Wednesday, March 08, 2006

st: RE: how to compare two skewed distributions, or calculate confidence intervals for quantiles of each?

percentiles or percentile differences (which are a slightly different thing).

If you want to derive confidence intervals for differences between percentiles, then a good method might be the percentile bootstrap, with a suitably large number of replicate samples. In Stata, type

whelp bootstrap

to find about the bootstrap. If instead you prefer to calculate confidence intervals for percentile differences, then you might use the program -cendif-, which is part of the -somersd- package, downloadable from SSC using the -ssc- command in Stata. This calculates robust confidence intervals for median differences, and for other percentile differences. The -somersd- package includes a manual -cendif.pdf-, in which the concepts are explained and demonstrated.

I hope this helps.

Roger

Roger Newson Lecturer in Medical Statistics POSTAL ADDRESS: Respiratory Epidemiology and Public Health Group National Heart and Lung Institute at Imperial College London St Mary's Campus Norfolk Place London W2 1PG STREET ADDRESS: Respiratory Epidemiology and Public Health Group National Heart and Lung Institute at Imperial College London 47 Praed Street Paddington London W1 1NR TELEPHONE: (+44) 020 7594 0939 FAX: (+44) 020 7594 0942 EMAIL: r.newson@imperial.ac.uk WEBSITE: http://www.imperial.ac.uk/nhli/r.newson/ Opinions expressed are those of the author, not of the institution.

-----Original Message----- From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of daniel waxman Sent: 08 March 2006 19:55 To: statalist@hsphsun2.harvard.edu Subject: st: how to compare two skewed distributions, or calculate confidence intervals for quantiles of each?

I'd be appreciative if someone could point me in the right direction:

I am trying to compare two populations with skewed distributions--queuing times for real patients, and queuing times for simulated patients (the output of a discrete event simulation program).

I am most interested in comparing the 50th, 75th, 90th, and 95th percentiles between the real and simulated patients, and am struggling with a way to describe this.

I have only one set of data for the real patients, but I can generate as many simulated patients as I want (and thus it is easy to generate confidence intervals for the simulated patients). The real and simulated patients can sort of be thought of as paired observations, although this is not strictly speaking true.

The distribution for the real patients is as follows;

. su q, detail

Percentiles Smallest 1% 2.8125 0 5% 8.4375 0 10% 11.25 0 Obs 3219 25% 28.125 0 Sum of Wgt. 3219

50% 64.6875 Mean 131.8957 Largest Std. Dev. 179.5722 75% 157.5 1245.938 90% 326.25 1409.063 Variance 32246.18 95% 492.1875 1513.125 Skewness 2.907777 99% 897.1875 1681.875 Kurtosis 13.70393

How can I calculate confidence intervals for these quantiles, or better yet, compare this population to a similarly distributed group (say another variable q2, with the same number of observations)?

Many thanks.

* * For searches and help try: * http://www.stata.com/support/faqs/res/findit.html * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

* * For searches and help try: * http://www.stata.com/support/faqs/res/findit.html * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/


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