Intro
In biomechanics, we commonly use summary metrics, like averages, maximums, values at events, and summary statistics like t-tests to describe our data. While these tests are useful, a summary statistic can overgeneralize the signal, and remove important information about the signal. This is why we have introduced Statistical Parametric Mapping (SPM) into Sift. SPM introduces the ability to do statistical analysis in the same space as our original data. When used in tandem with Random Field Theory (RFT), we can produce interpretable results across the entire field of data, and identify specific sections which are statistically relevant.
Let us show an example where SPM might provide insights where we otherwise might not be able to:
Example
Above we can see the average gait cycle for the left and right knees in flexion/extension across multiple participants. Both traces follow a similar trend, but how can we determine if they are statistically different? Or if the differences are just due to random noise? We want to test if the two knee angles above come from the same distribution (i.e. are they statistically different). In doing so, however, it is not immediately clear how to apply a common test, like a t-test.
- We might average the value across the cycle, but the value fluctuates, and may not accurately represent the gait.
- We could choose a specific point across both signals, like the max value, and apply a t-test there. This will similarly lose information about the rest of the cycle, and not accurately represent the gait.
Clearly reducing our signals into a single point is unintuitive, and may not be accurate. These two examples give the following results:
| p-value | |
| Average T-Test | 0.727 |
| Max T-Test | 0.658 |
SPM Analysis
Our t-test results show that there is no statistical difference between the 2 groups, but does this pass the eye test? We can clearly see visual differences throughout the entire gait cycle. There are different peaks/valleys and crossings between the groups, which one-off values do not capture. To correct for this, you may think, could we run a t-test on the entire cycle and see where there might be significant differences? Absolutely! This is where SPM comes in: using SPM and RFT, we can apply a t-test across all of the points in time, and create a global threshold. This threshold is based on the interdependence of all of our data, and can identify significant regions within the cycle.
SPMs allow us to keep the data’s original dimensionality, which is extremely useful when creating visualizations for our analysis. Above, we can see our statistical parametric map. Highlighted in blue is the region exceeding the a=0.05 threshold (i.e. p-value of 0.05 or less) signifying significant differences between the two groups at this threshold. This map provides us with much more information than the standard t -test results we saw earlier. This shows us that there are three separate but statistically significant regions:
- A large region during the middle of the gait cycle
- A small region at ~25% of the gait cycle
- A small region at ~90% of the gait cycle.
This information is useful in helping us understand the differences between the two groups, which typical summary statistics in biomechanics do not capture.
Conclusion
We can see the inherent benefits of doing an SPM analysis: Identifying regions within your data that are statistically significant is a key benefit, and is not possible with simple summary statistical tests. SPM analysis also keeps your data in its original dimensionality, making it easier to interpret and pull meaning from the graph. The uses for SPM are clear, and we think that SPM should be embraced in the biomechanics field.
Addendum: Registering Curves
We believe that limiting time variance between groups helps improve the outcome of an SPM analysis. Intuitively, this makes sense: How can we do any meaningful time analysis if the same events occur at different times across trials? That’s why we (and many other SPM users) recommend registering your data before analyzing it with SPM. When you register your data, you warp the data to align specific events (like gait events) across groups. Doing so significantly reduces the residuals produced in an SPM analysis while increasing the dependence between data points. This allows for a reduced threshold value, and even more accurate identification of statistically significant areas. In the SPM graph below, we registered the curves according to a local maximum in the 50%+ section of the gait cycle. We observe the same trend as the unregistered curves, with a reduced threshold and an increase in the SPM values.
Registering curves is not an exact science, there is no best method to choose what to register with. What it attempts to do is reduce some of the randomness inherent within our data. Reducing randomness ensures cleaner and better analysis for your research.