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# Re: st: Bootstrapping question

 From Steve Samuels To statalist@hsphsun2.harvard.edu Subject Re: st: Bootstrapping question Date Wed, 6 Feb 2013 22:24:22 -0500

```Lenth's site states that he use the "exact", presumably Clopper-Pearson,
intervals, which is known to be conservative. But this is not
what Stata computes. Since a 50% sample proportion is not possible with
n = 27, the closest one can get to 50% is with k = 13 or 14 events. I'm
not sure what Lenth's applet shows (I don't have Java enabled), but Stata
does not show a 17.3% margin of error, rather a number closer to 20%

. cii 27 13
-- Binomial Exact --
Variable |        Obs        Mean    Std. Err.       [95% Conf. Interval]
----------+---------------------------------------------------------------
|         27    .4814815     .096159        .2866725    .6805035

. cii 27 14
-- Binomial Exact --
Variable |        Obs        Mean    Std. Err.       [95% Conf. Interval]
----------+---------------------------------------------------------------
|         27    .5185185     .096159        .3194965    .7133275

You could have skipped the trip to Length's site and used Stata's own -cii- command
with the Wilson intervals, recommended for n < 40 (Brown et al, 2008).

. cii 27 13, wilson
------ Wilson ------
Variable |        Obs        Mean    Std. Err.       [95% Conf. Interval]
----------+---------------------------------------------------------------
|         27    .4814815     .096159        .3074323    .6601438

. cii 27 14, wilson
------ Wilson ------
Variable |        Obs        Mean    Std. Err.       [95% Conf. Interval]
---------+---------------------------------------------------------------
|         27    .5185185     .096159        .3398562    .6925677

Brown, L. D., T. T. Cai, and A. DasGupta. 2001. Interval estimation for
a binomial proportion. Statistical Science 16: 101–133

Steve

Steven J Samuels
Consulting Statistician
18 Cantine's Island
Saugerties NY 12477
Voice: 845-246-0774

On Feb 6, 2013, at 8:08 PM, Nick Cox wrote:

I don't think I can add usefully to my previous comments. Saying that
you used a particular program does not convey much to me. What does
"improve the confidence intervals" mean?

Nick

On Wed, Feb 6, 2013 at 8:53 PM, Ilian, Henry (ACS)
<Henry.Ilian@dfa.state.ny.us> wrote:
> The sample size 1s 27, which is the largest number the case readers can handle in the amount of time allotted. The population the sample is drawn from is 140. To get a confidence interval for proportion I used Lenth's on-line application, http://homepage.cs.uiowa.edu/~rlenth/Power/. Since the items have different proportions, there are several confidence intervals. Using 50% as the proportion (meaning that for a particular item, 50% of the sample were awarded the highest ordinal rating, and the other 50% were awarded other ratings), I got a margin of error of 17.3%. For a proportion of 70%, the margin of error is 16%, etc.
>
> I'm new to the idea of bootstrapping, but it seemed to be a way to improve the confidence intervals.
>
> -----Original Message-----
> From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Nick Cox
> Sent: Wednesday, February 06, 2013 2:04 PM
> To: statalist@hsphsun2.harvard.edu
> Subject: Re: st: Bootstrapping question
>
> For once, my line differs slightly from Maarten's.
>
> The crunch is that nowhere did Henry state where his confidence
> intervals come from. If they were based on inappropriate assumptions,
> bootstrapping may do better. But if the confidence intervals one way
> are wide, the expectation is of a similar story from -bootstrap-.
>
> Nick
>
> On Wed, Feb 6, 2013 at 6:55 PM, Maarten Buis <maartenlbuis@gmail.com> wrote:
>> On Wed, Feb 6, 2013 at 5:28 PM, Ilian, Henry (ACS)  wrote:
>>> I am working with samples that result in very large confidence intervals, and there is no way to get larger samples. Therefore bootstrapping is an appealing option.
>>
>> Unfortunately the bootstrap is not going to help. The large confidence
>> intervals mean that there is very little information present in your
>> data, and no statistical technique can add information that was not
>> present in your data to begin with. So it seems that you will just
>> have to live with the very large confidence intervals.
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