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Re: st: Missing confidence intervals for median after using -bootstrap- or -bpmedian-

From   "Roger B. Newson" <>
Subject   Re: st: Missing confidence intervals for median after using -bootstrap- or -bpmedian-
Date   Tue, 13 Nov 2012 11:49:56 +0000

The problem here seems to me to be a zero standard error for the median, caused by a zero variance for the median, caused by a constant variable. For some reason, Stata is displaying the confidence interval as if the standard error was missing. This may possibly have something to do with version control (-bpmedian- is a Stata Version 10 command).

For what it's worth, the -parmest- package (also downloadable from SSC) displays the confidence intervals for a Bonett-Price median of a constant variable "correctly", with a zero standard error and upper and lower confidence linits equal to the median. After -bpmedian-, the user may type

parmest, list(,)

and display the "correct" confidence interval. You might also like to try using the -sccendif- module of the -scsomersd- package, which can also be downloaded from SSC, and which also calculates confidence intervals for medians, allowing the possibility of clustering and/or sampling-probability weights.

I hope this helps.

Best wishes


Roger B Newson BSc MSc DPhil
Lecturer in Medical Statistics
Respiratory Epidemiology and Public Health Group
National Heart and Lung Institute
Imperial College London
Royal Brompton Campus
Room 33, Emmanuel Kaye Building
1B Manresa Road
London SW3 6LR
Tel: +44 (0)20 7352 8121 ext 3381
Fax: +44 (0)20 7351 8322
Web page:
Departmental Web page:

Opinions expressed are those of the author, not of the institution.

On 13/11/2012 00:49, Nick Cox wrote:
I am not a statistician; in fact many, perhaps most, people on this
list wouldn't call themselves statisticians.

You are asked to make clear where user-written programs you refer to
come from. -bpmedian- is from SSC or Roger Newson's website.

You don't tell us anything much about your data, either what it is
(the name "var" is not revealing) or any descriptive statistics. But I
see you have a large sample size. It seems likely therefore that the
confidence interval for anything will be narrow at worst. However, it
seems likely also from your results that you have lots of ties. If so,
the unusual result of a confidence interval of length 0 is likely to
be an artefact of coarseness in data recording.  If so, then reporting
a confidence interval isn't really possible, as it should be more like
.8 +/- smidgen where smidgen is less than the resolution of
measurement. By resolution, I mean the minimum difference between
reported measurements. If possible data are values like .7, .8, .9
the resolution is 0.1.

Conversely, if I were reviewing or examining this research, I would
want a report on the fraction of values that were recorded as .8. In
fact I would want a graph of the data. Of course, you may intend to do
all that.


On Mon, Nov 12, 2012 at 9:32 PM, Vasyl Druchkiv <> wrote:
Dear statisticians,

I try to estimate CI's for the median with -bpmedian- or with -bootstrap-

*--------------------- begin example ------------------
centile var
bootstrap median=r(p50): sum var, detail
*--------------------- end example --------------------

The problem is that I get empty cells on standard error and confidence
intervals either by implementing -bpmediam- or -bootstrap-.

*--------------------- begin example ------------------
Bonett-Price confidence interval for median of: var
Number of observations: 16872
        var |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
        _cons |        -.8          .        .       .            .
*--------------------- end example ------------------

I looked for the calculation method used in -bpmedian- . This method is
described in:
     Bonett, D. G. and Price, R. M.  2002.  Statistical inference for a
linear function of medians:  Confidence
     intervals, hypothesis testing, and sample size requirements.
Psychological Methods 7(3): 370-383.

Furthermore, I tried  to estimate CI's with SPSS using bootstrap and got
(-0.8;-0.8) for 95% CI's. It means that the problem occurs when both limits
coincide with the median. However, the method described in Bonnett-Price
uses the formula:
sum(cjηj)±Za/2(sum(cj2varηj))^1/2  (pp: 372)
So, even if the last term is equal to 0 due to the pointy distribution  (var
ηj=0), lower and upper limits must be displayed in stata output and be equal
to -0.8 in my example. Can I just assume that CI's are  equal to median?

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