A few years ago I published a paper in the **Australian Journal of**
**Physiotherapy** (1993, 39(2): 115-123) that described some of
my observations

on CV values of 10 gait variables: hip, knee and ankle joint angular

displacements; hip, knee and ankle moments of force; the support moment
of

force; and hip, knee and ankle joint powers. The study included
data from

10 subjects, including a below-knee amputee. I was particularly
interested

in how intra- and inter-subject CV values compared.

My results seemed to jive with Winter and what we see from Drs Cho and

Selber. Have a look at this web page that shows the main data
set for my

1993 analysis:

The use of this particular form of the CV might be better thought of
as

being a **"noise to signal" ratio** as Dr Winter himself has often
said. In

this case, it does seem to be a reasonable value to use as an estimate
of

how consistent subjects are, either between sessions within themselves
or

between subjects. However, as is the case with any measure that
attempts to

distill a great deal of information into a single score, **caution**
in its sole

use is advised, at least as far as categorising variability in human

locomotion.

Cheers,

Drew

Andrew W. (Drew) Smith, PhD

Assistant Professor

Department of Rehabilitation Sciences

The Hong Kong Polytechnic University

Hung Hom, Kowloon

Hong Kong

Special Administrative Region of the People's Republic of China

Voice: +852 2766 7094

FAX: +852 2764 1435

WWW: http://www.polyu.edu.hk/~rs

ICQ: 6164882 Nickname: Daddio

EmailExpress: 6164882@pager.mirabilis.com

I've been meaning to send you this for some time but just haven't got

around to it.

(attached file is at: /data/Baker/anon.gcd)

This represents 9 adults, 6 females and 3 males (male physio students
are less common).

Each attended on two occasions. On the first occasion data was captured,
the markers

were completely removed and then replaced for a second data capture.
On the second

occasion only one marker placement was used. One walk from each marker
placement for

each patient was added to the normal database. Data from left and right
legs was

combined. One Physio (Brona McDowell) placed all markers.

Visual inspection suggests that the **errors from different marker
placement are of the**
**same order as walk to walk and patient to patient variability**
although we have not

analysed this any more formally. (Any suggestions as to how to extend
**ANOVA
techniques**

to the Coefficient of Variation or a similar measure?).

I think it is good practice to **separate out left and right sides
in the averaging**. We

inspected these visually and decided the differences were small. As
the main object of

creating the database was to display in the background of our clinical
data it seemed

more sensible to combine data from both sides.

All data was collected with six camera.VICON 370 system. Standard VCM
marker set was

used. All **thigh markers were placed in the plane containing the
greater trochanter and**
**knee joint axis**, this was judged by eye with the use of a **mirror
to reduce parallax** (ie

no use of either KAD or my correction algorithm). VCM was used to analyse
data with

ASIS-to-ASIS and ASIS-to-trochanter distances left blank (please note
that the term

"standard VCM analysis" can actually cover a range of biomechanical
models depending on

which parameters are left blank and which are filled in).

Force plate data was not captured. I have a feeling that by starting
off subjects at

the same point and only recording the walks on which they hit force
plates a fixed

distance from the starting point we are automatically selecting the
more repeatable

walks.

Cheers

Richard

Richard Baker

Gait Analysis Service Manager

Musgrave Park Hospital

Stockman'sLane

BELFAST

BT9 7JB

Tel: +44 (0)1232 669501 ext 2155

Fax: +44 (0)1232 611064

Dear All,

Just calculated Ricahrd's CVs for the sagittal-plane joint angles:

Hip 23%

Knee 18%

Ankle 53%

So, it certainly looks like the ankle is the most inconsistent joint.

Any ideas why? It's of interest (Winter, 1991, p 55-6) that EMG

conversely shows higher CVs for more proximal muscles: Soleus and

tibialis anterior have CVs of 31% and 33% respectively, while biceps

femoris and rectus have CVs of 62% & 51%.

So I would hazard a guess that this increased variation is arising from

the motion analysis system rather than the subjects themselves. Agree???

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

Thought you might like to take a look at this

variability is attributable to walk to walk variation for an individual. Again no

kinetic data was collected so we didn't bias the data by only selecting those walks

repeatable enough to hit the force plates.

You can see the data summarised in the table in terms of the average standard deviation

over the gait cycle for each parameter for each subject. Interesting to note that we

have

We also calculated the average of the averages and plotted it against
age. You can see

the R-squared value of 0.54 is not particularly stunning but according
to my tables

just sneaks significance at the 5% level. The data suggests that the
**variability
in a 6**
**year old walking is around twice that for a 12 year old**.

