observations |
| Conservative Method (Grok): | 37 consecutive observations |
| Difference: | 24 additional observations (185% increase) |
Cohen's h = 0.647 (medium effect) — same for both methods
Legal Significance:
Even using the most lenient calculation (Simple Method), Ptuj Police would need 13 consecutive "light on" observations to establish their case with 90% statistical power.
Using the conservative approach recommended by Grok, they would need 37 consecutive observations.
Ptuj Police recorded: ZERO observations
| H₀ (%) | Cohen's h | Effect Size | Random n | Consecutive k (Simple) | Consecutive k (Grok) | Raw Difference |
|---|
Legal Interpretation:
If normal behavior involves lights on 75% of visible hours, an observer would need 144 random observations to distinguish this from cannabis growing behavior (98% on) with 90% confidence and α = 0.05.
For consecutive observations (ignoring "off" sightings):
The Cohen's h effect size is 0.647, which is considered a medium effect per Cohen's benchmarks.
Ptuj Police made zero recorded observations. Their warrant was issued on literally nothing.
The Five Pollyannaisms of Ptuj Police: