Dear Allstatters,
Thankyou to everyone who answered my query on constructing confidence
intervals for medians.
the main consesus of opinion was to refer to:
Gardner, M.J. - Editor.
Altman, Douglas G. - Editor.
TITLE Statistics with confidence: confidence intervals and statistical
guidelines
IMPRINT London, British Medical Journal, 1989.
ISBN 0727902229
SHELFMARK F 519.02 Gar
or
Campbell M J and Gardner M J (1988) Calculating confidence intervals
for some non-parametric analyses. British Medical Journal, 296,
1454-1456.
Other useful responses were:
Here is a large sample Binomial method for any quantile q.
For the median q = 0.5. Sample size = n.
calculate j = nq - 1.96 root(q(1-q)/n)
k = nq - 1.96 root(q(1-q)/n)
round j and k. Then the j'th and k'th observations give
the 95% confidence interval for the quantile.
See Conover 1980 Practical non-parametric statistics, Wiley.
According to Moroney - Facts from figures - the standard error of
the median is 1.25xsigma/root(n) for a large sample. Sigma is the
population s.d., n the sample size.
if you have a continuous distribution with the ordered observations
x_(1), x_(2), ... ,x_(r), ... ,x_(s), ... ,x_(N) you can use the following
expression
(resulting from the binomial distribution) for determining the CI:
Pob[ x_(r)<= med <= x_(s) ]=(1/2)^N sum_(i=r, r+1,...,s-1) (N over i)
asymtotically (works well for N>15) use
r=N/2 - u_(alpha/2) sqrt(N/4)
(rounding down) for the lower and
s=N-r+1
for the upper bound.
Papadatos, N. Intermediate order statistics with applications to
nonparametric estimation. Statist. Probab. Lett. 22
(1995), no. 3, 231--238.
Hollander and Wolfe. Nonparametric Statistical Methods. Wiley New
York .
Pesarin F. (1999) Permutation testing of multidimensional hypotheses by
nonparametric combination of dependent tests.
CLEUP Padova.
Thankyou in particular to:
Miland Joshi, Luigi Salmaso, John hughes, Ly Mee Yu, Mike Campbell, Martin
Bland, Derek Christie, Robert Nemeth, Brian Faragher, Gilbert Mackenzie,
Lesley Fraser.
Best wishes
Derrick Bennett
Dr Derrick Bennett,
Clinical Trials Research Unit,
University of Auckland,
Private Bag 92 019,
Auckland,
New Zealand.
Ph : 64 9 373 1711 x4724
fax: 64 9 373 1710
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