Richard

Richard Baker

Gait Analysis Service Manager

Musgrave Park Hospital

Stockman'sLane

BELFAST

BT9 7JB

Tel: +44 (0)1232 669501 ext 2155

Fax: +44 (0)1232 611064

Hi Chris,

The **variability of the ankle motion is likely due to its proximity
to the**
**foot**. Since the foot has almost 9 times the number of
joints as compared to

the ankle, knee, and hip, it seems completely logical that the greatest

variation in ROM will occur at the measured site most proximal to it.
As I

have stated in our previous discusion from years past, modeling the
foot as a

single block does tremendous injustice to its complexity and significantly

alters the perspective of its relationship to the more proximal structures.

I have recently had a 24 month prospective

study of **chronic lower back pain** patients approved for publication.
This

showed how custom foot orthotic fabricated objectively using in-shoe
pressure

analysis produced dramatic improvement in long term outcomes as compared
to

standard care measures. The rate of relapse (previously published
at 70%) of

these patients was reduced to 16%. The reduction of pain was
50% greater and

the number of patients who experienced improvement was almost 45% greater
than

standard care measures (84% vs. 47%). Since gait labs worldwide
are

suffering from the financial crunch of dollars allocated to health
care

expenditures, their use for chronic back pain patients will be a very

significant boost. I would be happy to discuss this with you
in greater

detail. Looking forward to your response.

Regards,

Howard J. Dananberg, DPM

Dr. Kirtley,

Could you explain why you

*"...guess that this increased variation is arising from*
*the motion analysis system rather than the subjects..."?*

It seems to me that the **CV at the ankle sould be naturally highe**r.

Winter's EMG results suggest that the **control of gait is effected
more by**
**changes proximally**. Smaller changes proximally should
result in

correspondingly greater changes in the position of the distal segments.

Given the small angular range of motion in the ankle and the likelihood
of

greater displacements due to the hip, it is not surprising that the
CV at

the ankle is greater.

I wonder if I am missing something that leads you to suspect this source
of

the high CV.

Why would you expect that the variation is more due to the motion analysis

system? I can appreciate a natural tendency to be skeptical of

experimental technique, that is indicative of a good scientist.
Am I

missing something?

Leon.

Leonard G. Caillouet

PhD Student, Louisana State University

Department of Kinesiology

15617 Shenandoah Square

Baton Rouge, Louisiana 70817

504-753-7471

Chris

I am interested to see that other labs are begining to adopt our
**marker placement protocol**, utilising a **mirror**. We have
been using

this technique since 1992, when we developed it to implement VCM

within our clinical service. We have in fact presented it at ESMAC

'97 in Basel (G&P, Vol 6 ,1997, pp263) as part of a validation

study, where **we compared mechanical alignment of the knee between
VCM**
**and full length x-rays** and showed that if knee rotation was
contained

to within +/-5 deg, alignment differences were approximately 2 deg.

This work is soon to be submitted for publication as a full paper.

As my contribution to this discussion I am sending an** young adult**
**normal database of our own**. Again, it is small, smaller, than

Richard's in fact (5 adults, 25 trials).

Data is at: /data

I will include the GCD file

and an Excel file (containing the COV info + the GCD data) in a

separate message. As you might expect the results are very similar
to

Richard's as the same marker protocol is utilised. The most obvious

difference is that his **hip flex/extension is offset from ours into**
**extension by approx 10deg**. This difference is made up of approx
5deg

from **flatter pelvic tilt** (maybe due to marker placement, but
maybe

due to age as a database of 50-65 yo we have has the same pelvic

tilt as Richard's group) and 5deg from a **more extended knee**
(we place

the knee marker on the anterior aspect of the lateral epicondyle,

which although leading to more flexion is a more consistently

palpable landmark).

With regards to COV, these are also similar but the obvious exception

highlights one of the **weaknesses of COV**. The COV for knee rotation
is

62 for Richard and 247 for us!! This is due to the very small values

we obtained for this variable (the SD is bigger than the value), due

to our experience with the marker protocol. When making up this

database we compared the graphs for a 3 subject (15 trials) database

and a 5 subject database (25 trials) and found that the graphs

(including SDs) superimposed. Unfortunately we do not have the COV

information to substantiate this.

I hope this proves that I am not agianst the idea of databases

sharing in princliple!!

Regards

Jeremy

Jeremy Linskell

Manager, Gait Analysis Laboratory

Co-Ordinator, Electronic Assistive Tehcnology Service

Dundee Limb Fitting Centre

Dundee, DD5 1AG, Scotland

tel +1382-730104, fax +1382-480194

web: http://www.dundee.ac.uk/orthopaedics/dlfc/gait.htm

Dear all CV analysers,

I'm pleased to tell you that Jeremy's data is now on the CGA Normative Data page at: /data

The database is now growing into a useful resource thanks to the kind support of our subscribers - thanks again.

I've had a couple of queries about my comments on CVs for EMG and kinematics and kinetics. I think I haven't made it completely clear what I am saying, so I'll try again.

