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

From   Nick Cox <>
Subject   Re: st: Missing confidence intervals for median after using -bootstrap- or -bpmedian-
Date   Tue, 13 Nov 2012 00:49:30 +0000

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-
> using
> *--------------------- 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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