Antrometric V3.1: Long Bones Into Transparent Stature Evidence

Why I Rebuilt Everything From the Ground Up, and What the New Version Can and Cannot Do

Feedback has a way of arriving when you least expect it, and questions have a way of not leaving you alone once they take hold. Over the months since version 2.1 went live, messages came in from forensic anthropologists, archaeologists, police investigators, and pathologists in countries I had not anticipated when I first built the tool, asking variations of the same underlying question. The math works, but can the result be reviewed? Can the interval be trusted? Can I show this to a court? And, persistently, from several users who had measured multiple bones from the same individual: if I have five bones, why isn’t the estimate five times more precise?

That last question is the one that refused to leave me alone on the nights when I couldn’t sleep. Because it is the right question, and version 2.1 answered it only partially. The weighted mean was there. The uncertainty reduction was there. But the transparency was not. You could get a number. You could not easily see why the number was what it was, which bone was driving it, whether the bones were internally consistent with each other, or how far the estimate would shift if one measurement turned out to be less reliable than assumed.

The result of those nights is Antrometric V3.1.

What Is New, Feature by Feature

Version 3.1 is not an incremental update. The architecture, the interface, and several of the core statistical mechanisms have been rebuilt from scratch. The bones at the bottom are the same, the regression coefficients from Trotter and Gleser, Feldesman et al., and Mahakkanukrauh et al. are still there, but what sits above them has been fundamentally redesigned.

Measurement condition adjustment is the first change that practitioners will notice. Version 2.1 treated every entered bone as equally reliable. That was not realistic. A complete bone measured on an osteometric board from a well-preserved archaeological specimen is not the same measurement as a reconstructed length assembled from fragments at a crime scene. Version 3.1 requires the user to declare the actual measurement condition for each bone, choosing from Complete, Minor surface loss, Reconstructed, or Fragmentary, and each condition carries a documented quality multiplier that widens the standard error of the regression accordingly. Complete bone applies a multiplier of 1.00. Minor surface loss widens to 1.12. Reconstructed to 1.28. Fragmentary to 1.55. These multipliers are not arbitrary penalties, they are documented in the science-data.js file and visible in the scientific method section, and they propagate directly into the uncertainty of every downstream calculation.

Instrument uncertainty in quadrature is the second new mechanism. Even a complete bone measured by an experienced osteologist on a properly calibrated board is not measured with perfect precision. ISO 5725-2 distinguishes trueness from precision, and the repeatability of the measurement act itself has a floor of approximately 0.5 cm under typical laboratory conditions. Version 3.1 adds this instrument floor in quadrature with the adjusted regression standard error, so the total per-bone uncertainty reflects both the regression model and the measurement act. For a complete European male femur at 47.0 cm, the additional 0.5 cm in quadrature changes the total standard error from 3.27 to 3.31 cm, which is modest. For a fragmentary bone, the same floor is added to a much larger adjusted SEE and the effect compounds accordingly. The formula is:

[math]SEE_i^{tot} = \sqrt{(SEE_i \cdot q_i)^2 + \sigma_M^2}[/math]

Robust inverse-variance weighting with consistency diagnostics replaces the simple weighted mean of version 2.1. When multiple bones are entered, the engine now computes a standardized residual for each bone against the combined estimate, identifies the most discordant bone by name if it exceeds the threshold, and adjusts the influence of that bone rather than simply including it at full weight or excluding it silently. The standardized residual for each bone is:

[math]z_i = \frac{|\hat{S}_i – \hat{S}_{combined}|}{SEE_i^{tot}}[/math]

Residuals at or below 1.65 are labeled high consistency. Above 1.65, moderate consistency. Above 2.65, possible outlier, with the specific bone named in the result and an eight-point penalty applied to the Accuracy Index. The combined uncertainty is computed conservatively as the larger of the weighted naive SEE with a correlation factor and completeness adjustment, or fifty percent of the smallest single-bone total SEE, ensuring that correlated bones from the same skeleton never produce an implausibly narrow interval.