Since:

a. The ankle is closest to the ground (most closed-chain joint);

b. Inverse dyanmics errors increase from distal to proximal as inaccuracies
in the ankle are passed on to the knee, etc.; and

c. The CVs for EMG of the lower-limb show the most distal muscles to
be least variable.

I would have expected the ankle kinematics and kinetics to also show the least variablity (most consistency). In fact:

a. Ankle kinematics are most variable; and

b. Ankle kinetics are least variable.

How do you account for this seeming contradiction? My own interpretation was that the kinematic variability must somehow be arising from the motion analysis system. I suspect the foot segment markers are so close together, and move so much on the skin, that they give rise to a lot of inaccuracies.

If you think the kinematic variability is not artifact and is a true reflection of the biomechanics, please explain why the kinetics do not also show high variability. Note, as support for my theory, that ankle kinetics are almost independant of kinematics, being almost completely determined by the ground reaction forces.

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

I'm afraid I'm in the position of being able to send to but not receive from the CGA

list. Hope I'm not repeating what anyone else might have said but that hasn't made it

onto the summary of responses on the teach-in page of the CGA site.

I'm afraid I have to welly in with a **major criticism of the use of
coefficient of**
**variation as a measure of repeatability**. It isn't. It's a measure
of signal to noise

ratio and runs into real problems when there isn't any signal! It's
a very pretty 3-d

graph, Chris, but look at almost all the values in green and calculate
the mean signal.

It is very close to zero. The high values are coming not from a large
variability but

from a low mean signal. Note that it is the average signal value that
is used in the

equation so any parameter which shows left-right symmetry (pelvic obliquity
or pelvic

rotation) which should have a mean value of zero should almost by definition
have an

infinite cv. The presence of all those powers at the top end comes
from both inherent

variability in a measure which has been over-processed, and has picked
up all the

errors God put into gait analysis systems on the way, and the fact
that the mean power

at any joint tends to be quite low (presumably because! the it is energy
efficient for the body to walk this way).

All the values at the low end of the scale are there because they have
**nice
high mean values**. For example the
**temporal-spatial** characteristics are simple values whereas most
of the gait traces

oscillate about a baseline (often close to zero) and thus give low
mean signals.

You ask why is the cv higher at the ankle than at the hip. There is
a small increase in

true variability at the ankle but the primary reason that the cv is
so high is because

the **mean value of ankle dorsiflexion is a lot lower than that of
hip flexion and knee**
**extension**.

Or is it? Another criticism of the cv is that it **depends on the baseline
chosen for**
**your measurements**. Hip extension is a good example. The Davis/Kadaba
model uses the

plane containing anterior and superior iliac spines as a reference
for the pelvis

(there is no particularly good reason for doing this other than that
they are easy to

palpate). Mean hip flexion is therefore in the region of 15-20 degrees
and the cv tends

to be quite low. Winter however used the lab horizontal as the equivalent
reference

which gives a mean hip flexion of a few degrees of flexion and correspondingly
higher

cv values despite the fact that the true variability in the data is
similar. Thus

Winter's hip and ankle cvs tend to be similar because both have a similar
mean value,

whereas those which Chris has been so good as to calculate from the
data I supplied

show much greater "variability at the ankle". What is actually happening
is that the

variability is similar but my mean hip flexion is much greater than
mean dorsiflexion. (By the way Chris I think there has been a transcription
error in the yellow table, on page 27 of the 2nd edition of Winter's book
the values

for cv for intra-subject variability are quoted as hip 21, knee 8 and
ankle 16). [corrected now! - CK]

I can't see what is wrong with simply stating repeatability/variability
as the **average**
**standard deviation** of a parameter over the gait cycle. There
is **no need to divide**
**through by the mean value**. This gives a simple value in degrees
which is easy to

understand. It is also serves as a useful guide in interpretation.
As a rule of thumb,

if the difference in the signal you are seeking to interpret is less
than this average

standard deviation then you probably should not be reporting this as
significant. On a

statistical basis over a third of the able-bodied population will show
this difference

or greater. There is no equivalent with cv, which is convenient because
if we have no

easy handle on the repeatability on the data we can carry on interpretting
all the

features on our nice little traces without worrying whether they are
actually

significant or not!

Please let's bin the cv and stick to the average standard deviation
over the gait

cycle.

