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Thanks: CIs for medians

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Tue, 04 May 1999 10:08:44 +1200

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 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 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%