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# RE: st: comparing differences in Kendall's tau or Spearman's coefficient using somersd and/or bootstrap

 From "Chong, Qi Lin Andrew" To "statalist@hsphsun2.harvard.edu" Subject RE: st: comparing differences in Kendall's tau or Spearman's coefficient using somersd and/or bootstrap Date Wed, 28 Apr 2010 00:37:50 -0400

```Hi all,

thanks a lot to Dr. Newson for responding to my question. To him and all others, I am unsure how I should proceed with the bootstrap command. As Dr. Newson explained accurately, I am "trying to measure the tau-a correlation between "Efficiency definition 1" (ED1) in Year A and ED1 in Year B, and then measure the tau-a correlation between "Efficiency Definition 2" (ED2) in Year A and ED2 in Year B, and then calculate a confidence interval for the difference between the 2 taus."

If I were to reorder the data set so that each firm has "ED1 YearA" "ED1 YearB" "ED2 YearA" "ED2 YearB" lined up next to each other, etc, ed1a ed1b ed2a ed2b, how should I go about estimating this interval?

If it is easy to give me the exact commands, I would very much appreciate it, but if not any advice would be much appreciated. I am trying to calculate the statistical significance of their difference, so should I be drawing bootstrap samples of firms with ed1a ed1b ed2a ed2b all together? And then calculating one difference between ed1a ed1b & ed2a ed2b for each sample?

Would this involve some kind of programming using bootstrap alone and w/o somersd? Also, does it matter that Spearman is in terms of RANKS, so if I happen to draw the same sample twice from say the 6000 observations I have, then there would be a tie in the bootstrap drawn sample (6000 obs from original 6000 but with replacement)? Would this tie be a problem?

Andrew

________________________________________
From: owner-statalist@hsphsun2.harvard.edu [owner-statalist@hsphsun2.harvard.edu] On Behalf Of Roger Newson [r.newson@imperial.ac.uk]
Sent: Monday, April 26, 2010 6:08 AM
To: statalist@hsphsun2.harvard.edu
Subject: Re: st: comparing differences in Kendall's tau or Spearman's coefficient using somersd

As I understand it, you are trying to measure the tau-a correlation
between "Efficiency definition 1" (ED1) in Year A and ED1 in Year B, and
then measure the tau-a correlation between "Efficiency Definition 2"
(ED2) in Year A and ED2 in Year B, and then calculate a confidence
interval for the difference between the 2 taus.

The somersd package unfortunately does not yet do this, The examples in
the manual are more similar to the case where there is a third
efficiency definition (ED3), which is thought too be a "gold standard".
We would then compare the tau-a between ED3 and ED1 with the tau-a
between ED3 and ED2, and find out which is greater.

To do what you want to do, the best answer will be to use either the
jackknife or the bootstrap. Both of these are available in Stata.
However, your query has drawn attention to an important limitation of
the -somersd- package. It would be an improvement if -somersd- could
output the delta-jackknife pseudovalues or the delta-jackknife influence
function to an output dataset (or resultsset) with 1 observation per
cluster and data on the pseudovalues or influence function. This is one
of many improvements I would like to make to -somersd- when I have the time.

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
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 25/04/2010 19:11, Chong, Qi Lin Andrew wrote:
> The scores are bounded from 1 to infinity, and a half-normal
> distribution has been assumed for them in the original stochastic
> frontier (and a normal distribution for the errors). A score of say
> 1.25 indicates a firm incurs 25% more costs than the most efficient
> firm it can be compared
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```