The diurnal and age correction addresses something that has been a known source of bias in stature estimation for decades but has never been integrated into an estimation tool in a usable form. Living stature is not constant across the day. Intervertebral discs lose hydration under gravitational load, and the spine can shorten by one to 1.2 centimeters over a typical waking day. The reference regressions of Trotter and Gleser were calibrated against either morning living stature or cadaveric length, which means that a comparison against an afternoon measured reference introduces a small but real systematic bias. Version 3.1 gives the user an optional correction: enter the hours since waking, and the engine applies a transparent adjustment. If estimated age above 50 years is also entered, a small additional age term is applied for vertebral height loss. The formula is:

[math]\Delta h = 0.083 \cdot \min(h, 14) + 0.012 \cdot \max(0, age – 50) \cdot 0.4[/math]

The 0.083 cm per hour term integrates to approximately one centimeter of correction over a twelve-hour waking day, consistent with the controlled disc-compression studies of Tyrrell, Reilly, and Troup (1985). The correction is entirely opt-in. When hours since waking are left at the default, the engine applies zero correction and the result is identical to the classical approach.

The Accuracy Index is perhaps the most consequential new addition, because it addresses a specific problem that the forensic community has raised repeatedly about stature estimation tools: the tendency to present a number without communicating how much confidence is warranted in that number. The Accuracy Index is a percentage score that summarizes, in a single figure, how tightly the V3.1 model can constrain adult stature for the specific inputs provided. It is built from six components: the interval half-width, the bone count gain, the average quality penalty across all bones, the consistency penalty, and the scenario and model penalties for unknown sex, generic population, or single-bone input. The formula is:

[math]AI = \text{clamp}(100 – 3.7H + B – Q – C – S, 32, \text{cap})[/math]

Three complete consistent European male bones with known sex and known population produce a score in the high 80s. A single fragmentary bone with unknown sex and generic population context can produce a score of 32, the floor. The floor is intentional: even the weakest adult measurement scenario carries some orientation value, and the interface does not pretend otherwise. The cap prevents weak scenarios from appearing stronger than they are, and different caps apply depending on which limitations are present. The Accuracy Index is explicitly not an identification probability. It is a model confidence score, and the distinction is stated clearly on its own dedicated page of the site.

The live skeleton feedback is a visual audit trail embedded in the calculator itself. As the user selects bones, the corresponding elements on an anatomical skeleton diagram are highlighted in red in real time. This makes the measurement source visible before the calculation runs, and provides an immediate cross-check on whether the entered configuration is anatomically sensible. It is a small feature but one that has been appreciated by the users who tested the early version: it forces the user to see the skeleton as a whole rather than as a list of numbers.

The Subadult Beta module is intentionally and explicitly locked. This deserves explanation rather than apology. It would have been technically simple to wire a set of juvenile equations into the calculator and display a result. The problem is that adult linear regression formulas do not apply to growing individuals, because diaphyseal growth is not constant across childhood, epiphyses fuse at different times, and body proportions change in ways that adult regression assumptions cannot accommodate. A subadult stature estimate requires age-aware growth models, appropriate subadult measurements, and validated prediction intervals specific to the juvenile growth context. None of this exists inside V3.1, and displaying a number that cannot be properly supported would be scientifically indefensible. The Subadult Beta tab is present so the boundary is visible to every user, not hidden behind a disclaimer. The roadmap for a future subadult module is published on the site.

Over 1,000 Test Calculations: What They Confirmed and What They Revealed

Before publishing V3.1, more than a thousand individual test calculations were run across all available population and sex combinations, covering single-bone inputs, full six-bone inputs, discordant bone scenarios, fragmentary measurement conditions, unknown sex conditions, generic population conditions, and all combinations of the diurnal and age correction. The testing confirmed that the weighted combination consistently narrowed the uncertainty interval as additional bones were added, that the consistency diagnostic correctly identified discordant bones in constructed test cases without false positives under normal anatomical variation, and that the Accuracy Index scores moved in the direction the formula predicts when each parameter changes individually.

What the testing revealed is that the most consequential source of remaining uncertainty is not the regression model itself but the appropriateness of the chosen reference population and the measurement protocol match between the analyst’s bone measurement and the protocol used in the source regression study. These are not computational problems, they are judgment problems, and V3.1 addresses them not by solving them but by making them explicit: the population and sex selection are visible in the result, the measurement condition is recorded per bone and reflected in the uncertainty, and the Accuracy Index penalizes scenarios where the biological context is less specific.

Who This Tool Is For

Forensic anthropologists need stature estimation in the context of biological profile construction for unknown remains, and they need results that can be reviewed and defended in court, which is why V3.1 separates the point estimate, the interval, the formula family, and the precision score into distinct elements of the output rather than presenting a single number. Archaeologists need it for the biological profiling of historical and archaeological populations, where fragmentary material is the rule rather than the exception, and where the condition-specific uncertainty modeling of V3.1 is directly relevant. Criminalists and investigating authorities need a fast, trustworthy orientation value from crime scene skeletal material, delivered without requiring specialized software installation or institutional licensing. Pathologists and forensic medical examiners work with skeletal material in identification contexts that sometimes require stature estimation as a biometric anchor for cross-referencing missing person data.

