# Myelin g-ratio statistics: axons within animals, axon diameter and comparing myelination

> Compare g-ratios with one value per animal, not hundreds of axons. Adjust for axon size from each animal's own fibre-versus-axon diameter line, because smaller axons alone can change the mean g-ratio. Python and R code.

Canonical: https://www.licklider.ai/guides/myelin-g-ratio/
Section: Guides › Correlation, regression and survival
Author: Licklider · Published 2026-11-12 · Last reviewed 2026-11-12 (UTC)

> **Quick answer.** The g-ratio (axon diameter ÷ fibre diameter, from electron micrographs) is measured on hundreds of axons per animal, but the **animal** is the unit, and axons within an animal are not independent. Give each animal one value and compare animals with a Welch t-test. A mean g-ratio per animal is safe only when axon sizes are similar between groups: if small axons have relatively thick myelin in your data (plot g-ratio against axon diameter to see; Gow argues that in healthy tracts the g-ratio is close to constant), a group with smaller axons can show a lower mean g-ratio even when myelin is normal. For that case, this guide fits **a straight line predicting fibre diameter from axon diameter for each animal**. First check that each animal's points follow a straight line, with similar slopes in both groups. Then compute each animal's g-ratio at one common axon diameter inside every animal's range (here 1 µm ÷ the fibre diameter the line predicts for a 1-µm axon), and compare animals. In a simulation of 5 vs 5 mice with about 100 axons each and no real difference, a t-test on all axons gave false positives in 54.8% of simulated studies and a per-axon regression in 64.5%; when knockout axons were 20% smaller with normal myelin, the per-mouse mean g-ratio reported a myelin difference in 51.0% of studies and the per-mouse g-ratio at 1 µm in 4.0%.

**Terms used below.** *g-ratio*: inner (axon) diameter ÷ outer (fibre) diameter of a myelinated axon; lower means thicker myelin relative to the axon. *Fibre diameter*: axon plus myelin sheath. *Myelin thickness*: (fibre − axon diameter) ÷ 2. *Oblique* axons are cut at an angle and *outfolded* myelin loops away from the axon; both distort diameters. A standard deviation of 0.06 *on the log scale* means about ±6%. *Mixed model*: a regression with a *random effect* (an adjustment for each animal), so axons or regions of one animal are not treated as independent. *Binning*: grouping axons into ranges of diameter. *Deming regression*: a straight-line fit that allows measurement error in both variables. *Intercept*: the fibre diameter a line predicts at axon diameter 0; a positive intercept means small axons have relatively thick myelin. *Hypomyelination*: thinner myelin than normal, giving higher g-ratios. *n*: the number of independent units in a test, here mice rather than axons. *Experimental unit*: the thing randomised to a group, here the mouse. *Pseudo-replicate*: a measurement that repeats the same unit, such as another axon from the same mouse. *Per-axon regression*: a regression fitted to all axons pooled, treating each as independent. *Welch t-test*: a two-group t-test that does not assume equal spread. *95% confidence interval (CI)*: the range of values compatible with the data. *Power*: the chance of detecting an effect that is really there. *False positive*: a "significant" result when there is no real effect.

## Which analysis for your question

| Question | Analysis | Report |
| --- | --- | --- |
| Is myelin thinner relative to axon size? | Each animal's straight line of fibre on axon diameter (check that the points follow a line and the slopes look similar between groups), g-ratio at a common axon diameter inside every animal's range, Welch t-test across animals | Difference with 95% CI, n animals (axons) |
| Do groups differ in axon size distribution as well? | Median axon diameter per animal, compared across animals; report it next to the g-ratio | Difference with 95% CI |
| Overall g-ratio, with axon sizes similar between groups | Mean g-ratio per animal, Welch t-test | Difference with 95% CI |
| Proportion of axons myelinated | Myelinated ÷ all axons counted per animal, compared across animals | Difference in proportion with 95% CI |
| Several regions or ages | The same per region, with animal as the unit; choose the regions in advance or correct for the number of tests; when the same animals give several regions, a mixed model with animal as a random effect | Results per region |

