ArticleInternational journal of general medicine2026
First-Digit Distributions of Human Long-Bone Morphometric Parameters: An Exploratory X-Ray-Based Comparison with Benford's Law.
Article in International journal of general medicine, 2026. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Not yet cited in PubMed.
What it found
Each row is one number read from the abstract, on the scale the paper reported it, with its interval. Left of the dashed line favours the treatment, right favours the comparator. Under each row is the sentence it came from. New to these charts? A ten-minute tutorial.
The abstract states no effect estimate the extractor could read, or names no intervention and outcome on the map, so this paper lights no cell and moves no belief. It is still indexed, cited and linked below.
The trial behind it
Trials whose registry record cites this paper, or whose number appears in the abstract. A trial that started after this paper was published is citing it as background, not reporting it.
Neither the registry nor the abstract names a trial number. If this is a trial report, that itself is worth knowing.
Who cites it
0 citing papers in PubMed.
No citing paper in PubMed yet.
Corrections and comments
PubMed lists nothing against this paper. Absence here is not a guarantee, only a check that was made.
Authors and funding
2 authors.
Funding
No grant is acknowledged in the PubMed record.
Abstract
Background: Benford's Law describes a theoretical first-digit distribution observed in many natural and scientific datasets. However, empirical datasets rarely match this distribution exactly, and the appearance of a Benford-like pattern may depend on the numerical range and data-generating process. Objective: This exploratory study aimed to describe the first-digit distributions of X-ray-based human long-bone measurements and derived quantities, and to compare these observed distributions with the theoretical distribution predicted by Benford's Law. Methods: Anteroposterior X-ray images of half of the long bones from three adult patients were retrospectively retrieved from the Picture Archiving and Communication System. The lengths, perimeters, and projected areas of each long bone were measured. The squares and cubes of bone lengths were subsequently calculated as exploratory dimension-based transformations. First-digit distributions were compared with the Benford-expected distribution using Pearson's chi-square goodness-of-fit test as an exploratory statistical comparison. Mean absolute deviation (MAD) between observed and expected first-digit proportions was additionally calculated as a descriptive measure of discrepancy. Results: The first-digit distributions of raw lengths and perimeters showed statistically detectable discrepancies from the Benford-expected distribution (both P = 0.001). Projected areas and squared length values did not show statistically detectable evidence against the Benford-expected distribution in the chi-square comparison (P = 0.260 and P = 0.292, respectively). Cubed length values showed the smallest apparent discrepancy among the variables examined (P = 0.910). MAD values were 0.042 for length, 0.037 for perimeter, 0.024 for projected area, 0.026 for square of length, and 0.014 for cube of length. Conclusion: In this small exploratory dataset, projected areas and derived squared or cubed length values showed more Benford-like first-digit patterns than raw lengths and perimeters. These findings should be interpreted as descriptive evidence of digit-distribution characteristics in long-bone morphometric data rather than as categorical evidence establishing conformity or nonconformity to Benford's Law.
Indexed as
Identifiers
What OpenQuestion holds
Registered trials
Read under generation 80e0d062 · epoch 390. Bibliography from PubMed, PubMed Central and OpenAlex; grants from NIH RePORTER; trial links from ClinicalTrials.gov; estimates, votes and beliefs from the OpenQuestion graph.