All of these users share a requirement that version 2.1 did not fully meet: not just a number, but a number that can be explained, reviewed, and defended, together with an honest statement of how confident the model is in that number.

What Antrometric V3.1 Cannot Do

This matters as much as what it can do.

Antrometric does not perform identification. A stature interval is one parameter of a biological profile, alongside sex, ancestry assessment, age-at-death, and individuating features. Comparing a stature estimate against a missing person’s recorded height can narrow or widen a set of candidates. It cannot close an identification. No tool based on regression stature estimation can, and V3.1 does not claim otherwise.

The diurnal and age correction is a population-level approximation. Individual variation in intervertebral disc compression and vertebral aging is real and is not captured by the linear terms in the correction formula. The correction aids in reconciling reference baselines with comparison contexts, but it is not an individualized diagnosis.

The tool does not validate whether the measurement protocol used in the laboratory matches the protocol of the source regression equation. A femur measured oblique-to-board cannot substitute for a Trotter-protocol maximum femoral length without bias, and V3.1 cannot detect that discrepancy. The analyst is responsible for protocol consistency, and V3.1 documents this clearly in the scientific method section.

The Subadult Beta module does not calculate. Until a vetted subadult engine with citable prediction intervals is implemented and documented, refusing to compute is the scientifically correct behavior.

Privacy by design: Antrometric V3.1 processes every calculation entirely in the browser with client-side JavaScript. No bone measurements are submitted to a server. No account is required. No tracking cookies, analytics pixels, or third-party profiling scripts are present. The calculation never leaves the user’s device. For practitioners handling sensitive case material, this is not a minor technical detail, it is a structural protection.

The Result That Can Be Reviewed

The principle behind V3.1 is stated on the front page of the site: long bones into transparent stature evidence. The word transparent is not marketing language. It is a description of what the output contains. The formula family is shown. The source metadata is visible. The measurement condition is recorded per bone. The interval is labeled with its statistical level. The consistency is diagnosed and named where relevant. The Accuracy Index explains its own score. The diurnal correction is displayed when applied.

The result can be reviewed instead of merely trusted, and that difference is the entire point.

Antrometric V3.1 is available at antrometric.com, runs without installation in any current web browser, and requires no account or registration.

References

• Albanese, J., Tuck, A., Gomes, J., and Cardoso, H. F. V. (2016). An alternative approach for estimating stature from long bones that is not population- or group-specific. Forensic Science International, 259, 59-68.
• Bidmos, M., and Brits, D. (2025). Evaluating the accuracy of population-specific versus generic stature estimation regression equations in a South African sample. International Journal of Legal Medicine, 139, 411-418.
• Chu, E. Y., and Stull, K. E. (2025). An investigation of the relationship between long bone measurements and stature: Implications for estimating skeletal stature in subadults. International Journal of Legal Medicine, 139, 441-453.
• Cline, M. G., Meadors, A. K., Cole, T. M., Boyles, J. R., and Lukens, A. (1989). Decline of height with age in adults in a general population sample. Human Biology, 61, 415-425.
• Feldesman, M. R., Kleckner, J. G., and Lundy, J. K. (1990). The femur/stature ratio and estimates of stature in mid and late-Pleistocene fossil hominids. Journal of Forensic Sciences, 35(2), 431-446.
• Mahakkanukrauh, P., Khanpetch, P., Prasitwattanaseree, S., Vichairat, K., and Troy Case, D. (2011). Stature estimation from long bone lengths in a Thai population. Forensic Science International, 210(1-3), 279.e1-279.e7.
• Rauscher, G. A. (2026). Antrometric V3.1. International Institute of Forensic Expertise (IIFE). https://antrometric.com
• Trotter, M., and Gleser, G. C. (1952). Estimation of stature from long bones of American Whites and Negroes. American Journal of Physical Anthropology, 10(4), 463-514.
• Trotter, M., and Gleser, G. C. (1958). A re-evaluation of estimation of stature based on measurements of stature taken during life and of long bones after death. American Journal of Physical Anthropology, 16(1), 79-123.
• Tyrrell, A. R., Reilly, T., and Troup, J. D. (1985). Circadian variation in stature and the effects of spinal loading. Spine, 10, 161-164.
• White, A. A., and Panjabi, M. M. (1990). Clinical biomechanics of the spine (2nd ed.). J. B. Lippincott.