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

 From Nick Cox To statalist@hsphsun2.harvard.edu Subject Re: st: Missing confidence intervals for median after using -bootstrap- or -bpmedian- Date Tue, 13 Nov 2012 23:39:55 +0000

```I don't see why you say that 54% of values are -.8. This is

I am not clear what advice you seek. The results you are getting seem
especially in the middle of the distribution. They are difficult to
report using conventional practices, so you need different practices,
not least graphs so your readers can see what is going on.

Historical, one main purpose of inferential statistics was to stop
researchers making fools of themselves by over-interpreting (very)
small samples. With large samples the game often requires different
emphasis.

Nick

On Tue, Nov 13, 2012 at 10:55 PM, Vasyl Druchkiv <dvv1985@yahoo.de> wrote:
> Hello Nick and Roger,
>
> thank you for your quick reply! Sorry, that I haven't provided background to the data. The variable from the example contains astigmatism of  the eyes that describes cornea steepness. This variable is not symmetric. In fact it is extremely skewed to the left. To get an idea of the data here are some descriptive statistics:
>                           astigmatism
> -------------------------------------------------------------
>       Percentiles      Smallest
>  1%         -4.5             -7
>  5%           -3           -6.5
> 10%         -2.3           -6.5       Obs               16872
> 25%         -1.3           -6.5       Sum of Wgt.       16872
>
> 50%          -.8                      Mean          -1.005293
>                         Largest       Std. Dev.      .9449402
> 75%          -.3              0
> 90%            0              0       Variance       .8929119
> 95%            0              0       Skewness      -1.812464
> 99%            0              0       Kurtosis       7.150496
>
> So, you can see that the variable is not a constant one: there is a variation, although 54% of the eyes had an astigmatism  of -.8. I've applied already -parmest-  (-bpmedian- and -parmest- I downloaded from SSC) as suggested by Roger and indeed got the confidence intervals that are equal to median.
> However it is not only the confidence intervals that concern me. In another case I try to run a quantile regression with bootstrap estimation method and  the difference between  thinnest and central points of the cornea as dependent variable. The dependent variable is also not symmetric and has positive skewness:
>            cct-tpct
> -------------------------------------------------------------
>       Percentiles      Smallest
>  1%            3              0
>  5%            4              0
> 10%            4              1       Obs               16872
> 25%            5              1       Sum of Wgt.       16872
>
> 50%            8                      Mean           9.485479
>                         Largest       Std. Dev.      8.423524
> 75%           11            122
> 90%           16            124       Variance       70.95575
> 95%           20            380       Skewness       14.34001
> 99%           33            380       Kurtosis       487.1662
>
> When I use for instance ocular side (right/left) as a dummy independent variable I get:
>
> Median regression, bootstrap(20) SEs                 Number of obs =     16872
>   Raw sum of deviations    68401 (about 8)
>   Min sum of deviations    68061                     Pseudo R2     =    0.0050
>
> ------------------------------------------------------------------------------
>      ccttpct |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
> -------------+----------------------------------------------------------------
>          eye |         -1          .        .       .            .           .
>        _cons |          8          .        .       .            .           .
> ------------------------------------------------------------------------------
> So, there is a difference between eyes. However there are no statistics to report. Of course I could use for example Wilcoxon  signed-rank test to check the differences (and would probably find insignificant results). But my idea is to fit a multivariate model with more independent variables.
> If you could help me further it would be great.
>
> Thank you in advance and sorry, if I was unclear about some points.
> Best regards,
> Vasyl
>
> -----Ursprüngliche Nachricht-----
> Von: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] Im Auftrag von Roger B. Newson
> Gesendet: Tuesday, November 13, 2012 12:50 PM
> An: statalist@hsphsun2.harvard.edu
> Betreff: Re: st: Missing confidence intervals for median after using -bootstrap- or -bpmedian-
>
> 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
>
>
> 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 UNITED KINGDOM
> Tel: +44 (0)20 7352 8121 ext 3381
> Fax: +44 (0)20 7351 8322
> Email: r.newson@imperial.ac.uk
> Web page: http://www.imperial.ac.uk/nhli/r.newson/
> 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.
>>
>> Nick
>>
>> On Mon, Nov 12, 2012 at 9:32 PM, Vasyl Druchkiv <dvv1985@yahoo.de> 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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