# Re: st: confidence interval for median

 From "moleps islon" To statalist@hsphsun2.harvard.edu Subject Re: st: confidence interval for median Date Sat, 9 Aug 2008 17:21:27 +0200

```Thank you. Just what I was looking for. You state that jackknife is
inappropriate. Principles of medical statistics, feinstein 2002 claim
the contrary-I have no clue what is right..

7.7.2 Bootstrap Method
The bootstrap method could be applied, if desired, to produce a
confidence interval for the stability of
a median. The approach will not be further discussed, however, because
currently it is almost never used
for this purpose.
7.7.3 Jackknife Method
The jackknife process is particularly simple for medians. Because the
original group in Table 7.1 contains
20 members, the reduced group will contain 19 members, and the reduced
median will always be in the
10th rank of the group. This value will have been the 11th rank in the
original group. Counting from
the lower end of the original data, the 11th ranked value is 96. It
will become the reduced median after
removal of any original item that lies in the first 10 ranks, i.e.,
between 62 and 91. The value of 91 will
become the reduced median after removal of any items that lie in the
original ranks from 11 to 21, i.e.,
from 96 to 400.
Thus, the reduced median will be either 91 or 96, as noted in the far
right column of Table 7.1. We can
also be 100% confident that the reduced median will lie in the zone
from 91 to 96. Because the original
median in these data was (91 + 96)/2 = 93.5, the reduced median will
always be 2.5 units lower or higher
than before. The proportional change will be 2.5/93.5 = .027, which is
a respectably small difference and
also somewhat smaller than the coefficients of stability for the mean.
Furthermore, the proportional change
of 2.7% for higher or lower values will occur in all values and zones
of the reduced median. Accordingly,
with the jackknife method, we could conclude that the median of these
data is quite stable.
If the data set has an even number of members, the jackknife removal
of one member will make the
median vary between some of the middlemost values from which it was
originally calculated. For an odd
number of members, most of the reduced medians will vary to values
that are just above or below the
original median and the values on either side of it. Thus, if the data
set in Table 7.1 had an extra item of
94, this value would be the median in the 21 items. When one member is
removed from the data set, the
reduced median would become either (94 + 96)/2 = 95, or (91 + 94)/2 =
92.5, according to whether the
removed member is above the value of 96 or below 91. The median would
become (87 + 94)/2 = 90.5
with the removal of 91, (91 + 96)/2 = 93.5 with the removal of 94, and
(94 + 97)/2 = 95.5 with the removal
of 96. Thus, if Xm is the value at the rank m of the median, the
maximum range of variation for the reduced
median will be from (Xm−2 + Xm)/2 to (Xm+2 + Xm )/2.
Although seldom discussed in most statistical texts, this type of
appraisal is an excellent screening
test for stability of a median.

On Sat, Aug 9, 2008 at 4:46 PM, Maarten buis <maartenbuis@yahoo.co.uk> wrote:
> --- moleps islon <moleps2@gmail.com> wrote:
>> I need to find the confidence interval for my mean. I thought to use
>> a jackknife command, but I cant get it to work: Jknife: sum age.
>
> What do you want, the median (subject title) or the mean (the
> question)? The jacknife is not appropriate for the median. For the mean
> you can use -mean-, and for the median you can use -centile-. If you
> want to use a resampling method you can use -bootstrap-, which is
> appropriate for both the mean and the median. See the example below and
> the helpfiles of these commands:
>
> *--------------------- begin example ------------------
> sysuse auto, clear
>
> mean mpg
> centile mpg
> bootstrap mean=r(mean) median=r(p50): sum mpg, detail
> *---------------------- end example -------------------
> (For more on how to use examples I sent to the Statalist, see
> http://home.fsw.vu.nl/m.buis/stata/exampleFAQ.html )
>
>
> -----------------------------------------
> Maarten L. Buis
> Department of Social Research Methodology
> Vrije Universiteit Amsterdam
> Boelelaan 1081
> 1081 HV Amsterdam
> The Netherlands
>
> Buitenveldertselaan 3 (Metropolitan), room Z434
>
> +31 20 5986715
>
> http://home.fsw.vu.nl/m.buis/
> -----------------------------------------
>
>
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```