# Reporting chi-square tests for weighted data

I was wondering if you could share your experience in reporting chi-square tests for complex survey data in journal publications. Normally Chi-square tests are reported as $\chi^2_1(2,\text{ N} = 90)= 0.89, \text{ p} = .35$. (for example, although I guess there can be some variations). However the concept of N becomes rather tricky with complex survey design, and I'm not sure whether I should report the probability weighted sample size or just the sample size.I'm also interested in whether people would report different Ns if the sample was just subject to probability weighting (e.g. for example if strata or cluster information was unfortunately missing) or probability weighting with clustering and stratification. And if the sample size was reported in the format above should this be reported as n rather than N?

Just to give an example: Lumley's R package returns the following:

data(api)
dclus1<-svydesign(id=~dnum, weights=~pw, data=apiclus1, fpc=~fpc)
svychisq(~sch.wide+stype,dclus1, statistic="Chisq")

Pearson's X^2: Rao & Scott adjustment

data:  svychisq(~sch.wide + stype, dclus1, statistic = "Chisq")
X-squared = 11.94, df = 2, p-value = 0.005553


Would you report as N

sum(xtabs(~sch.wide+stype, data=apiclus1)) #or
sum(svytable(~sch.wide+stype, dclus1))


See this page for details on computation and Rao-Scott corrections to the Pearson chisquared test.

Very interested in your opinion. Many thanks

• I think reporting df is what to do; it's also what I usually see in "regular" reporting of $\chi^2$ – Peter Flom Nov 21 '12 at 10:59