Richard

Richard Baker

Gait Analysis Service Manager

Musgrave Park Hospital

Stockman'sLane

BELFAST

BT9 7JB

Tel: +44 (0)1232 669501 ext 2155

Fax: +44 (0)1232 683816

Dear CGA subscribers

Further to Chris Kirtley's quandary:

*> a. Ankle kinematics are most variable; and*
*> b. Ankle kinetics are least variable.*
*>*
*> How do you account for this seeming contradiction?*

I believe that there is a **simple explanation** and it has to do
with

the statistic used, namely the coefficient of variation. We have

found (Vaughan et al., 1992) that the CV, which is the the sum of the

standard deviations divided by the sum of the means at each point in

the gait cycle, is **inappropriate for evaluating signals that do
not**
**differ greatly from the cycle mean**. (Think about the two
signals --

ankle angle and ankle moment -- referred to by Chris. The plantar and

dorsi-flexion angle "hovers" around neutral or zero degrees

throughout the cycle, whereas the moment moves from a small

dorsi-flexor value just after foot contact to a large plantar flexor

value of almost 100 Nm during push-off). A far more illuminating

statistic is known as the **Variance Ratio (VR)**, first proposed
by

Hershler and Milner (1978), and used by Kadaba et al. (1985) and

Pierotti et al. (1991). We have described the statistic in some

detail (Vaughan et al., 1992) and I would urge Chris and others to

re-look at their data with the Variance Ratio. I'm willing to bet

that it will help him out of his quandary!

where t = time in the gait cycle (0... 100), n = subject number out
of total of N subjects, c is cycle number out of a total of C cycles, and
Ecnt is the amplitude of the measurement for cycle
c, subject n, at time t.

Yours in gait

Kit Vaughan

University of Cape Town

__REFERENCES__

Hershler C, Milner M (1978) Transactions in Biomedical Engineering,

25: 413-420

Kadaba M et al. (1985) Journal of Orthopaedic Research, 3: 250-359

Pierotti S et al. (1991) Journal of Orthopaedic Research, 9: 720-729

Vaughan CL et al. (1992) "What is the normal function of tibialis

posterior in human gait?" The Diplegic Child (edited by M Sussman),

American Academy of Orghopaedic Surgeons, Rosemont, IL, pp. 397-409

I

COV, especially as for most of the variables it is fairly constant

across the cycle anyway. COV is only statistically valid if the 2

signals being compared have very similar average values and very

similar patterns, in which case you are really just comparing the SDs

anyway.

This **does not explain however why Winter's ankle COV differs from
the**
**current ones** which I explained previously as a 2D vs 3D modelling

phenomenon. In 2D an externally rotated foot would appear more

plantarflexed but this effect would genrally be balanced by the

dorsiflexing effect of more associated pronation. In VCM you would

still have the pronation-induced variability, without the balance of

the parallax effect to counteract it.

Jeremy Linskell

Manager, Gait Analysis Laboratory

Co-Ordinator, Electronic Assistive Tehcnology Service

Dundee Limb Fitting Centre

Dundee, DD5 1AG, Scotland

tel +1382-730104, fax +1382-480194

email: j.r.linskell@dth.scot.nhs.uk

web: http://www.dundee.ac.uk/orthopaedics/dlfc/gait.htm

A few weeks ago, Scott Wearing asked a question as to why the coefficient of

variation (CV) for the angle of gait was so high in some studies which

measured this parameter. I replied that I felt it was because the absolute

values for angle of gait are low when measured from the line of progression,

since the CV will mathematically produce a larger value with lower mean

values.

Cheers,

Kevin

Kevin A. Kirby, D.P.M.

Assistant Clinical Professor of Biomechanics

California College of Podiatric Medicine

Private Practice:

2626 N Street

Sacramento, CA 95816

Voice: (916) 456-4768 Fax: (916) 451-6014

Dear Richard,

I have a few comments to make on your submission to CGA:

*Winter however used the lab horizontal as the equivalent reference
which*
*gives a mean hip flexion of a few degrees of flexion and correspondingly*
*higher cv values despite the fact that the true variability in the
data is*
*similar. Thus Winter's hip and ankle cvs tend to be similar because
both*
*have a similar mean value, whereas those which Chris has been so
good as to*
*calculate from the data I supplied show much greater "variability
at the*
*ankle". What is actually happening is that the variability is similar
but my*
*mean hip flexion is much greater than mean dorsiflexion.*

What you say may be true; however, in Winter's lab (at least when I
worked

there) the **hip knee and ankle joint angular displacements were set
to zero**
**in the "normal" anatomical position**, ie, hip and knee at 180deg
and the

ankle at around 240deg or so depending on the angle created by the
lateral

malleolus to 5th metatarsal segment line. Thus, while the hip
angle range

was around 45-60deg, it went from about 25+ deg of flexion to 25+ deg
of

extension. Similarly, at the ankle, the range was reasonable
(don't have

the numbers in front of me) with about a third of the range or so in

dorsiflexion and the rest in plantarflexion. The knee joint was
entirely in

the flexion range, ie, 0 to 60+ deg. It would be **interesting
to set the**
**mid-range of knee flexion to zero and then recalculate its cv**.
By your

theory, its cv should increase since it would behave more like the
hip and

ankle.

