CGA FAQ: Coefficient of Variation...

I have compiled a summary of responses to my recent request for information on coefficient of variation (CV). Thankyou to all
who replied.

The main findings from my request are:

1. 1. Winter's estimates of CV
2. 2. Winter's calculation of CV
3. 3. Comments on the usefulness of this statistic
Details of these can be found in the contents of the postings attached.

I am still exploring how applicable and useful this statistic is. I'll keep you posted.

Kindest regards.

Mick Dillon

Dear Mike,

Here's Winter's values, (which agree with my own findings):

Intra-subject (%)
Angle Moment Power
Hip         21     33         45
Knee     8         37         39
Ankle     16     16         49

Inter-subject (%) ... note much larger
Angle Moment Power
Hip             52         140     221
Knee         23         135     157
Ankle         72         42       100

Best wishes,

Chris
--
Dr. Chris Kirtley MD PhD
Dept. of Rehabilitation Sciences
The Hong Kong Polytechnic University
Hong Kong
Special Administrative Region of The People's Republic of China

Tel: +852 2766 6755 Fax: 2330 8656
http://www.polyu.edu.hk/~rs/kirt/index.htm

Clinical Gait Analysis: http://www.polyu.edu.hk/cga
Send subscribe/unsubscribe to listproc@info.curtin.edu.au

Dear Mick,

CV = 100*SQRT(Mean Variances)/(Mean "Mean")

i.e. simply total up (SD)squared at each point in the cycle and divide by the number of points, then do the same for the means.
Divide the square root of the first by the second.
It's just a sort of intuitive average Standard Error really. The only thing is that the SDs have to be squared first then rooted.

By the way, it's usually called "coefficient of variation" not variability.

Chris
--
Dr. Chris Kirtley MD PhD
Dept. of Rehabilitation Sciences
The Hong Kong Polytechnic University

You may be interested in:

Kadaba, M.P. Ramakrishnan, H.K., Wootten, M.E. et at. Repeatability of Kinematic, Kinetic and Electromyographic Data in Normal Adult Gait. J Orthop Research. 7:849-860, 1989.

In summary, in a group of 40 adults, the coefficient of multiple determination was used to assess the within and between day variability.Sagittal plane angles were high within day, ranging a low of .669 for pelvic tilt, to .996 for hip flexion. Between day variability was considerably worse, from .240 for pelvic tilt, to .983 for hip flexion. Most of this was felt to be due to marker
replacement issues. Transverse plane angles had higher variability (.860-.918 within day, .410-.768 between day). Moments had
lower variability, primarily because in swing, the values are constantly near zero (.856-.992 within, .840-.960 between day).

A similar study, performed at our facility on 50 children over the last several years showed similar trends, however the variability
was in general, lower. This was a surprise since it was a pediatric population, but on closer examination, the marker set has
changed sufficiently over the past ten years that much of the decreased variability may be related to improvements in technique
and mechanisms for minimizing marker replacement error (eg - using a "knee alignment device" and eliminating a pelvic wand with

Winter has also reported CV for a small group of subjects within and between days.

Hope this helps.

Sincerely
George Gorton.

*********************************************
George E. Gorton, III
Director, Gait Analysis Laboratory
Shriners Hospitals for Children
516 Carew Street
Springfield, MA 01082

Tel: (413)735-1269
email: ggorton@shrinerspfld.org
*********************************************

I have never found the coefficient of variability to be a very useful measure of trial-to-trial or subject-to-subject variablility. the
reason is that if the motion pattern crosses zero, the CV values can be extremely high at these points. Taking the CV of the entire
motion pattern can also have its problems, especially if the pattern is symmetrical around zerio (ie hip). Instead, I have begun
looking at the average standard deviation or average standard error of the mean for each point in the motion I am interested in (eg
every 2% of stance phase).

Mark W. Cornwall, PhD, PT, CPed Gait Research Laboratory Department of Physical Therapy Northern Arizona University
P.O. Box 15105 Flagstaff, AZ 86011 Voice: (520) 523-1606 FAX: (520) 523-9289 email: mark.cornwall.nau.edu

______________________________________________________________________________

Hi,

I remember that Winter and Kadaba have publishing such result but I do not
remember references. Please find enclosed my references to those authors...

Good luck and thank to send me your results or others bibliographics
references...

