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

 From Steven Samuels To statalist@hsphsun2.harvard.edu Subject Re: st: How to obtain Rao-Scott chi(2) (not the F-stat) for two-way svy:tab Date Thu, 23 Dec 2010 18:55:49 -0500

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.
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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

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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
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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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