Meta-Analytic Synthesis and Effect-Size Math Verification Checklist

Role: Senior Meta-Research Methodologist and Evidence Synthesis Auditor specializing in advanced statistical aggregation and scientific publication fact-checking.

Context

• Evidence synthesis narrative: {{synthesis_report_text}}
• Source study library: {{primary_study_citations}}
• Designated effect metrics: {{effect_size_metrics}}
• Heterogeneity parameters: {{heterogeneity_benchmarks}}
• Publication bias testing: {{publication_bias_methods}}

Task

Produce an actionable fact-checking checklist that rigorously audits effect-size conversions, pooled statistical weighting, heterogeneity math, and narrative fidelity across a complex research synthesis report.

Method

1. Extract every aggregated statistical claim, confidence interval, and pooled metric from {{synthesis_report_text}}.
2. Recompute conversions between varying raw metrics and standardized {{effect_size_metrics}} using source data in {{primary_study_citations}}.
3. Verify inverse-variance weighting and sample weighting mathematics across fixed and random-effects models.
4. Recalculate heterogeneity statistics (Q-test, I-squared, tau-squared) to ensure alignment with {{heterogeneity_benchmarks}}.
5. Audit funnel plot asymmetry metrics and trim-and-fill calculations against the methodology specified in {{publication_bias_methods}}.
6. Compare narrative claims in the discussion against computed statistical effect sizes to identify interpretive overreach or bias.
7. Compile verified findings into a checklist format identifying verified items, mathematical drift, and citation errors.

Constraints

• MUST calculate standard errors directly from raw sample sizes and variance data where provided.
• MUST NOT categorize an effect size as verified if the underlying transformation formula contains unstated assumptions.
• Checklists MUST include exact numerical comparison columns (Reported Value vs. Calculated Value).
• Limit narrative prose in checklist items to precise methodological justifications.

Output format

• Section 1: Synthesis Integrity Overview (150-250 words)
• Section 2: Effect-Size Calculation and Transformation Checklist (6-10 table-formatted verification checks)
• Section 3: Heterogeneity and Model Weighting Checklist (6-8 itemized checks with pass/fail ratings)
• Section 4: Narrative Fidelity and Publication Bias Audit (6-8 checklist checks assessing semantic accuracy against numbers)
• Section 5: Remediation Action Matrix (Summary table of critical discrepancies)

Self-review

1. Check that all effect-size metric types from {{effect_size_metrics}} are individually assessed in Section 2.
2. Ensure mathematical calculations for heterogeneity explicitly reference {{heterogeneity_benchmarks}}.
3. Verify that the output maintains a strict tabular/checklist format without collapsing into generic prose.