Insufficient Statistical Rigor and Sample Size

[murr2k]

Problem Description

The quality control audit identified multiple statistical deficiencies that undermine the scientific validity of the results.

Statistical Issues Identified

1. Sample Size Problems

• Individual experiments: n = 3 (E. coli, Salmonella, Pseudomonas)
• Statistical power: ~25% (need 80% minimum)
• Required sample size: n ≥ 30 for adequate power (0.8) with medium effect size

2. Missing Statistical Tests

• No p-values reported for any claims
• No significance testing performed
• No confidence intervals calculated
• No multiple testing correction (Bonferroni, FDR)

3. Statistical Discrepancies Found

• Total experiments: Claimed 23, found 20 in data
• Average analysis time: 16.4% relative error
• High confidence rate: 4.3% discrepancy
• Several metrics show >1% deviation from claims

4. Lack of Statistical Framework

• Confidence scores (0-1) lack statistical foundation
• No null hypothesis defined
• No control group for comparison
• No variance or standard error reported

Power Analysis Results

Current configuration:

• Effect size: 0.5 (medium)
• Alpha: 0.05
• Current power: ~0.25
• Required n for 0.8 power: 64 samples

Required Statistical Improvements

1. Increase Sample Size

• Minimum 30 organisms for basic statistics
• Preferably 64+ for adequate power
• Include diverse bacterial families

2. Implement Proper Testing

3. Add Statistical Measures

• 95% confidence intervals for all metrics
• Bootstrap analysis for confidence scores
• Standard errors for means
• Effect sizes (Cohen's d)

4. Multiple Testing Correction

• Bonferroni correction for multiple organisms
• False Discovery Rate (FDR) for trait detection
• Adjusted p-values in all reports

5. Validation Statistics

• Sensitivity and specificity
• Positive/negative predictive values
• ROC curves with AUC
• Cross-validation results

Impact of Current Deficiencies

1. Type I Error Risk: May report false positives
2. Underpowered: Cannot detect true effects reliably
3. No Significance: Cannot claim results are non-random
4. Irreproducible: No confidence intervals for replication

Acceptance Criteria

• Minimum 30 real experimental samples
• All claims supported by p-values < 0.05
• 95% confidence intervals for all metrics
• Power analysis showing ≥ 0.8 power
• Multiple testing correction applied
• Statistical methods section in documentation
• Raw data and analysis scripts provided
• Comparison with null distribution

Priority: HIGH
Type: Statistical Deficiency
Impact: Results not publishable without these improvements