The Dazzle Farm Hypothesis: Statistical Power Analysis

Context & Methodology

Location: Ptuj, Slovenia (August 2020)

Observation periods:

Hypotheses:

Test parameters: One-tailed z-test, α = 0.05, Power = 90%

Analysis 1: Random Observations

Using G*Power methodology with arcsine transformation for proportions:

h = 2|arcsin(√p₁) - arcsin(√p₀)|
n = ((z_α + z_β) / h)²
where z_α = 1.645 (one-tailed, α=0.05), z_β = 1.282 (power=0.90)

Result for H₀ = 75%:

n = 144 random observations needed                           MISPRINT  n = 15  THE CHART IS CORRECT

Cohen's h = 0.647 (medium effect size)                                                                          NO, IT'S 0.763 LIKE IT SAYS IN THE CHART

Analysis 2: Consecutive "Light On" Observations

⚠️ Methodological Comparison:

Two statistical approaches for consecutive observations yield different results. Both are mathematically valid but serve different purposes.

Method 1: Basic Sequential Test

Standard SPRT using Type I and Type II error thresholds:

Find k where:
p₀^k < β (Type II)
AND (1 - p₁^k) < β

k = 13

Use case: Standard scientific research

Method 2: Conservative (Wald-style)

Likelihood ratio test with conservative threshold to account for overshoot and legal standards:

LR = (p₁/p₀)^k = (0.98/0.75)^k
Find k where: LR ≥ 20,000
k ≥ log(20000) / log(1.3067)
k ≥ 37

k = 37

Use case: Legal proceedings requiring extreme confidence

Why the 185% difference?

  • Method 1 (k=13): Uses standard power analysis error rates (α=0.05, β=0.10)
  • Method 2 (k=37): Requires likelihood ratio of 20,000:1 odds in favor of H₁
  • The conservative method accounts for:
    - Sequential testing overshoot
    - Legal evidentiary standards
    - Minimizing false accusations

Both are mathematically sound. Method 2 prioritizes avoiding Type I errors (false positives) at the cost of requiring more observations.

Legal Verdict for H₀ = 75%:

Standard method: 13 consecutive observations required
Conservative method: 37 consecutive observations required
Ptuj Police recorded: ZERO observations

Even using the most lenient statistical standard, the warrant lacked the evidentiary basis required for 90% confidence in distinguishing normal lighting from abnormal lighting patterns.

Full Comparison Table

H₀ (%) Cohen's h Effect Size Random n Sequential k (Basic) Sequential k (Conservative)

Summary for Defense:

The warrant was issued without meeting any scientifically defensible evidentiary threshold.

Generated: | Cohen's h = 0.647 (medium effect)