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

.................................................. ..........

-----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

.................................................. ..........

................

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

.................................................. ..........

.......................

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

.................................................. ..........

.......................

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

.................................................. ..........

........................

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

.................................................. ..........

........................

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.

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

.................................................. ..........

-----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

.................................................. ..........

................

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

.................................................. ..........

.......................

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

.................................................. ..........

.......................

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

.................................................. ..........

........................

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

.................................................. ..........

........................

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.