Chomiak and Hu describe the g-ratio as "the ratio of the inner axonal diameter to the total outer diameter" and note that it is widely regarded as "a highly reliable ratio for assessing axonal myelination" ([Chomiak and Hu 2009](https://doi.org/10.1371/journal.pone.0007754)). Gow and colleagues write that measurements of many axons from one animal "are actually pseudo-replicate data (measurements from a single animal under identical experimental conditions)", and recommend "a single estimate per mouse" for testing ([Gow et al. 2025](https://doi.org/10.1080/17590914.2024.2447336)). Gow writes that the usual practice of fitting a line of g-ratio against fibre diameter (or taking an arithmetic mean), which suggests that small fibres have proportionately thicker sheaths, is "used almost universally to assess changes to myelin, lacks a consistent mathematical framework and may lead to incorrect conclusions for many studies" ([Gow 2026](https://doi.org/10.1080/17590914.2025.2612034)). Analysis D below is this guide's own approach, an adjustment for axon size within each animal (the idea behind [ANCOVA](/guides/normalizing-to-body-weight-ratio-or-ancova/)); Gow and colleagues instead start from "axon versus fiber diameter plots – test for linearity", then use "unbiased binning of fiber diameters / mouse" and a mixed-effects analysis of the median g-ratio in each bin ([Gow et al. 2025](https://doi.org/10.1080/17590914.2024.2447336)). Kaiser and colleagues quantified micrographs "blinded of their genotypes" with the MyelTracer software ([Kaiser et al. 2021](https://doi.org/10.1523/ENEURO.0558-20.2021)).

## Worked example: a knockout with no real effect

Constructed data: axon and fibre diameters for **80 to 120 myelinated axons in each of 5 wild-type and 5 knockout mice** (1,032 axons). The model assumes that fibre diameter rises in a straight line with axon diameter and has a positive intercept, so small axons have relatively thick myelin and low g-ratios (an assumption: Gow argues that in healthy tracts the g-ratio is close to constant across fibre sizes); axon diameters vary with a standard deviation of 0.35 on the log scale; mice differ in myelin thickness (0.06) and each axon's myelin thickness scatters around its mouse (0.12). By design, **the knockout changes neither myelin nor axon size**. The data's random seed was the first one tried and was not chosen for its result. Stored code and data: [axons.csv](/guides/myelin-g-ratio/axons.csv), [model.py](/guides/myelin-g-ratio/model.py), [make_data.py](/guides/myelin-g-ratio/make_data.py), [analysis.py](/guides/myelin-g-ratio/analysis.py), [analysis.R](/guides/myelin-g-ratio/analysis.R) and [the analysis output](/guides/myelin-g-ratio/analysis_output.txt); analysis.py and analysis.R print the same output.

The mean g-ratio was 0.712 in wild-type and 0.713 in knockout mice, and the median axon diameter per mouse averaged 0.78 µm in wild-type and 0.79 µm in knockout mice.

| Analysis of constructed data with no real effect, knockout vs wild-type | Result |
| --- | --- |
| A. (Not valid: axons share mice) Axons as n (482 vs 550), Welch t-test on g-ratio | difference 0.001, p = 0.58 |
| B. (Not valid: axons share mice) Regression of g-ratio on genotype and axon diameter, all axons | genotype difference −0.002, p = 0.25 |
| C. Mice as n, mean g-ratio per mouse (5 vs 5), Welch t-test (valid when axon sizes are similar) | difference 0.001 (95% CI −0.024 to 0.026), p = 0.91 |
| **D. Mice as n, each mouse's g-ratio at 1 µm axon diameter, Welch t-test** | **difference −0.003 (95% CI −0.028 to 0.022), p = 0.79** |

With this data set no analysis found a difference; with 5 mice per group a study like this excludes only large differences, and the confidence interval shows which remain possible. The simulation shows how often the per-axon analyses find differences that do not exist. Across 5,000 simulated studies of this design ([simulation.py](/guides/myelin-g-ratio/simulation.py), [the simulation output](/guides/myelin-g-ratio/simulation_output.txt)):

| Scenario | A. Axons as n (invalid) | B. Regression, axons as n (invalid) | C. Mean g-ratio per mouse | D. g-ratio at 1 µm per mouse |
| --- | --- | --- | --- | --- |
| No difference (false positives) | **54.8%** | **64.5%** | 4.4% | 4.6% |
| Knockout axons 20% smaller, myelin normal ("myelin difference" by mistake) | 96.0% | 64.4% | **51.0%** | 4.0% |
| Myelin thickness reduced by 15% (power) | 99.9% | 100.0% | 93.1% | **94.0%** |