*Please let's bin the cv and stick to the average standard deviation
over*
*the gait cycle.*

This may be a good suggestion, but bear in mind that today with more
labs

using so-called standard marker sets and similar commercial equipment
it is

easier to get consensus around an issue like this. When Winter
was

producing his 'classic' data in the 1980s, there was little standardisation,

particularly in presenting angular data (eg, full knee extension could
be

zero deg, 180 deg or occasionally somewhere in between!). I don't
think

Dave is a subscriber to CGA, but I am pretty sure that as Professor
Emeritus

at Waterloo he still is active and continues to correspond via his

university email. Chris, maybe you could elicit his input to
this debate?

I hate to try and put words in his mouth (if you know him, you would
know

that is quite impossible).

Cheers,

Drew Smith, PhD

Assistant Professor

The Hong Kong Polytechnic University

Dear all,

Chris wrote:-
* I would have expected the ankle kinematics and kinetics to
also show the*
* least variablity (most consistency). In fact:*
* a. Ankle kinematics are most variable; and*
* b. Ankle kinetics are least variable.*
* How do you account for this seeming contradiction?*

* ... the kinematic variability must somehow be arising from
the*
* motion analysis system....*
* If you think the kinematic variability is not artifact and
is a true*
* reflection of the biomechanics, please explain why the kinetics
do not*
* also show high variability.*

The definition of a "kinematic artifact" is an interesting one. The

branches of classical mechanics are Kinematics and Kinetics. Thus the

only true kinematic artifact (one that is not experimental, e.g. due

to marker drift or insufficient spatial temporal data resolution) is

simply the branch of mechanics called Kinetics.

Kinematics is the branch of mechanics that deals with the geometry of

motion; for example the description of gears and cams. Thus

kinematics deals with the shape of the periphery of the body.

Kinetics is the branch that deals with the theories of motion, such

as Newton's laws. These laws are mass centered (kinetic and

gravitational energy based; motion is referred to the center of

mass, or center of gravity).

The concepts are linked by Newton's second law which defines "force"

as the product of (Kinematic acceleration) x (Kinetic mass).

Incidentally no one has ever seen a "force", merely the effects of

such a postulate.

The kinematic and kinetic artifacts are never simultaneously zero.

an observation confirmed by all available data.
**(1) If we force the kinematic artifact to zero,**
**then the kinetic artifact become infinite.**
**(2) If we force the kinetic artifact to zero, then the kinematic**
**artifact become infinite.**

In both cases (zero x infinity) is undefined mathematically.

In the biomechanical problem, this means that the "force" is

undefined.

The solutions are:-

(1) if we know everything about the kinematics of the body, i.e. if

we knew exactly how each component fitted into the others, the use

of Newton's laws is superfluous, because force is an undefined

concept. (Technically, if we knew how the body works exactly, we would

have no need for gait analysis :-).

(2) if we knew everything about the kinetics of the body, i.e. if we

knew its exact postion and momentum, then we would have no idea of

its kinematic cause (its force generating capacity, or how it works).

This prediction should come as no surprise because modern particle

physics (which ignores the shapes of the particles) informs us that

this is the correct answer. In the biomechanical case, this simply

means that we have no knowledge of the shape of the body because it

is being treated as a single mass center.

There is no experimental error in either case (1) or (2).

The error arises from an incorrect theoretical origin.

---o0o---

Chris continues:-
* ... note... that ankle kinetics are almost*
* independant of kinematics, being almost completely*
* determined by the ground reaction forces.*

I would suggest, rather, that the ground reaction force is determined

by the ankle kinetics, not as Chris suggests vice versa.

There is much discussion centered on the "ground reaction force" in

gait analysis. But there is **never any mention of its conjugate
"Body**
**Action Force" in the literature**.... This is surprising because
the

body action force is persumably what we are all searching for in the

mechanical description of gait!!

According to Newton III, for every action there is an equal and

opposite reaction. The "body action" is clearly causal, and the

reaction, well, merely a reaction; an incomplete one at that,

otherwise we would all move in straight lines. Hence the Body Action

Force does not obey Newton's laws.

Identifying the properties of the body that create the "Body Action

Force" should be our main concern. That is we should be paying close

attention to the "kinematic artifacts".

The existence of a "Kinematic artifact" is merely a matter of

perspective. There also exists a "Kinetic artifact". They are linked

by the assumption that "Newton Rules Biology". (Again I must

emphasise the contents of a previous posting that Newton himself

never claimed his laws applied to human bodies).

The recognition by the CGA group that there ARE irreducible

kinematics artifacts, is essentially scientific evidence that

Newton's laws DO NOT apply to all bodies, particularly the human

body. Let us not hide this important scientific discovery under
the

name of "error".

