Teach-in 2002 : Gait Cycle Data Averaging Techniques
by Chris Kirtley, The Catholic University of America, Washington DC

It is standard practice when collecting gait data to ensemble average (Winter, 1991) several strides (trials) together in order to derive a mean and standard deviation for each point (e.g. at 2% intervals) in the cycle. We often then compare selected measurements between two data sets (patient versus normative data; pre-op versus post-op etc.). For example, we might compare a patient's peak knee swing flexion angle with that derived from a group of normals...

In such circumstances, it is usual to not only compare the means of the point in question on the two curves, but also to take into account the standard deviation (the grey region in the example above) - a difference of, say, 2° being considered insignificant if the SD were to be, say, ± 5°. In the example shown, the patient would appear to be just about within the normal range for peak swing phase knee flexion. So far so good...

A colleague here suggested an alternative method. Supposing we were not to ensemble average the data from all these trials at all. We simply measure the peak knee swing flexion in all the different trials individually (rather laborious, I know, but let's assume we can do it) and derive a mean and SD of these measurements in the two groups to be compared (patient/normative dataset, or pre-op/post-op). So might have, for example:

 Patient Normative Peak Knee Swing Phase Flexion 60 ± 5° 70 ± 10° Peak Knee Stance Phase Flexion 30 ± 4° 23 ± 5° Peak Knee Extension in Late Stance 18 ± 5° 2 ± 4° etc. etc. etc.

Of course, this might be a bit inconvenient because we would have to set up a big database with all these conceivable measurements, and would perhaps have to maintain the normative data in another big database in case we ever want to introduce a new measurement. But I want you to consider these two techniques purely from a mathematical standpoint.

Questions
• Would the mean and SD calculated for a given selected point (e.g. peak knee swing flexion) be identical if it were calculated by the second method as opposed to the original, ensemble averaging method?

•
• If not, then which technique is the more mathematically correct?

### Bibliography

Winter DA (1991) The biomechanics and motor control of human gait: normal, elderly and pathological. University of Waterloo Press, Ontario, Canada (page 9).

Winter DA. Electromyogram recording, processing, and normalization: procedures and considerations. Journal of Human Muscle Performance. 1991;1:5-15.

Yang JF, Winter DA. Electromyographic amplitude normalization methods: improving their sensitivity as diagnostic tools in gait analysis. Arch Phys Med Rehabil. 1984;65:517-521

Jacobsen WC, Gabel RH, Brand RA. Surface vs fine-wire electrode ensemble-averaged signals during gait. J Electromyogr Kinesiol. 1995;5:37-44

Rice J.A., Silverman B.W., (1991) Estimating the mean and covariance structure nonparametrically when the data are curves. Journal of the
Royal Statistical Society, Bath. Vol 53 (1) pp. 233-243.

A. Kneip and Th. Gasser (1992). Statistical tools to analyze data representing a sample of curves. Annals of Statistics 20 1266-1305.

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