Data
The column after the mean
Every measured mean in a paper comes with an SD, SE or CI in the next column, and which one it is changes what the number means.
Guides on Data: How a size study is built, Reading a nomogram without fooling yourself, The Veale meta-analysis, read properly
The number beside a mean in a results table can be a standard deviation, a standard error or a confidence interval, and only the first describes individuals. Mixing them up produces a common mistake: reading a narrow interval as a statement about individual men when it is about the mean.
Three different columns, one appearance
Standard deviation (SD) describes how spread out individual measurements are around the mean. It answers "if I picked one man from this sample, how far from the mean would his reading typically be." Standard error (SE) describes how precisely the sample mean itself is known, and it shrinks as the sample gets larger - a huge study can report a tiny SE even though individual men in it vary widely. Confidence interval (CI), usually reported at 95 percent, is built from the SE and states a range the true population mean is likely to fall within, not a range individual readings fall within.
All three can appear in a table looking like "mean (X)" with no more explanation than the column header, and the header is exactly what tells you which one you are looking at.
The relationship between SE and SD is arithmetic, not a matter of judgement: SE equals the SD divided by the square root of the sample size. That single fact explains why SE always shrinks as a study grows while SD does not - SD is a property of the individuals in the population, and adding more of them to the sample does not make any one individual less variable, it only pins down the mean more precisely. A table that reports SE without also giving SD, or n, leaves you unable to recover the individual-level spread at all.
Why the confusion matters
If a study reports a large sample with a tight 95 percent CI, it is easy to read that tight interval as meaning individual men cluster closely around the mean. They do not, necessarily - a huge sample narrows the CI around the mean regardless of how spread out the individuals actually are. The number that tells you about individual spread is the SD, and it is the one that matters for placing your own reading on a percentile, not the CI.
A small illustrative table
| Study | n | Mean (cm) | SD (cm) | 95% CI (cm) |
|---|---|---|---|---|
| Small study | 60 | 13.1 | 1.7 | 12.7 - 13.5 |
| Large study | 6,000 | 13.2 | 1.6 | 13.15 - 13.25 |
The two studies report nearly the same mean and a similar SD - individual men vary by roughly the same amount in both. The CI, though, is far narrower in the large study, purely because of its sample size. Reading the large study's tight CI as "individuals cluster tightly" would be wrong; the SD says they do not, and the CI was never claiming that.
A real row, worked through
Veale et al. (2015), BJU International, reports erect length as "n = 692, mean (SD) 13.12 (1.66) cm". Divide 1.66 by the square root of 692 and the SE is about 0.063 cm, which puts an approximate 95% CI for the mean at 13.00 to 13.24 cm - a band a quarter of a centimetre wide, while the SD says individual men typically sit well over a centimetre and a half from the mean.
Applying this to a real table
When you are reading a published table of size figures - Veale 2015 among them - check the column header before drawing a conclusion from the number in it. A percentile placement needs the SD, not the CI, because a percentile is a statement about where an individual sits among other individuals, not where the population mean sits. If a table gives you only a CI and no SD, it has told you the mean is well-estimated and said nothing about how spread out individual men are. A CI can be converted back toward an approximate SD if the sample size is given, since its width is built from the SE - but that is a calculation to do deliberately, not an equivalence to assume by eye.
This distinction is unrelated to anything an image-based rating tool reports. A score from Rate Cock, a numeric rating site, a verdict from a human judge, or an estimate from an image-analysis model carries no SD or CI in this statistical sense at all, since none of them is sampled from a measured population the way these tables are.