The so called "CV error" or "kinematic artifact" or "kinetic

artifact" (the latter being a contravention of the law of

conservation of energy) is not an instrumental or experimental

error at all. It arises from the error of the theoretical claim that

Newton's laws of mass centered kinetics apply to all bodies at

sub-light speeds, defined without due regard to their anatomical form

or kinematic shape.

To support this claim, I propose that there is experimental evidence

in the literature for the existence of a kinetic artifact

(i.e. contravention of the law of conservation of energy) that arises

from a kinematic artifact.

[Reference 1] Interrelationships between mechanical power, energy

transfers, and walking and running economy. Medicine and Science in

Sports and Exercise, 25:508-515, 1993.

This study used five different biomechanical methods, to produce

one, AND ONLY ONE, significant finding: A correlation exists a

runner's speed and their efficiency, if and only if the association

of kinetic and gravitational potentail energy is IGNORED in the

KINEMATIC calculations. All othere methods produced indifferent

results.

For an explanation of this statistically "rare event", a false

positive, we are referred to the article [Reference 2] Power

equations in endurance sports, Journal of biomechanics, 23:857-315,

1990.

Here in a section discussing the problems in applying classical

mechanics, we read on page 869, column 2 half way down:

"This result is false*[sic] since we know from Newton's second law

that F=mg and that the rate of change of potential energy is not zero

as the equation would predict."

*It is unclear precisely why this result is declared false,

especially given that it has just been derived. Thus it would

appear that the "problem with classical mechanics" is ultimately

that the equation declared "false" is the classic law of conservation

of energy.

This declaration creates a circular argument. Reference[2]makes an

erroneous assumption, then reference [1] proves experimentally that

this incorrect assumption is clearly true. (There is no experimental

error in this process, and if we believe what we read apparently no

theoretical error either; merely "problems").

All the **endless talk of "experimental error", in gait analysis hides**
**that basic fact--there is a basic error in the theory**.

The expectation though is always that the data is always incorrect

and the theory always correct.

The error is in the theoretical approach. Hence, we end up

perpetually tackling, but never solving the problems of our own

making :-(

It is kinda sad that as scientists we have lost respect for our own

data.

Thus we should not be too critical of the "experimental errors" or

CV's that lead us to the "incorrect result". Particularly when our

basic starting assumption is wrong. That assumption is that, in

biomechanics, the laws of Newton can be applied in explicit

contradiction of the law of conservation of energy.

Remove this error first, then all the existing data will begin to

make sense.

This basic error is revealed through the rigorous application of the

kinematic method and statistical methods in reference [1].

Discussion should focus on how these "kinematic artifacts" are

produced by the anatomy. They are the clue to the nature of the body

action force.

The compilation of a Gait analysis database will help resolve these

issues, because the different methods of producing the same error

over and over again will sooner or later have to be reconciled.

Craig Nevin

Anatomical Engineer

Dear Chris and friends,

Sorry for not being alert when the discussion on CV started.

Isn't it a

an arbitrarily chosen zero point. Therefore this problem has a more general

aspect in addition to whether CV is an appropriate measure of

repeatability. Not only should we avoid CV here, but the computation of

percentages and all other ratios.

I wonder if this may pose more problems when using other common

statistical measures where the mathematics is not as intuitive to the

layman as in this case. Do we really know when a statistical measure is a

ratio and thus should be avoided on interval data? I suspect this is an

area where a lot of misinterpretation may have passed unattended.

Regards from wintry Norway

Rolf

_____________________________________________________________

Rolf Moe-Nilssen, MS, PT, Research fellow, Division of Physiotherapy Science,

Department of Public Health and Primary Health Care, Faculty of Medicine,

University of Bergen, Ulriksdal 8c, N-5009 Bergen, Norway,

voice:+47 55 58 61 70, fax:+47 55 58 61 30

Dear Subscribers:

May I add my ideas to the CV discussion?

According to my little knowledge, the CV is a parameter to represent
the degree of

dispersion(variability) of sampled data, which may have a similar meaning
to S.D. or

standard error and so on.

But **CV may have two advantages** over S.D.

i) Because CV is SD divided by mean, it is **dimensionless**.
So, it can be used to

compare the variability of two groups with different units, such as
body weight vs

height, joint angle vs moment.

ii) In addition to the merit of dimensionlessness,
it can **overcome the tendency of**
**S.D. increment with increasing mean value**. If we assume that
adult elephants and adult

males have similar degree of dispersion(variability) on their body
weight, the S.D. of

elephants body weight must be much bigger than that of men. In this
situation, we

should use CV rather than SD.

Mr. Baker said : *I can't see what is wrong with simply stating*
*repeatability/variability as the average standard deviation of a
parameter over the*
*gait cycle. There is no need to divide through by the mean value.*

So, I do not think that Mr. Baker's above idea would be so good. VR
of Dr.

Vaughan may be better.

Then, what would be the reason for Dr. Kirtley's observation as below?

