Re: simple question

On Thu, 6 Dec 2007 18:57:46 -0800 (PST), cabrautccp4@xxxxxxxxx wrote:

Hello All,

Sorry for the simplicity of this question, but I can't seem to find an
answer in my elementary statistics textbooks.

We are measuring a quantity that involves the nonlinear fit of a
sigmoidal curve. The fitting algorithm optimizes several parameters,
and each has an "error" associated with it that indicates the
uncertainty in the minimized value of the parameter. Fine.

However, we perform these experiments several times, fitting the data
each time. Let's say the experiment is performed five times Now we
have five values of the parameter of interest, and each has an
associated "error." We have been using the mean as the best estimate
of the parameter of interest, and, ignoring the fitting "errors,"
reporting the standard deviation of that mean. But I have the nagging
feeling that the errors from the fit should somehow be incorporated
into the sdom that we report. Is there a way to do this, or am I
worrying overmuch?

Should you ignore the separate errors? No.

The difference between runs provides another
estimate of error. You might call this the "between
experiment" error. Is the error "between experiments"
a whole lot larger than the error "within experiments"?

The Between estimates might be somewhat robust. However,
if the Within error is relatively tiny, that would indicate - for
one thing - that the model is apparently wrong. Why did the
experiments come out so different? This is probably more
important when you are reporting the averages of several
parameters instead of just one.


If the Within errors on parameters are relatively large,
that would make me suspicious. I can't figure how that
would happen, unless the within-error is reported with
some inflation from correlated parameters.


--
Rich Ulrich, wpilib@xxxxxxxx
http://www.pitt.edu/~wpilib/index.html
.