These percentages describe this simulated design (5 mice per group, about 100 axons each, the variation in model.py), not every myelin study. Treating hundreds of axons as independent found a "difference" in more than half of the null studies, because axons from one mouse share its fixation, processing and biology. The mean g-ratio per mouse was valid when axon sizes were the same, but when knockout axons were simply smaller it reported a myelin change in 51.0% of the studies, because in this model small axons have lower g-ratios. Reading each mouse's g-ratio at a common axon diameter removed that and kept the power to detect real thinning. The model makes fibre diameter increase in a straight line with axon diameter, which suits analysis D; a first version of D that fitted a straight line of g-ratio on axon diameter gave 13.1% false positives in the smaller-axon scenario (column E of the linked simulation output), because the g-ratio is not a straight-line function of axon size.

Which to use: if the groups' axon sizes differ, or g-ratio changes with axon diameter in your plots, use D; otherwise C is simpler and gives the same answer. Before using D, plot fibre against axon diameter for each animal: the points should follow a straight line, and the slopes should look similar in both groups. If the slopes clearly differ, report the g-ratio at two or three named axon diameters instead of one. Our simulation used 80–120 axons per animal; an animal with far fewer, or with a curved plot, gives an unreliable line. Measurement error in axon diameter also flattens each line; Gow and colleagues note that "experimental errors are present in both axon and fiber diameter measurements" and analyse these plots with Deming regression, so treat D as an approximate adjustment that works when both groups are measured the same way. Choose the common diameter between the smallest and largest axon of every animal; if 1 µm is outside that range for any animal, choose a diameter that every animal covers and say so.

The code expects one row per myelinated axon with columns `genotype` (labels exactly `wild-type` and `knockout`), `mouse`, `axon` (an ID for your records; the code does not use it), `axon_um` and `fibre_um` (diameters in µm, for example from area as 2 × √(area ÷ π)). Rename your columns and labels to match, save the table as axons.csv (or change the file name in the code), and run the code in that folder (`python analysis.py` or `Rscript analysis.R`). Python needs NumPy, pandas 2.2 or later and SciPy 1.11 or later (`pip install numpy pandas scipy`); the R code uses base R only. The printed difference is knockout − wild-type, and its confidence interval is for that difference.

```python
import numpy as np, pandas as pd
from scipy import stats

d = pd.read_csv("axons.csv"); D0 = 1.0                                     # common axon diameter, um
def g_at(x):                                                              # each mouse's own line of fibre on axon diameter
    b = np.polyfit(x.axon_um, x.fibre_um, 1); return D0 / (b[0] * D0 + b[1])     # b = slope, intercept
m = d.groupby(["genotype", "mouse"]).apply(g_at, include_groups=False)
t = stats.ttest_ind(m["knockout"], m["wild-type"], equal_var=False); ci = t.confidence_interval()
print(f"g-ratio at {D0:g} um: difference {m['knockout'].mean() - m['wild-type'].mean():.3f} (95% CI {ci.low:.3f} to {ci.high:.3f}), p = {t.pvalue:.2g}")
# g-ratio at 1 um: difference -0.003 (95% CI -0.028 to 0.022), p = 0.79
```

```r
d <- read.csv("axons.csv"); D0 <- 1.0
m <- do.call(rbind, lapply(split(d, paste(d$genotype, d$mouse)), function(x) { b <- coef(lm(fibre_um ~ axon_um, data = x))   # b = intercept, slope
  data.frame(genotype = x$genotype[1], g1 = D0 / (b[[1]] + b[[2]] * D0)) }))           # g-ratio at 1 um per mouse
t.test(g1 ~ genotype, data = m)       # Welch; knockout - wild-type -0.003, 95% CI -0.028 to 0.022, p = 0.79
```

