Re: st: How to obtain Rao-Scott chi(2) (not the F-stat) for two-way svy:tab

[Steven Samuels <sjsamuels@gmail.com>]

Correction: The First Order Rao-Scott Chi Square *is* calculated by  
the formula (R-1)*(C-1)*F, as I originally said.
(The 1st order and second order corrected F's are identical; only the  
reference distributions differ.) So the p-values in Stata and SAS  
_should_ differ, just as you observed.

Steve



Bo, it turns out that Stata and SAS are computing different Rao-Scott  
statistics. Stata computes the F approximation to the second-order Rao- 
Scott statistic, but SAS offers only the first-order statistic.   
Thomas and Rao (1987) show that the second-order correction affords  
better control of type I error under certain conditions and confirm  
this in  Chapter 7 of  Chambers and Skinner (2003). So here SAS is  
inferior to Stata.

I made a mistake: The Chi-Sq = (R-1)(C-1) x F  conversion formula that  
I gave you applies only to the first-order corrected Rao-Scott  
statistics, not the second order variant. It's a little more  
complicated, but possible, to get the second order corrected-Chi  
Square from Stata's F statistic result.

Steve

References

DR Thomas and JNK. Rao (1987)  Small-Sample Comparisons of Level and  
Power for Simple Goodness-of-Fit Statistics Under Cluster Sampling,   
Journal of the American Statistical Association, Vol. 82, No. 398, pp.  
630- 636

Rao JNK, Thomas DR. (2003) "Analysis of categorical response data from  
complex surveys: An appraisal and update". In: Analysis of survey  
data. Chambers RL, Skinner CJ, editor. New York: Wiley; pp. 85-108.


sjsamuels@gmail.com
Steven J. Samuels
sjsamuels@gmail.com
18 Cantine's Island
Saugerties NY 12477
USA
Voice: 845-246-0774
Fax:    206-202-4783




On Dec 23, 2010, at 5:25 PM, Bo MacInnis wrote:

Thank you very much, Steve. However, for the same 2x2 table adjusting  
for the sampling weight, SAS produces (done by my colleague) Rao-Scott  
chi2(1) = 1.34 with p = .25, but I got F-stat = 1.48 with p = .22. Our  
boss is not comfortable considering these two statistics identical  
because their values are not close enough. I was wondering if SAS  
might do the Rao-Scott correction differently from Stata. Thank you  
much for your help! Bo

On 12/23/2010 7:31 AM, Steven Samuels wrote:
> Bo MacInnis-
>
> • Rao-Scott corrected chi square = (R-1)(C-1) x (corrected F)  where  
> R= no. of Rows  C = no. of Columns (Stata 11 Manual, page 130)
> • In your example with R=2, C=2, the statistics are identical.
> • SAS reports only the F approximation p-value, just as Stata does.
>
> Steve
>
> Steven J. Samuels
> sjsamuels@gmail.com
> 18 Cantine's Island
> Saugerties NY 12477
> USA
> Voice: 845-246-0774
> Fax:    206-202-4783
>
>
>
> On Dec 22, 2010, at 1:36 PM, Bo MacInnis wrote:
>
> Dear Statlist mates,
>
> I'd like to obtain the Rao-Scott chi(2) statistic for two-way  
> svy:tab. The two-way svy:tab provides the Pearson statistics  
> (uncorrected for design-effect as well a design effect adjusted  
> based on Rao-Scott (1984). However, the design-based Pearson is  
> converted into a F-stat. In my project, I'd need the chi(2) version  
> of the Rao-Scott statistic (like what is provided in SAS, but I do  
> not use SAS).
>
> Here is the output from a two-way (2x2) svy:tab:
> Pearson:
>  Uncorrected   chi2(1)         =    2.3737
>  Design-based  F(1, 2803)      =    1.4764     P = 0.2244
>
> Thank you very much for your help!
> Bo
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