The RaoScott likelihood ratio chisquare test is a designadjusted version of the likelihood ratio test, which involves ratios of observed and expected frequencies. For details about designadjusted chisquare tests, see Lohr (2010, Section 10.3.2), Rao and Scott (1981, 1984, 1987); Thomas, Singh, and Roberts (1996).
PROC SURVEYFREQ provides a firstorder RaoScott likelihood ratio test by default. If you specify the LRCHISQ(SECONDORDER) option, PROC SURVEYFREQ provides a secondorder (Satterthwaite) likelihood ratio chisquare test.
The procedure computes the RaoScott likelihood ratio test by applying design adjustments to the weighted likelihood ratio statistic that is based on estimated totals. This computation is identical to the RaoScott chisquare test computation except that it uses the likelihood ratio statistic in place of the Pearson chisquare statistic . See the section RaoScott ChiSquare Test for details.
For oneway tables, the LRCHISQ option provides a RaoScott (designbased) goodnessoffit test for oneway tables. By default, this is a test for the null hypothesis of equal proportions. If you specify null hypothesis proportions in the TESTP= option, the goodnessoffit test uses the specified proportions.
The RaoScott likelihood ratio test uses the likelihood ratio statistic that is based on the estimated totals,

where n is the sample size, is the estimated overall total, is the estimated total for level c, and is the expected total for level c under the null hypothesis. For the null hypothesis of equal proportions, the expected total for each level equals

For specified null proportions, the expected total for level c equals

where is the null proportion that you specify for level c.
The computation of the RaoScott likelihood ratio test for oneway tables uses in place of in the RaoScott chisquare test computation and is otherwise identical to the chisquare test computation. See the sections FirstOrder Test and SecondOrder Test for details.
If you specify the LRCHISQ(MODIFIED) option, PROC SURVEYFREQ computes the design corrections by using null hypothesis proportions instead of proportion estimates. By default, null hypothesis proportions are equal proportions for all levels of the oneway table. Alternatively, you can specify null proportion values in the TESTP= option.
For twoway tables, the LRCHISQ option provides a RaoScott (designbased) test of association between the row and column variables.
The RaoScott likelihood ratio test uses the likelihood ratio statistic that is based on the estimated totals,

where n is the sample size, is the estimated overall total, is the estimated total for table cell (r, c), and is the expected total for cell (r, c) under the null hypothesis of no association. The expected total for cell (r, c) equals

The computation of the RaoScott likelihood ratio test for twoway tables uses in place of in the RaoScott chisquare test computation and is otherwise identical to the chisquare test computation. See the sections FirstOrder Test and SecondOrder Test for details.
By default for a firstorder test, PROC SURVEYFREQ computes the design correction from proportion estimates. If you specify the LRCHISQ(MODIFIED) option for a firstorder test, the procedure computes the design correction from null hypothesis proportions.
Secondorder tests, which you request by specifying the LRCHISQ(SECONDORDER) option, are computed by applying both firstorder and secondorder design corrections to the weighted likelihood ratio statistic. For secondorder tests for twoway tables, PROC SURVEYFREQ always uses null hypothesis proportions to compute both the firstorder and secondorder design corrections.