## Before you analyse

1. **Sample micrographs and axons by a rule fixed in advance**, for example a fixed number of random non-overlapping fields per animal and every myelinated axon in them, and measure blind to genotype.
2. **Define the measurement**: axon or inner-myelin diameter, diameters from areas or from minimum and maximum widths, and which axons are excluded (oblique, outfolded, unmyelinated), applying the same rules to every animal.
3. **Report axon size per animal** alongside the g-ratio, and compare myelination at a common axon diameter when sizes differ.
4. **Use the animal as n**; plan animals, not axons.
5. **Keep fixation and processing the same across groups**, and process animals of both groups together, because tissue shrinkage during fixation and embedding changes diameters.
6. **Check cages and litters**: mice in a group that share a cage or litter are not independent; use the cage or litter as the unit, or model it as a random effect ([what counts as n](/guides/what-counts-as-n/)).

## Check what an AI assistant ran

1. **The assistant ran a t-test or regression on all axons.** Ask for one value per animal.
2. **The assistant compared mean g-ratios when axon sizes differed between groups.** Ask for the g-ratio at a common axon diameter.
3. **The assistant reported a g-ratio scatterplot slope from all axons as the result.** Ask for one estimate per animal, such as its g-ratio at a common axon diameter.
4. **The assistant did not say how axons were chosen.** Ask for the sampling and exclusion rules.

## Report it

> Axon and fibre diameters were measured blind to genotype on [80–120] myelinated axons from [10] random non-overlapping micrographs per mouse ([5] wild-type and [5] knockout). For each mouse, fibre diameter was regressed on axon diameter (the points followed a straight line in every mouse) and the g-ratio at [1] µm axon diameter was calculated; genotypes were compared with a Welch t-test on these per-mouse values (R [4.3.3]). Median axon diameter per mouse averaged [0.78] µm in wild-type and [0.79] µm in knockout mice.

> In the constructed example, which has no effect built in, the g-ratio at 1 µm did not clearly differ between genotypes (knockout − wild-type [−0.003], 95% CI [−0.028] to [0.022]; p = [0.79]; n = [5] mice per genotype, [1,032] axons).

Replace the bracketed values with your own.

## References

- Chomiak T, Hu B (2009). What is the optimal value of the g-ratio for myelinated fibers in the rat CNS? A theoretical approach. *PLoS ONE* 4:e7754. [doi:10.1371/journal.pone.0007754](https://doi.org/10.1371/journal.pone.0007754)
- Gow A, Dupree JL, Feinstein DL, Boullerne A (2025). A statistically-robust model of the axomyelin unit under normal physiologic conditions with application to disease states. *ASN Neuro* 17:2447336. [doi:10.1080/17590914.2024.2447336](https://doi.org/10.1080/17590914.2024.2447336)
- Gow A (2026). Myelin g ratios: the model is in the details. *ASN Neuro* 18:2612034. [doi:10.1080/17590914.2025.2612034](https://doi.org/10.1080/17590914.2025.2612034)
- Kaiser T, Allen HM, Kwon O, et al. (2021). MyelTracer: a semi-automated software for myelin g-ratio quantification. *eNeuro* 8:ENEURO.0558-20.2021. [doi:10.1523/ENEURO.0558-20.2021](https://doi.org/10.1523/ENEURO.0558-20.2021)

## Related

- [Normalising to body weight: ratio or ANCOVA](https://www.licklider.ai/guides/normalizing-to-body-weight-ratio-or-ancova/)
- [Nested data: means or mixed model](https://www.licklider.ai/guides/nested-data-mixed-model/)
- [Correlation vs linear regression](https://www.licklider.ai/guides/correlation-vs-linear-regression/)
- [What counts as n](https://www.licklider.ai/guides/what-counts-as-n/)

## How this page was made

- Written and published by Licklider. Recommendations cite peer-reviewed methods papers listed under References; cited passages were checked against the source text.
- The worked example uses constructed data. Its numbers were produced by stored code (Python 3.13 with SciPy 1.18.1; R 4.3.3, base R), and the two languages print identical output; the simulation was run in Python.
- Separate review passes checked the statistics, the citations and readability before publication.