Jeremy Bauer wrote:
> We currently have 220 children participating in an exercise intervention.
> My task is to estimate the stresses imposed on the hip (femoral neck) in
> these children during the activity. In order to estimate stresses on the
> hip, I need to have a computer model of the lower body of these children
> that includes muscle and bone geometry. In order to acquire muscle and bone
> geometry I need to have MRI's (magnetic resonance imaging) of the lower body
> for input into the model. I can currently only afford to pay for 10 MRI
> sessions and therefore 10 subjects. This phase of the research is mostly
> model development.
OK... practically engineering <grin>
I'm about to go way out of my area of expertise and make some
suggestions that you might want to look into.
My first suggestion: do not try to make your sample representative.
Instead, try to spread it fairly uniformly over the range of
age/height/weight. Once you know how these factors affect the results,
you can predict for any child in the survey, and (if you actually need
them) means.
As age, height, and weight are strongly correlated, you might want to
do some sort of principal component analysis for your population. The
idea is that if you plot (age,height,weight) for your 220 kids the
points will form a "spindle" in 3-space. (If it's warped you might want
to transform in some way to straighten it.) The long axis of the
spindle is a sort of generalized "bigness" variable that conveys *most*
of the information. With so few runs available you *might* want to
simply divide that range into 10 equal chunks, pick a kid at random from
each. Schematically:
e
e e
E
d d
D d d d
c d
c C c
B c
b b b
a
a A
However, it gets better. Once you've taken out the first component, you
can repeat this game on the residuals. What you end up with would be
three new axes which might (for instance) be appropriately labelled
"bigness", "bigness for age" and "body mass index". (You won't know till
you try, though it's fairly clear that "bigness" will be a good label
for the main one..)
You can then try to structure your experiment to ensure that you can
answer questions such as "how does bone shape differ between bigger kids
and smaller kids?" and "how does bone shape vary between skinny kids and
chubby kids?" Residuals from this model will tell you how much
variation in bone shape is *not* explained by the three variables you
have.
The point is that I don't think you *want* to just make inferences
about the average behavior of the parent sample; you want a model that
can tell you how bone shape varies between kids. But you will need an
expert (not me) for this.
-Robert Dawson
.
.
=================================================================
Instructions for joining and leaving this list, remarks about the
problem of INAPPROPRIATE MESSAGES, and archives are available at:
. http://jse.stat.ncsu.edu/ .
=================================================================
