A Statistical Investigation of the Synoptic Problem

TL;DR

Using 807 vocabulary items across 19 HHB synoptic categories, the paper fits Poisson models with likelihood-ratio tests and an overdispersion correction to test directional vocabulary prediction among Matthew, Mark, and Luke. It reports statistically significant support for Markan priority, Luke’s use of Matthew, and a sayings source, concluding the Three Source Hypothesis best fits the data.

Key findings

• Markan priority: distinctively Markan vocabulary predicts Mark/Matthew shared material; the anchor relationship 121 → 221 remains significant at the order of 10⁻⁸ after correction and clears even the most conservative dispersion factor tested, while the reverse 211 → 221 does not appear.
• Luke’s use of Matthew and the minor agreements: 211 → 212 has corrected p = 8.0 × 10⁻⁴ and 210 → 212 has corrected p = 8.0 × 10⁻⁵, indicating distinctively Matthean vocabulary predicts passages where Matthew and Luke agree against Mark.
• Sayings source: both 201 → 202 and 102 → 202 predict the double tradition with near-equal weights (β = .1576 and β = .1484), which the paper reads as the symmetry of a shared source; 122 → 002 is reported as exploratory with corrected p = 2.0 × 10⁻⁶.
• Overall: 17 relationships survive the paper’s filters; all 17 clear FDR at φ = 1.8, eight clear Bonferroni, and six form a “robust core” at φ = 2.5 spanning Markan priority, the Markan origin of triple-tradition agreements, the sayings source, and the minor agreements as Matthean.

Methods

• Data: the Hoffmann, Hieke, and Bauer Synoptic Concordance, restricted to 807 fully tabulated vocabulary items across 19 synoptic categories, with each cell recording absolute occurrence counts.
• Model: Poisson count models with maximum likelihood estimation and likelihood ratio tests; each ordered pair asks whether a predictor category improves prediction of a test category beyond the corpus-wide baseline, with 171 possible pairwise comparisons and a 66-comparison hypothesis-testing family.
• Corrections: overdispersion estimated at φ ≈ 1.8 (1.88 for 222, 1.76 for 122, 1.80 for 002), applied by dividing each likelihood ratio statistic by φ; multiple-comparison control uses Bonferroni threshold .05/66 ≈ 7.6 × 10⁻⁴ and Benjamini-Hochberg FDR at q = 0.05, with robustness checks at φ = 2.17 and φ = 2.5.

Limitations

• Stated: the study does not establish a proto-Mark or proto-Luke; the proto-Luke discussion is speculative, the Marcion question cannot be adjudicated, and the statistical evidence cannot adjudicate proto-Mark.
• Stated: 122 → 002 lies outside the hypothesis-testing family and is reported as exploratory; direct Mark → Luke relationships clear only the FDR threshold, not Bonferroni, and some reported weights are not individually significant.
• Stated/evident: the analysis depends on HHB concordance category assignments, excludes rarer items with incomplete data, excludes 200 → 202 on methodological grounds because the concordance distributes Matthean doublets across categories, and applies conservative overdispersion and multiple-comparison corrections; the paper also discloses AI assistance for copyediting, drafting, condensing, and consultation on overdispersion.