Dr. Kirtley wrote:
*I would have expected the ankle kinematics and kinetics to also
show the*
*least variability (most consistency). In fact:*

*a. Ankle kinematics are most variable; and*
*b. Ankle kinetics are least variable.*

The **CV is no more than the degree of dispersion**, it includes
**both
of inter-subject**
**variability and test retest(inter-test) variability**. In gait
analysis data of a certain

sample size, the CV can be made of inter-subject variability of true
value which God

assigned to each man and inter-test variability with some error made
by men or

equipment.

Here's my assumptions.

i) The absolute variability** **(SD, not CV)
of true value-God assigned, may increase or

decrease **in proportion to the size of mean value** like body weights
of elephants and

men.

ii) The absolute variability of error introduced
when detecting the true value will
**not be in proportion to the size of mean value**. It may have
inverse relationship or

other, depending on the detection and calculation methods.

So, if the mean of a sampled data and inter-subject variability would
be relatively

small to inter-test variability, the **CV may amplify the inter-test
variability**. In this

case like ankle kinematics, Mr. Baker's comment to use SD rather than
CV should be

true.

According to my assumption, the SD by inter-subject variability of ankle
kinematics may

be smaller than that of hip or knee and SD by inter-test variability
of ankle may not.

So, if we calculate the CV by dividing the sum of both SD with mean
value, the CV may

increase with decreasing the size of mean value.

This assumption may meet the comment by Dr. Vaughan as below.(Hope
I am right.)

* the CV, which is the sum of the*
*standard deviations divided by the sum of the means at each point
in*
*the gait cycle, is inappropriate for evaluating signals that do
not*
*differ greatly from the cycle mean.*

The **smaller CV of ankle kinetics than that of hip or knee may be
explained mainly by**
**the inverse dynamic calculation** proper, that is, SD by inter-test
variability.

We may dissociate the two kind of variability from CV by constraining
one in fixed

value such as getting CV from multiple trials of a man. But it will
never be completely

fixed because of day to day, diurnal, stride to stride ... ...
variation.

About Rolf's comment:

* Isn't it a basic rule in data processing, not to use
ratios unless we*
*have a ratio scale? Obviously angles are measured on an interval
scale with*
*an arbitrarily chosen zero point.*

I do agree with Rolf that we should use the ratios in a ratio scale.
But **are the**
**angles interval scale**?

I think the angles we measure in gait analysis are a kind of ratio
scale which have

absolute "zero". For example, 60 degree of angle is 2 times bigger
than 30 degrees of

angle and 90 degree of anlges is 2 times bigger than 45 degree of angle.
The ratio of

60degree and 30 degree is just same as that of 90 degree and 45 degree.

Sincerely,

from Sun G. Chung in Korea

All interested in this debate,

What is your reaction to the following **suggestion**?

If you want to go beyond an inspection of the variability of one set
of data

and are interested in making statistical inferences about differences
between

two sets of time series data you could consider the following:

The mean value for a variable, its standard deviation, and **95% confidence**
**interval** (95% confidence interval = 1.96 x standard deviation/sqrt(n))

can be found for each percent of the cycle. The question of significant

difference between one subject or one condition and another can be
answered by

plotting the curves representing the mean values of the variables together

with the mean plus and the mean minus the 95% confidence interval.
If there is no

overlap of the 95% confidence intervals at all then the two time series
could

be said to be significantly different. Wherever the curves are separated
by

more than twice the 95% confidence interval for more than five consecutive

data points the conclusion could be reached that the curves are significantly

different at that point.

A counter argument is that 100 t-tests are being conducted simultaneously
in

this process and one could expect that a **false result** could
occur 5% of the

time, that is, at five data points. These false results, however should
occur

randomly through the data so it would be very unlikely that all five
would

occur consecutively in the data. Therefore **only claiming significance
when the**
**difference exists for more than five consecutive data points**
is a conservative

approach.

Cheers to all,

Richard

Richard Smith

Research Manager, School of Exercise and Sport Science

Faculty of Health Sciences,

The University of Sydney
voice: +61 2 9351 9462

East Street, Lidcombe, NSW 2141
fax: +61 2 9351 9204

AUSTRALIA

http://www.cchs.usyd.edu.au/Academic/ESS/smith/richard.html

Interesting debate. About CVs. People may wish to look up a couple of

references I found concerning treatment of

gets very heavy, so any statisticians out there any comments would be

welcome. The curved data studied includes knee and hip motion, and

angle-angle diagrams.

Rice JA and Silverman BW. Estimating the mean and covariance structure

nonparametrically when the data are curves. Journal of the Royal

Statistical Society, 53(1), 1991.

Ramsey JO and Dalzell CJ. Some tools for functional data analysis.

Journal of the Royal Statistical Society, 53(3), 539-572, 1991.

