Understanding Phase Dispersion, Coupling, and Circular Statistics in CatWalk
Last updated: Sep 21, 2026
In this article
- What phase dispersion and coupling measure
- How the values are calculated
- Interpreting the numbers, including negative values
- When to use phase dispersion vs coupling
- Why circular statistics matter for these parameters
- Recommended tests, tools, and reporting practices
What phase dispersion and coupling measure
Phase dispersion and coupling are interlimb coordination parameters in CatWalk. They describe the temporal relationship between two paws during locomotion, answering one question: when one paw completes its step cycle, at what point in that cycle does another paw make initial contact with the ground?
The two parameters describe the same underlying measurement. They differ only in how the value is displayed.
| Parameter | Range | Best used for |
|---|---|---|
| Coupling | 0 to 100 percent | Scanning values, exporting to standard statistical packages |
| Phase dispersion | Signed value (can be negative) | Circular plots, correct averaging near the wrap point |
Both are calculated for pairs of paws, with one paw designated as the anchor (the reference cycle) and the other as the target (the paw whose contact is being timed).
The paw pair categories
Rodent gait analysis groups paw pairs into three anatomical categories, each with distinct expected coordination patterns.
| Pair type | Combinations | Coordination pattern |
|---|---|---|
| Diagonal | LF-RH, RF-LH | Near-synchronous contact |
| Girdle | LF-RF, LH-RH | Alternating (front pair or hind pair) |
| Lateral (ipsilateral) | LF-LH, RF-RH | Alternating (same side of body) |
How the values are calculated
The calculation places the target paw's initial contact on the anchor paw's step cycle, expressed as a percentage of that cycle.
Formula (conceptual):
(Time of target initial contact − Time of anchor initial contact) / Anchor step cycle duration × 100 percent
Example:
The right front (RF) paw is the anchor and the left hind (LH) paw is the target. The RF paw's step cycle lasts 20 milliseconds. The LH paw makes its initial contact 15 milliseconds after the RF paw's initial contact.
Value = 15 / 20 × 100 = 75 percent
The LH paw touches the ground three-quarters of the way through the RF paw's step cycle.
Interpreting the values
Reference values for a healthy rodent walking at moderate speed
| Pair type | Expected value | Physical meaning |
|---|---|---|
| Diagonal (LF-RH, RF-LH) | ~0 percent (or ~100 percent) | Paws strike the ground almost simultaneously |
| Girdle (LF-RF, LH-RH) | ~50 percent | One paw lands halfway through the other's cycle |
| Lateral (LF-LH, RF-RH) | ~50 percent | Ipsilateral paws also alternate |
These reference values assume a symmetric walking gait. Trot, bound, and high-speed running patterns produce different expected values.
Reading a deviation
| Observation | Likely biological signal |
|---|---|
| Diagonal pairs drift away from 0 percent | Forelimb to hindlimb coordination is degrading |
| Girdle pairs drift away from 50 percent | Left-right asymmetry (limp, hemiparesis, unilateral injury) |
| Lateral pairs drift away from 50 percent | Ipsilateral coordination is off (often cerebellar or spinal) |
| Increased variability across runs | Coordination instability, common in ataxia and neurodegeneration |
Variability across runs is often as biologically meaningful as a shift in the mean, especially in progressive disease models.
Understanding negative values in phase dispersion
Since CatWalk 10.7, phase dispersion is calculated using circular statistics. This introduces two visible changes for users:
- Values can be negative.
- Results are displayed on a circular graph rather than a linear axis.
Why negative values exist
The step cycle is inherently repetitive. The moment labeled 0 percent (start of the cycle) and 100 percent (end of the cycle) are the same instant. On a circle, they occupy the same point at the top.
A negative percentage is simply the counterclockwise way of describing a point on the far side of the circle. -19 percent and 81 percent mark the same instant. The target paw's contact occurs 19 percent of a cycle before the anchor's next cycle starts, or equivalently, at 81 percent of the way through the current cycle.
Why this matters most for diagonal pairs
Diagonal pairs sit right at the 0 / 100 wrap point. In practice, a healthy animal's diagonal readings across a single trial might include values like 98 percent, 2 percent, 99 percent, and -3 percent. These are all near-synchronous contacts. Signed phase dispersion makes the clustering visually obvious. Linear coupling values do not.
