Hi,
Some more information:
The experiment relates to fertility of a fish species with respect to the
concentration of some chemical, E, say, in its habitat. There are overall
four treatments, a water control, and three treatments of, nominally low,
medium and high concentrations of chemical E. Over several periods of time
the number of fertile eggs produced was measured for each treatment. There
is no discernable difference between the counts of fertile eggs in the
control, low and medium treatments (I carried out a Page test and a
Jonkheere-Terpstre test). The high treatment produced no fertile eggs.
The concentrations present in the treatments vary quite considerably, but
are reasonably distinct between treatments. We do not know if the
measurements of concentration were made at the same time as the egg counts.
I am interested in the EC50 (the concentration at which the count of fertile
eggs is half that of the control). All I can deduce is that the EC50 lies
between the concentrations found in the medium and high treatments. Ideally
I would like to give some kind of confidence interval for the EC50.
Many thanks,
Colin.
-----Original Message-----
From: Peter Flom [mailto:[log in to unmask]]
Sent: 12 January 2006 16:54
To: Colin Millar
Subject: Re: confidence intervals
Bootstrapping does not work well for extreme quantiles, and even then, I
don't see how
you could get a CI.....
Why don't you write back to allstat with a little more detail of what
you've got and what you are
trying to do?
HTH
Peter
Peter L. Flom, PhD
Assistant Director, Statistics and Data Analysis Core
Center for Drug Use and HIV Research
National Development and Research Institutes
71 W. 23rd St
http://cduhr.ndri.org
www.peterflom.com
New York, NY 10010
(212) 845-4485 (voice)
(917) 438-0894 (fax)
>>> Colin Millar <[log in to unmask]> 1/12/2006 11:31 am >>>
Dear all,
This question is about estimating a confidence interval for a
parameter
about which all we know is its extremes.
The situation is that we have two treatments; medium and high stress,
say.
The stress applied is quite variable and has been measured at various
point
in time. We know that between these two points a parameter exists
(specifically the EC50). What is needed is a pragmatic solution as
the
experiments design is not ideal. All I can think of is to estimate,
via
bootstrapping, the distribution of the extremes.
My question is: is it possible to infer a confidence interval from
these two
estimates? I was thinking we could use the CDF of the minimum and the
reverse CDF of the maximum to estimate a kind of coverage probability
but I
am unsure of the validity of this.
Any help or references would be greatly appreciated.
Kind regards,
Colin Millar.
Colin Millar,
Statistics,
Fisheries Management.
FRS Marine Laboratory,
PO Box 101,
375 Victoria Road,
Aberdeen, AB11 9DB,
UK.
Tel(direct) +44(0)1224 295395
Tel(reception) +44(0)1224 876544
Fax +44(0)1224 295511
email [log in to unmask] <mailto:[log in to unmask]>
webpage www.frs-scotland.gov.uk <http://www.frs-scotland.gov.uk>
FRS is an agency of the Scottish Executive
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