Dear Allstat,

I have a set of data I’d like to analyze fairly quickly (in a few hours).  I
have no experience in the area of agreement between instruments or
measurement error, so I’m asking for a little guidance before hitting the
books.  Note that this problem is unlike those asked recently of the list
regarding agreement between two instruments as the instruments here measure
different samples, there is a time factor involved, and normality is not
assumed.

I would like to compare the measurements from two instruments, but the two
sets of measurements were made at different times.  Instrument 1 was used to
make n measurements on n samples at times 1 to n (one measurement per
sample).  Instrument 2 was then used to make m measurements on m additional
samples from times (n+1) to (n+m) (one measurement per sample).  The (n+m)
samples measured are independent of each other, but not necessarily of time.
The times are recorded.

The measurements from each instrument are not assumed to be normally
distributed, but symmetry within each instrument can be assumed.  The sample
size from at least one instrument is probably too low to invoke the CLT, if
needed: there are greater than 50 measurements from instrument 1 and only 8
measurements from instrument 2.

The instruments have different precisions and these precisions are known.
Instrument 2 has better precision than instrument 1.

I have some ideas myself, but none addresses all issues very well
(nonnormality, possible time-dependence, different (known) precisions).
This problem sounds like a situation where a measurement error model might
work, but I’d like not to assume normality – or any parametric distribution,
for that matter.  If I could "adjust" the _values_ from one instrument to
the precision of the other, then I could possibly eliminate the precision
difference and try some sort of randomization or bootstrap test that also
accounts for the times.

I’m more open to a complicated bootstrapping solution or permutation
solution than a complicated modeling problem that assumes a specific
distribution.
But, of course, I’ll read everything.

Thanks for your help.




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