R help - Aug 2010 - Comparing samples with widely different uncertainties

Hi
This is probably more of a statistics question than a specific R
question, although I will be using R and need to know how to solve the
problem in R.

I have several sets of data (ejection fraction measurements) taken in
various ways from the same set of (~400) patients (so it is paired data).
For each individual measurement I can make an estimate of the percentage
uncertainty in the measurement.
Generally the measurements in data set A are higher but they have a
large uncertainty (~20%) while the measurements in data set Bare lower
but have a small uncertainty (~4%).
I believe, from the physiology, that the true value is likely to be
nearer the value of A than of B.
I need to show that, despite the uncertainties in the measurements
(which are not themselves normally distributed), there is (or is not) a
difference between the two groups, (a straight Wilcoxon signed ranks
test shows a difference but it cannot include that uncertainty data).

Can anybody suggest what I should be looking at? Is there a language
here that I don't know? How do I do it in R?
Many thanks for your help
Sandy

--

Sandy Small
Clinical Physicist
NHS Greater Glasgow and Clyde
and
NHS Forth Valley

Phone: 01412114592
E-mail: Sandy.Small at NHS.net


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On Aug 25, 2010, at 3:57 PM, Sandy Small wrote:
> Hi
> This is probably more of a statistics question than a specific R
> question, although I will be using R and need to know how to solve the
> problem in R.
> 
> I have several sets of data (ejection fraction measurements) taken in
> various ways from the same set of (~400) patients (so it is paired data).
> For each individual measurement I can make an estimate of the percentage
> uncertainty in the measurement.
> Generally the measurements in data set A are higher but they have a
> large uncertainty (~20%) while the measurements in data set Bare lower
> but have a small uncertainty (~4%).
> I believe, from the physiology, that the true value is likely to be
> nearer the value of A than of B.
> I need to show that, despite the uncertainties in the measurements
> (which are not themselves normally distributed), there is (or is not) a
> difference between the two groups, (a straight Wilcoxon signed ranks
> test shows a difference but it cannot include that uncertainty data).
> 
> Can anybody suggest what I should be looking at? Is there a language
> here that I don't know? How do I do it in R?
> Many thanks for your help
> Sandy
Hm, well...

I don't think the issue is entirely well-defined, but let me try and give
you some pointers:

For bivariate normal data (X,Y), the situation is that even if V(X) != V(Y) you
still end up looking at X-Y if the question is whether the means are the same.
It's sort of the only thing you _can_ do...

For non-normal data, it is not clear what the null hypothesis really is. The
signed-rank test assumes that X-Y has a symmetric distribution, which is dubious
if X is not symmetric and its variation dominates that of Y. You could also do a
sign test and see if the differences has a median of zero (bear in mind that the
median of a difference is different from the difference of the medians, but it
could actually suffice.)

I'd probably start off with a simple plot of Y vs X and look for fan-out
effects indicating that the variance depends on the mean. If it does, perhaps
take logs or square roots and see if it makes the variances appear more stable
and perhaps improve on the normality. Then maybe just do a paired t-test.

-- 
Peter Dalgaard
Center for Statistics, Copenhagen Business School
Solbjerg Plads 3, 2000 Frederiksberg, Denmark
Phone: (+45)38153501
Email: pd.mes at cbs.dk  Priv: PDalgd at gmail.com

On Aug 25, 2010, at 8:57 AM, Sandy Small wrote:
> Hi
> This is probably more of a statistics question than a specific R
> question, although I will be using R and need to know how to solve the
> problem in R.
> 
> I have several sets of data (ejection fraction measurements) taken in
> various ways from the same set of (~400) patients (so it is paired data).
> For each individual measurement I can make an estimate of the percentage
> uncertainty in the measurement.
> Generally the measurements in data set A are higher but they have a
> large uncertainty (~20%) while the measurements in data set Bare lower
> but have a small uncertainty (~4%).
> I believe, from the physiology, that the true value is likely to be
> nearer the value of A than of B.
> I need to show that, despite the uncertainties in the measurements
> (which are not themselves normally distributed), there is (or is not) a
> difference between the two groups, (a straight Wilcoxon signed ranks
> test shows a difference but it cannot include that uncertainty data).
> 
> Can anybody suggest what I should be looking at? Is there a language
> here that I don't know? How do I do it in R?
> Many thanks for your help
> Sandy

The first place that I would start is at Martin Bland's page pertaining to
the design and analysis of measurement studies:

  http://www-users.york.ac.uk/~mb55/meas/meas.htm

The papers he co-authored with Doug Altman are the "go to" resource
for this domain.

HTH,

Marc Schwartz