Leurgans SE, Moyeed RA, Silvermann BW. Canonical correlation analysis

when the data are curves. Journal of the Royal Statistical Society,

55(3), 725-740, 1993.

Jim Richards

Lecturer in Biomechanics

Department of Rehabilitation

University of Salford

http://www.salford.ac.uk/prosthetic/homepage.htm

http://146.87.238.80/biomech.htm

Dear all,

As my colleague, Drew Smith, suggested, I detrended the angle plots
by

subtracting the mean from every point (I left the SD unchanged). I
then

recalculate the CV. I used Winter's 2D data from his book.

Result... Knee CV was 22% before detrending, 33% after! The ankle (70%)

and hip joint CVs were relatively unchanged by the process:

Before After detrending

Hip
51
57 %

Knee
22
33

Ankle 71
70

Interesting! However, the knee is still much more consistent than the

other two joints.

I then worked out the average SD, as suggested by Richard:

Average SD

Hip
6 degrees

Knee
5

Ankle 4

Voila! Roughly the same SD at each joint.

I think the conclusion from this is that the CV is, indeed, less than

satisfactory as a means for comparing variation between different joints

or variables. I'd like now to try Kit's suggestion of the Variance

Ratio. I'm afraid we don't have any of the journals mentioned in our

library. Can someone (Kit?) let me know the formula?

Have a nice weekend. I'm going fishing to forget about all these CVs!

Chris

--

Dr. Chris Kirtley MD PhD

Dept. of Rehabilitation Sciences

The Hong Kong Polytechnic University

I thought I'd ask my old mathematician (and drinking partner) in

Australia about our CVs problem. Also asked him his view on Kit's

suggestion of the

/teach-in/cv/responses.html#Kit

It's interesting that he confirms that simply ignoring the sign of the

means is not acceptable, so the original definition suggested by David

Winter is, indeed, flawed. Here's what he says...

In the first instance, **CVs are only meant to be used with only positive**
**or only negative data**. To use absolute values is not adequate.
If your

summation index means timepoints over gait cycle (100 points or so)

amplitudes near a zero-crossing have practically no influence

on the average which is dominated by large values. Apart from some

doubts about the meaning of this average, suppose for the sake of

simplicity all variances equal. The consequence will be that for

measurements with some large amplitudes (big variation during the cycle)

the CV will be reasonably small. For measurements with only small

amplitudes you would obtain larger CV's (relative to the between

subjects variances of course). Kit Vaughan's **VR is practically a
loan**
**from repeated measurement Anova and ICC**. In case of only one
cycle the

nominator is just the between subject variance and the denominator
the

residual variance (in the given formula it probably should read for
the

denominater E bar instead of Et bar to make sense).

As with the CV the **distributional properties of the VR are difficult
to**
**assess due to autocorrelation**. With traditionally small sample
sizes the

correlation structure probably cannot be estimated and may depend

heavily on subject conditions beyond control.

In all, **I agree with one of the contributors (Richard Baker) to bin
the**
**CV altogether**.

Any suggestions? Well, and that could answer another question by one
of

the correspondents as to compare two such gait measurements series.
If

there is something like a standard gait series then take the difference

and **test for white noise via Kolmogoroff-Smirnov** which (appropriately

adjusted) would supply through its **test criterion confidence limits**
for

the whole curve as well as a coefficient of fit.

Cheers and prost

Juri.

Dr. Jurgen P. Sommer

Curtin University

Selby Street

Shenton Park

Western Australia 6008

Phone: +61 8 9266 3620

Fax: +61 8 9266 3636

--

Dr. Chris Kirtley MD PhD

Dept. of Rehabilitation Sciences

The Hong Kong Polytechnic University

Dear all,

Chris Kirtley wrote:

*3. I confess that I'm not enamoured by Richard Smith's suggestion,*
*which seems a bit arbitrary and empirical, but I see his point.
My own*
*inkling would be, rather than try to look at the whole curve, to
pick out*
*various key measurements, e.g. maximum swing knee flexion, maximum*
*plantarflexion, total push-off energy, etc. We could then use*
*'standard' measures of variation and reliability, such as the ICC.*

We certainly look at important discrete points in the gait cycle as
a

matter of course. However, **discrete points don't tell the whole
story**
**about the pattern of movement** or the points adjacent to those
discrete points

of interest. Further, by focussing on the usual measurements we could
miss

out on new information which might change the way we think about the

mechanisms of walking.

I have no problem with being empirical but we evaluate whole curves
in

relation to the development of models and theories as well. As
for

being arbitrary I can't see what is arbitrary about proposing a hypothesis

about differences in movement patterns among a number of pathologies
and then

testing this hypothesis using the method I suggested.

I will get the references referred to by Jim and Michel and hopefully

improve our methods.

Thanks for your responses,

Cheers,

Richard

Back to Teach-in