KADABA M.P., RAMAKRISHNAN H.K., WOOTTEN M.E., GAINEY J., GORTON GAUCHE. &
COCHRAN G.V., 1989
"Repeatability of kinematic, kinetic, and electromyographic data in normal
adult gait.", J. Orthop. Res., 7(6), 849-60
KADABA M.P., H. RAMAKRISHNAN & M. WOOTTEN., 1990
"Measurement of lower extremity kinematics during level walking.", J.
Orthopaedic Res., 8, 383-392
RAMAKRISHNAN H.K. & KADABA M.P., 1991
"On the estimation of joint kinematics during gait.", J. Biomech., 24(10),
969-77
WINTER D.A., H.G. SIDWALL & D.A. HOBSON, 1974
"Measurement and Reduction of Noise in Kinematics of Locomotion", J.
Biomech., 7, 157-159
WINTER D.A., A. O. QUANBURY & G.D. REIMER, 1976
"Analysis of Instantaneous Energy of Normal Gait", J. Biomech., 9, 253-257
WINTER D.A., 1978
"Energy Assessments in pathological gait", Physiother. Can., 30, 183-191
WINTER D.A. & D.G. ROBERTSON, 1978
"Joint Torque and Energy Paterns in Normal Gait", Biol. Cybern., 29,
137-142
WINTER D.A., 1979
"A new Definition of Mechanical Work Done in Human Movement", J. Appl.
Physiol., 46, 79-83
WINTER D.A., 1980
"Overall principle of lower limb support during stance phase of gait", J.
Biomech., 13(11), 923-927
WINTER D.A., 1981
"Use of kinetic analyses in the diagnostics of pathological gait",
Physiother. Can., 33, 209-214
WINTER D.A., 1982
"Camera speeds for normal and pathological gait analyses", Med. Biol. Eng.
Comput., 20, 408-412
WINTER D.A., 1983
"Energy generation and absorption at the ankle and knee during fast,
natural and slow cadences", Clin. Othop. Rel. Res., 197, 147-154
WINTER D.A., 1983
"Moments of force and mechanical power in jogging", J. Biomech., 16(1),
91-97
WINTER D.A., 1983
"Biomechanical motor patterns in normal gait", J. Motor. Behavior., 302-320
WINTER D.A., 1984
"Kinematic and kinetic patterns in human gait : variability and
compensating effects", Hum. Move. Sci., 3, 51-76
WINTER D.A., 1984
"Biomechanics of human movement with applications to the study of human
locomotion", Biomedical engineering, 9 (4), 287-314
WINTER D.A., 1984
"Pathologic gait diagnosis with computer-averaged electromyographic
profiles", Arch. Phys. Med. Rehabil., 65, 393-398
WINTER D.A., 1985
"Concerning the scientific basis for the diagnosis of pathological gait and
for rehabilitation protocols", Physiother. Canada, 37(4), 245-252
WINTER D.A., 1987
"Mechanical power in human movement : generation, absorption and transfer",
Med. Sport Sci., vol. 25, 34-45
WINTER D.A. & H.J. YACK, 1987
"EMG profiles during normal human walking : stride-to-stride and
inter-subject variability", Electroencephalog. Clinical Neurophysio., 67,
402-411
WINTER D.A., 1990
"Biomechanics an motor control of human movement", A Wiley Inters. Publ.,
Seconde Edition, New York
WINTER D.A., 1991
"The biomechanics and motor control of human gait", 2nd ed., Ed. Press
Universitaire de Waterloo, Ontario
WINTER D.A., C.D. McKINNON, G.K. RUDER & C. WIEMAN, 1993
"An integred EMG/biomechanical model of upper body balance and posture
during human gait", Progress Brain Research, 97, chap 32, 359-367
WINTER D.A., 1993
"An integrated knowledge base approach to all clinical gait assessments",
Round table -3, ", ISB 93, Paris
WINTER D.A., A.J. FUGLEVAND & S.E. ARCHER, 1994
"Crosstalk in surface electromyography : theoretical and practical
estimates", J. Electromyog. Kinesiol., 4(1), 15-26

Mick,

You may want to look at the following references:

Kadaba MP, Ramakrishnan, HK, Wootten, ME, Gainey J. Gorton G, Cochran GVB:
Repeatability of kinematic, kinetic, and electromyographic data in normal
adult gait. Journal of Orthopaedic Research, 7: 849-860. 1989.

Yu, B, Kienbacher, T, Growney, ES, Johnson, ME, An, KN: Reproducibility of the
kinematics and kinetics of the lower extremity during normal stair climbing.
Journal of Orthopaedic Research, 15: 348-352, 1997.

Coefficient of variation (CV) may be a good measure of reproducibility of
discrete data points. Coefficient of multiple correlation (CMC) is a good
measure of reproducibility of a continuous procedure.

Good luck.

Bing Yu, Ph.D.
Assistant Professor
Division of Physical Therapy
The University of North Carolina at Chapel Hill

The biggest dataset that I have is kinematic data for the foot. I have mean standard error values of about .5 degrees or less. This
is on 150 subjects. Looking at every 2 or 1 percent of the gait cycle is simply a means to get the error (variability) over the time
span that I am interested in, usually stance phase duration.

Mark W. Cornwall, PhD, PT, CPed Professor, Department of Physical Therapy P.O. Box 15105 Northern Arizona University
Flagstaff, AZ 86004 (520) 523-1606 (520) 523-9289 FAX

Michael Dillon
B P&O Hons. PhD Student
Centre for Rehabilitation Science and Engineering
Queensland University of Technology
School of Mechanical, Manufacturing and Medical Engineering
GPO Box 2432
Brisbane. 4001.
Ph. +61 07 3864 2751 E-mail: m.dillon@qut.edu.au
Fax. +61 07 3864 1469
http://www.bee.qut.edu.au/mech/staff/mdillon.html