svyranktest.RdDesign-based versions of k-sample rank tests. The built-in tests are all for location hypotheses, but the user could specify others.
svyranktest(formula, design,
test = c("wilcoxon", "vanderWaerden", "median","KruskalWallis"), ...)Model formula y~g for outcome variable y and group g
A survey design object
Which rank test to use: Wilcoxon, van der Waerden's normal-scores
test, Mood's test for the median, or a function f(r,N) where
r is the rank and N the estimated population
size. "KruskalWallis" is a synonym for "wilcoxon" for more than two groups.
for future expansion
These tests are for the null hypothesis that the population or superpopulation distributions of the response variable are different between groups, targeted at population or superpopulation alternatives. The 'ranks' are defined as quantiles of the pooled distribution of the variable, so they do not just go from 1 to N; the null hypothesis does not depend on the weights, but the ranks do.
The tests reduce to the usual Normal approximations to the usual rank tests under iid sampling. Unlike the traditional rank tests, they are not exact in small samples.
Object of class htest
Note that with more than two groups the statistic element of the return value holds the numerator degrees of freedom and the parameter element holds the test statistic.
Lumley, T., & Scott, A. J. (2013). Two-sample rank tests under complex sampling. BIOMETRIKA, 100 (4), 831-842.
data(api)
dclus1<-svydesign(id=~dnum, weights=~pw, fpc=~fpc, data=apiclus1)
svyranktest(ell~comp.imp, dclus1)
#>
#> Design-based KruskalWallis test
#>
#> data: ell ~ comp.imp
#> t = 2.1367, df = 13, p-value = 0.05221
#> alternative hypothesis: true difference in mean rank score is not equal to 0
#> sample estimates:
#> difference in mean rank score
#> 0.1363158
#>
svyranktest(ell~comp.imp, dclus1, test="median")
#>
#> Design-based median test
#>
#> data: ell ~ comp.imp
#> t = 1.6866, df = 13, p-value = 0.1155
#> alternative hypothesis: true difference in mean rank score is not equal to 0
#> sample estimates:
#> difference in mean rank score
#> 0.1914286
#>
svyranktest(ell~stype, dclus1)
#>
#> Design-based KruskalWallis test
#>
#> data: ell ~ stype
#> df = 2, Chisq = 18.31, p-value = 0.003851
#>
svyranktest(ell~stype, dclus1, test="median")
#>
#> Design-based median test
#>
#> data: ell ~ stype
#> df = 2, Chisq = 15.792, p-value = 0.006481
#>
str(svyranktest(ell~stype, dclus1))
#> List of 6
#> $ parameter: num [1, 1] 18.3
#> ..- attr(*, "names")= chr "Chisq"
#> $ statistic: Named num 2
#> ..- attr(*, "names")= chr "df"
#> $ ddf : num 12
#> $ p.value : num [1, 1] 0.00385
#> $ method : chr "Design-based KruskalWallis test"
#> $ data.name: chr "ell ~ stype"
#> - attr(*, "class")= chr "htest"
## upper quartile
svyranktest(ell~comp.imp, dclus1, test=function(r,N) as.numeric(r>0.75*N))
#>
#> Design-based rank test
#>
#> data: ell ~ comp.imp
#> t = 2.0564, df = 13, p-value = 0.0604
#> alternative hypothesis: true difference in mean rank score is not equal to 0
#> sample estimates:
#> difference in mean rank score
#> 0.1732331
#>
quantiletest<-function(p){
rval<-function(r,N) as.numeric(r>(N*p))
attr(rval,"name")<-paste(p,"quantile")
rval
}
svyranktest(ell~comp.imp, dclus1, test=quantiletest(0.5))
#>
#> Design-based 0.5 quantile test
#>
#> data: ell ~ comp.imp
#> t = 1.6866, df = 13, p-value = 0.1155
#> alternative hypothesis: true difference in mean rank score is not equal to 0
#> sample estimates:
#> difference in mean rank score
#> 0.1914286
#>
svyranktest(ell~comp.imp, dclus1, test=quantiletest(0.75))
#>
#> Design-based 0.75 quantile test
#>
#> data: ell ~ comp.imp
#> t = 2.0564, df = 13, p-value = 0.0604
#> alternative hypothesis: true difference in mean rank score is not equal to 0
#> sample estimates:
#> difference in mean rank score
#> 0.1732331
#>
## replicate weights
rclus1<-as.svrepdesign(dclus1)
svyranktest(ell~stype, rclus1)
#>
#> Design-based KruskalWallis test
#>
#> data: ell ~ stype
#> df = 2, Chisq = 18.31, p-value = 0.003851
#>