Phase dispersion vs coupling: when to use each
Both parameters carry the same information. The choice comes down to workflow.
| Use case | Preferred parameter | Why |
|---|---|---|
| Reading a single value at a glance | Coupling | Always positive, simpler to skim |
| Displaying data on circular graphs | Phase dispersion | Signed values plot symmetrically around a reference point |
| Handing data to Prism or GraphPad | Coupling | Fewer confusing negative numbers for downstream users |
| Calculating group averages correctly | Either, using the circular mean | Avoids the wrap-around error |
Important caveat: switching from phase dispersion to coupling does not remove the circular nature of the data. If your values cluster near the wrap point (0 percent or 100 percent), you still need a circular mean and a circular test. See the next section.
Why circular statistics matter
The wrap-around problem
Linear statistics assume values live on an unbounded number line. Circular data lives on a loop. When averaging or testing values that cross the wrap point, linear methods produce incorrect results.
Illustrative example:
A trial produces four phase dispersion values: 75, 75, 5, 5.
- Linear mean = (75 + 75 + 5 + 5) / 4 = 40 percent
- Circular mean = 90 percent (equivalently, -10 percent)
The linear mean of 40 percent is misleading. It sits on the opposite side of the circle from where all four values actually cluster. The circular mean correctly identifies the group as clustered near the 0 / 100 wrap point.
CatWalk 10.7 calculates the circular mean automatically for group statistics. Users pulling numbers directly from the software get the correct value. Users exporting raw values to Excel and averaging in a spreadsheet do not.
When linear tests are safe (and when they are not)
If every value in every group sits well away from the 0 / 100 wrap point, a t-test or ANOVA will give a practically similar answer to a circular test. This is often the case for girdle and lateral pairs whose expected values sit near 50 percent.
If any values cross or cluster near the wrap point, linear tests can give misleading p-values. Diagonal pairs are particularly vulnerable because their expected value sits right at 0 percent.
Rule of thumb: check where your data lives on the circle before you pick the analysis. Girdle and lateral pairs are usually safe for linear tests. Diagonal pairs are not.
Recommended statistical tests
| Comparison | Test | Notes |
|---|---|---|
| Two groups, well-concentrated data | Watson-Williams | Circular analog of the t-test; assumes von Mises distribution |
| Two groups, no distributional assumption | Watson's U² | Nonparametric, safer default |
| Two or more groups | Mardia-Watson-Wheeler | Nonparametric |
| Repeated measures or mixed designs | Circular mixed models | Available in R via bpnreg, or a GLMM on sin/cos components |
Software support
| Software | Circular statistics support |
|---|---|
| R | Robust support via the circular, bpnreg, and CircStats packages |
| Python | Available via pycircstat, astropy.stats.circstats, and pingouin |
| GraphPad Prism | Not natively supported |
| SPSS | Not natively supported |
For most behavioral cores and users comfortable with light scripting, R with the circular package is the most direct path.
Reporting circular statistics in publications
When reporting phase dispersion or coupling results in a manuscript, best practice is to include:
- The circular mean (not the linear mean)
- A measure of concentration: either the angular deviation or the mean resultant length (r), which ranges from 0 (uniform) to 1 (perfectly concentrated)
- The circular test used and its assumptions
- The test statistic and p-value
The published CatWalk literature has historically applied linear statistics to these parameters. That precedent does not make it correct, and it does not protect authors from reviewers who understand circular data. As circular graphs and statistics become more visible in the software (introduced in 10.7), rigorous reviewers are increasingly likely to expect the appropriate methodology, especially for studies with values near the wrap point.
Quick reference summary
| Question | Answer |
|---|---|
| What does 75 percent mean? | The target paw contacts the ground three-quarters of the way through the anchor paw's step cycle |
| What does -19 percent mean? | Same point on the cycle as 81 percent |
| Why do diagonal pairs show values near 0 percent? | Diagonal paws normally strike the ground almost simultaneously |
| Why do girdle and lateral pairs show values near 50 percent? | These pairs alternate: one lands halfway through the other's cycle |
| Can I use a t-test in Prism? | Sometimes. Safe if values sit away from 0 / 100. Not safe for diagonal pairs or any data clustered near the wrap point |
| What test should I use instead? | Watson's U² for a nonparametric two-group comparison; Watson-Williams if data is well-concentrated |
| Where do I get the circular mean? | Directly from CatWalk 10.7 group statistics, or calculate in R with the circular package |
Related content
- Blog: Understanding phase dispersion in CatWalk
- White paper: What are phase dispersions? (available on the CatWalk resource page)
- Article: Interpreting interlimb coordination in disease models
- CatWalk parameter reference
Applies to CatWalk 10.7 and later. For earlier versions, phase dispersion is reported as a 0 to 100 percent value without circular graphing or automated circular means.