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Corey Scholes
10-12-2005, 02:08 PM
Hello Everyone,

Apologies for the late summary of replies from my question
regarding statistical analysis of joint moments. Thank you
very much to those that contributed. The original email and
the repliesare included below. Unfortunately I havent got
anything useful to contribute as yet, but trying hard
to become familiar with the concepts

Thanks Again

Corey Scholes

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-----Original Message-----
From: * Biomechanics and Movement Science listserver
[mailto:BIOMCH-L@NIC.SURFNET.NL] On Behalf Of Corey Scholes
Sent: Sunday, August 28, 2005 11:22 PM
To: BIOMCH-L@NIC.SURFNET.NL
Subject: [BIOMCH-L] Statistical analysis of joint moments

Hello everyone

I am planning a study to investigate the change in knee
moments over several repetitions of a step landing task with
3 different landing heights.

I am pretty sure that inter-individual variation may mask
subtle changes in knee loading across time, although a
number of papers that have compared this kind of measure,
such as peak moment and time to peak, across repeated trials
and different heights have used individual and group means
to conduct statistical analyses.

I am wondering if anyone is aware of a statistical approach
that may show a change in knee loading across repeated
trials and takes into account individual variation and
avoids fitting everyone onto the same curve which happens
with ensemble averaging.

Cluster analysis appears promising for this purpose, does
anyone have any thoughts????

Thanks for your help

Corey Scholes
PhD Candidate
School of Human Movement Studies
Queensland University of Technology

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Hey Corey,

I've recently been trying to tackle almost the exact same
questions. I
ended up posing my questions to the sci.stats.consult group
I found in
Google Groups. My original question and a few replies are
posted here:

http://groups.google.com/group/sci.stat.consult/browse_thread
/thread/4ede179
7fc2a2d14/0c522415b0b0a37d?q=within-
subjects+repeated+measures&rnum=1#0c5224
15b0b0a37d

However, a more intuitive response (to me anyway) was
emailed to me by Jeff
Miller. I'll paste the text below:
------------------------------------
REPLY 1
------------------------------------
> I have 10 subjects that have performed 10 trials of 3
different
> activities (walking, running, drop landing). I have
quantified the
> maximum ground reaction force (DV) for each activity and
trial for
> each subject. Therefore, I would have a two-way repeated
measures
> design where my two IVs are ACTIVITY (3 Levels) and TRIAL
(10 Levels).
>
> Now, let's say I don't care about a TRIAL effect and only
care about
> the ACTIVITY effect. Would it then be the same for me to
run a
> one-way repeated measures ANOVA on the means of the 10
trials for each
> subject and activity type?
Yes, it would be the same with respect to the usual
question: whether the
results can be generalized from your random sample of Ss to
the averages of
the full population of all Ss.

> Where I get confused is when I should use all 10 trials
for each
> subject in the analysis versus using only the mean of the
10 trials
> for each subject. Do I lose something power-wise by
including only the
> subjects' means in the analysis and not all 10 trials from
each
> subject?
No, you lose nothing like that. This is because the error
term for the
activity effect is the activity*Ss interaction, which is
computed averaged
over trials anyway.

> Do I lose something about intra-subject variability or is
it that when
> I use a repeated measures within-subject ANOVA I assumes
equal
> variance between subjects?
You lose something about intra-subject variability that
would be relevant to
the question of whether your results represent real effects
that would
generalize to the population of all possible trials from
these particular
Ss.
------------------------------------
REPLY 2
------------------------------------
[My response to REPLY 1]I guess in my case, the only reason
to collect
multiple trials for each subject then is to make sure that I
get a good
representative value for each subject as opposed to possibly
using one trial
where the IV could be an outlier or uncharacteristic
response for that
subject, correct?

[The consultant's reply to me] Sort of. The more trials you
use, the
smaller your measurement error on the subject's mean for
each activity, and
that in turn increases your power. It's just that all of
the increase in
power comes from taking the measurements in the first place
and letting them
help determine the subject's mean for that activity; there
is no _extra_
increase in power from actually including them in the
analysis.
------------------------------------

So, basically, a within-subjects repeated measure ANOVA on
your DVs (peak
Moment) of interest seem to be way to go. Some great,
entertaining, reading
on the benefits of using a within-subjects RM ANOVA can be
found here:

http://www.sussex.ac.uk/Users/andyf/teaching/rm2/twowayrm.pdf

In fact, And Field's website PDFs and text book have helped
me understand
more about statistics than any classes I have taken.

I hope some of this helps!
:-)
Jeremy

Jeremy Bauer, Ph.D. Candidate
Oregon Sate University
Bone Research Laboratory
Biomechanics Laboratory

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Have you looked at Nested ANOVA?
Not sure if that is appropriate.
Nest the subjects within the stair heights.
Probably should get some feedback if this method is
appropriate as well.

Regards,
Richard Banglmaier
Research Engineer
Passive Safety R&AE Department
Ford Motor Company
2101 Village Road
Bldg: SRL Room: 2621 Mail Drop: 2115
Dearborn, MI 48121
Phone: (313) 248-6849
Fax: (313) 248-9051
E-mail: rbanglma@ford.com

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Corey,

We are working on a functional data analysis based method
for clustering
this type of data. Ramsay and Silverman (2005) have a book
entitled
"Functional Data Analysis" out on the subject.

The main idea of functional data analysis is to use a
representation of
the whole curve rather than the landmark features of the
data (e.g., the
peak moments).

If you are interested specifically in the cluster analysis
of this data
let me know and I will send you a draft manuscript that I am
putting
together.

Cheers for now,

Jeff

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Corey, look into at a test which is called Model Statistic
that was developed by Bates and Dufek.
You can find a lot of info on your question in a book that I
edited for Human Kinetics.
The Model Statistic is there in Chapter 1.
Look into the link at this address
http://www.unocoe.unomaha.edu/hper/bio/NEWS/NEWS.HTM
and go further down under new textbook
or
paste this in your browser
http://www.humankinetics.com/products/showproduct.cfm?
isbn=0736044671

Take care,
****************************************
Nick Stergiou, PhD
Director of the HPER Biomechanics Laboratory
University of Nebraska at Omaha
6001 Dodge St.
Omaha, NE 68182-0216
tel. 402-5542670
fax. 402-5543693
e-mail: nstergiou@mail.unomaha.edu
http://www.unocoe.unomaha.edu/hper/bio/home.htm

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Hello Corey,

I think I know what you are asking for and had the same
issue with respect to within subject variability. I used a
mixed model MANOVA procedure. Combination of MANOVA and
regression - SAS. Of course, I had many dependent measures,
thus the MANOVA. I don't know exactly how this would relate
to gait and the number of dependent measures you are looking
at, but check out these two references.

Stodden, D. F., Fleisig, G. S., McLean , S. P., & Andrews,
J. R. (2005). Relationship of biomechanical factors to
baseball pitching velocity: Within pitcher variation.
Journal of Applied Biomechanics, 21, 44-56.


Stodden, D. S., Fleisig, G. S., McLean, S. P., Lyman, S. L.,
& Andrews, J. R. (2001). Relationship of trunk kinematics to
pitched ball velocity. Journal of Applied Biomechanics, 17,
164-172.