How were the nomograms in Veale et al. (2015) constructed and what do their full percentile tables show?

1. What the authors collected and excluded: the raw material

Veale and colleagues performed a systematic review of studies that reported penile measurements taken by health professionals and excluded samples with congenital or acquired penile abnormalities, prior surgery, self‑selected “small penis” complaints or erectile dysfunction, producing a pooled dataset representing up to 15,521 men drawn from multiple countries and study cohorts ^{[5] [1] [6]}. This selection aimed to estimate “normal” distributions but implicitly privileges clinic‑measured series and excludes groups known to bias size estimates (both upward and downward), a choice that shapes the nomograms’ applicability to any individual man ^{[1] [6]}.

2. How the nomograms were constructed: weighted means, pooled SDs, and simulation

The analytic pipeline reported by Veale et al. calculated weighted means and pooled standard deviations for each measured dimension, then simulated 20,000 observations from a normal distribution defined by those pooled parameters to generate the graphical nomograms; percentiles on the nomograms derive from the cumulative normal distribution of those simulated values ^{[1] [2]}. In short: meta‑analytic pooling produced summary µ and σ, simulation created a large synthetic population, and the cumulative normal was used to convert sizes to percentiles — a transparent, reproducible statistical route but one that rests on the assumption of approximate normality for each metric ^{[2] [1]}.

3. What the nomograms show: percentiles and interpretation

Graphically, the nomograms plot flaccid, flaccid‑stretched and erect lengths and circumferences against the proportion of men at or below each value, so a point on the curve gives the population percentile for that measurement (for example, an erect length at the 50th percentile corresponds to the pooled mean) ^{[2] [3]}. The paper’s figures and summary statistics provide means and standard deviations for each metric and the nomogram curves; however the publicly available versions of the article emphasize graphs rather than printing a full exhaustive table listing every conventional percentile (1st, 5th, 10th … 99th) in numeric form within the main text accessible here ^{[3] [7]}.

4. What the full percentile tables would contain — and what’s missing

If produced from the published µ and σ, full percentile tables are straightforward to compute (percentile = inverse cumulative normal of z scaled by µ and σ), and later papers following Veale’s method have simulated larger samples (e.g., 40,000) and produced tabulated percentiles for regional datasets ^[8]. The Veale paper itself provides the summary parameters and nomogram figures that permit reconstruction of percentile tables, but a ready‑made, comprehensive numeric table of every percentile for every dimension is not explicitly printed in the public copies cited here — investigators or clinicians must either read values off the nomogram figures or recreate tables from the reported µ and σ ^{[1] [2] [3]}.

5. Caveats, criticisms and alternative perspectives

The method assumes normality and homogeneity across pooled studies; reviewers of nomogram methodology warn that construction choices, population differences and measurement heterogeneity (technique, sample selection, geography) influence applicability and uncertainty — and more recent work documents geographic variation in penile dimensions, suggesting a single global nomogram can mislead if applied without context ^{[4] [6] [8]}. Veale et al. acknowledge cohort heterogeneity and frame the nomograms as clinical counseling tools rather than absolute truths, but clinicians should combine them with clinical judgment and, where relevant, region‑specific data ^{[1] [9]}.