st: Degrees of freedom formula for -svytab-

[Roger Newson <roger.newson@kcl.ac.uk>]

Fellow Statalisters (especially StataCorp):

I have a query about the degrees of freedom used to calculate the 
confidence intervals for the probabilities/percentages in -svytab-. The 
confidence interval formula is given near the bottom of Page 85 of -[SVY]-, 
and includes a symbol, which would be $\nu$ in TeX, for the degrees of 
freedom of a t-distribution. Near the top of Page 88, $\nu$ is defined as 
being equal to the number of PSUs minus the number of strata. This seems to 
imply that, if we use the Stata estimation results for -svytab-, then the 
degrees of freedom can be calculated by typing

scalar df=e(N_psu)-e(N_strata)

This formula appears to work in at least one example that I have tried in 
the -auto- data, where I have re-created the confidence intervals produced 
using the -ci- option of -svytab-. Is this formula always used by -svytab- 
to calculate confidence intervals?

More generally, are there any other estimation commands (apart from 
-svytab-, -svymean-, -svyratio- and -svytotal-) which calculate confidence 
intervals using a t-distribution with degrees of freedom other than those 
stored in -e(df_r)-? I ask because I am planning to update my -parmest- 
package (downloadable from SSC) so that the -dof- variable in the 
resultsset will contain the correct degrees of freedom after the -svytab- 
command, and would like to know if I should do the same for any other 
estimation commands. (For more information on -parmest-, see the on-line 
help for -parmest-, and also Newson (2003) and Newson (2004).) I am aware 
that -ttest- uses the Satterthwaite or Welch degrees of freedom if the 
-unequal- option is specified, but -ttest- is not an estimation command, 
and therefore cannot be used with -parmest-.

I would like to thank Jill Starkes and Lee Sieswerda of Thunder Bay 
District Health Unit for drawing my attention to the non-standard 
confidence interval formula used by -svytab-.

Best wishes (and thanks in advance)

Roger


References

Newson, R. 2003. Confidence intervals and p-values for delivery to the end 
user.  The Stata
Journal 3(3): 245-269. Also downloadable from Roger Newson's website at
http://www.kcl-phs.org.uk/rogernewson.

Newson, R. 2004. From datasets to resultssets in Stata.  Presented at the 
10th United Kingdom
Stata Users' Group Meeting, London, 29 June, 2004.  Also downloadable from 
Roger Newson's
website at http://www.kcl-phs.org.uk/rogernewson.


--
Roger Newson
Lecturer in Medical Statistics
Department of Public Health Sciences
King's College London
5th Floor, Capital House
42 Weston Street
London SE1 3QD
United Kingdom

Tel: 020 7848 6648 International +44 20 7848 6648
Fax: 020 7848 6620 International +44 20 7848 6620
  or 020 7848 6605 International +44 20 7848 6605
Email: roger.newson@kcl.ac.uk
Website: http://www.kcl-phs.org.uk/rogernewson

Opinions expressed are those of the author, not the institution.

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