pvrank (version 1.1.2)

qrank: Quantiles of exact and approximated null distribution of rank correlations

Description

For a given level of significance, this routine computes approximated or exact conservative and/or liberal critical values under the hypothesis of no association.

Usage

qrank(prob, n, index="spearman", approx="vggfr", print = FALSE,
	lower.tail = TRUE)

Arguments

prob

the nominal level of significance.

n

the number of ranks.

index

a character string that specifies the rank correlation used in the test. Acceptable values are: "spearman", "kendall","gini", "r4" (Tarsitano), "fy1" (Fisher-Yates based on means), "fy2" (Fisher-Yates based on medians),"sbz" (symmetrical Borroni-Zenga). Only enough of the string to be unique is required.

approx

a character string that specifies the type of approximation to the null distribution: "vggfr", "exact","gaussian","student".

print

FALSE suppresses partial output.

lower.tail

logical; if TRUE (default), probability \(P [X\leq x]\) is computed, otherwise \(P[X>x]\). In brief, lower tailed tests are used to test for negative correlation and upper tailed tests are used to test for positive correlation.

Value

a list containing the following components:

n

number of ranks.

Statistic

coefficient of rank order association

Level

nominal level

Cq

conservative quantile

Cv

conservative p-value

Lq

liberal quantile

Lv

liberal p-value

Details

This routine provides two exact quantiles corresponding to a conservative level (next smaller exact size) and a liberal level (next larger exact size). It can be noted that, liberal levels yield critical values of the two-sided \(2<alpha\)-level test.

In the case of \(n>26\) (Spearman) or \(n>60\) (Kendall) or \(n>24\) (Gini) or \(n>15\) (\(r_4\), fy1, fy2 and sbzZ), an approximated, but unique quantile is produced according to approx. The default option is "vggfr" in the case of Spearman and \(r_4\); "gaussian" for Kendall, "fy1", "fy2", and "sbz"; "student" for Gini's cograduation.

A recursive formula is employed in the case of Kendall's rank correlation. Exact computations use frequencies obtained by complete enumeration for the other coefficients.

Examples

# NOT RUN {
data(Insuhyper); attach(Insuhyper)
op<-par(mfrow=c(1,1), mgp=c(1.8,.5,0), mar=c(2.8,2.7,2,1),oma=c(0,0,0,0))
plot(PI,TG,main="Rank correlation between obesity and triglyceride response",
xlab="Ponderal Index", ylab="Plasma triglyceride concentration", pch=19,
cex=0.9, col= "rosybrown4")
text(PI,TG,labels=rownames(Insuhyper),cex=0.6,pos=c(rep(3,10),1,3,1,rep(3,4),1.3))
abline(v=mean(PI),col="black",lty=2,lwd=1)
abline(h=mean(TG),col="darkblue",lty=2,lwd=1)
par(op)
r<-comprank(PI,TG,"spearman","gh")$r
a1<-qrank(0.025, length(PI), "sp", "vggfr", print = FALSE,lower.tail = TRUE)$Cq
a2<-qrank(0.975, length(PI), "sp", "vggfr", print = FALSE,lower.tail = TRUE)$Cq
cat(round(a1,4),round(r,4),round(a2,4))
r<-comprank(PI,TG,"kendall")$r
b1<-qrank(0.95, length(PI), "ke", "ex", lower.tail = TRUE)$Cq # p = .05, one-tailed (upper)
b2<-qrank(0.05, length(PI), "ke", "ex", lower.tail = TRUE)$Cq # p = .95, one-tailed (upper)
cat(round(b2,4),round(r,4),round(b1,4))
detach(Insuhyper)
# }
# NOT RUN {
#####
#
a<-qrank(0.10,61,"Ke","St")
a<-qrank(0.01,25,"Sp","Ga",FALSE,FALSE);a$Cq
a<-qrank(0.03,11,"fy1","Ga",FALSE,FALSE);a$Cq
a<-qrank(0.03,11,"fy2","Ga",FALSE,FALSE);a$Cq
a<-qrank(0.03,11,"sbz","Ga",FALSE,FALSE);a$Cq
a<-qrank(0.001,15,"r4","Ex",FALSE,FALSE);cat(a$Cq,a$Lq,"\n")
a<-qrank(0.01,14,"fy2","Ex",FALSE,FALSE);cat(a$Cq,a$Lq,"\n")
#####
#
# }
# NOT RUN {
a<-qrank(0.05,27,"Gi","Vg",FALSE,FALSE);a$Cq
# }