[R] Siegel-Tukey test for equal variability (code)

[Daniel Malter]

The previously posted code contains bugs. The code below should work:


x: a vector of data

y: Group indicator (if id.col=TRUE); data of the second group (if
id.col=FALSE). If y is the group indicator it MUST take 0 or 1 to indicate
the groups, and x must contain the data for both groups.

id.col: If TRUE (default), then x is the data column and y is the ID column,
indicating the groups. If FALSE, x and y are both data columns. id.col must
be FALSE only if both data columns are of the same length.

adjust.median: Should between-group differences in medians be leveled before
performing the test? In certain cases, the Siegel-Tukey test is susceptible
to median differences and may indicate significant differences in
variability that, in reality, stem from differences in medians.

rnd: Should the data be rounded and, if so, to which decimal? The default
(-1) uses the data as is. Otherwise, rnd must be a non-negative integer.
Typically, this option is not needed. However, occasionally, differences in
the precision with which certain functions return values cause the merging
of two data frames to fail within the siegel.tukey function. Only then 
rounding is necessary. This operation should not be performed if it affects
the ranks of observations.

… arguments passed on to the Wilcoxon test. See ?wilcox.test

Value: Among other output, the function returns the data, the Siegel-Tukey
ranks, the associated Wilcoxon’s W and the p-value for a Wilcoxon test on
tie-adjusted Siegel-Tukey ranks (i.e., it performs and returns a
Siegel-Tukey test). If significant, the group with the smaller rank sum has
greater variability.

References: Sidney Siegel and John Wilder Tukey (1960) “A nonparametric sum
of ranks procedure for relative spread in unpaired samples.” Journal of the
American Statistical Association. See also, David J. Sheskin (2004)
”Handbook of parametric and nonparametric statistical procedures.” 3rd
edition. Chapman and Hall/CRC. Boca Raton, FL.

Notes: The Siegel-Tukey test has relatively low power and may, under certain
conditions, indicate significance due to differences in medians rather than
differences in variabilities (consider using the argument adjust.median).

Output (in this order)

1. Group medians (after median adjustment if specified)
2. Wilcoxon-test for between-group differences in medians (after the median
adjustment if specified)
3. Data, group membership, and the Siegel-Tukey ranks
4. Mean Siegel-Tukey rank by group (smaller values indicate greater
variability)
5. Siegel-Tukey test (Wilcoxon test on tie-adjusted Siegel-Tukey ranks)



siegel.tukey=function(x,y,id.col=TRUE,adjust.median=F,rnd=-1,alternative="two.sided",mu=0,paired=FALSE,exact=FALSE,correct=TRUE,conf.int=FALSE,conf.level=0.95){
if(id.col==FALSE){
   data=data.frame(c(x,y),rep(c(0,1),c(length(x),length(y))))
   } else {
	data=data.frame(x,y)
   }
 names(data)=c("x","y")
 data=data[order(data$x),]
 if(rnd>-1){data$x=round(data$x,rnd)}

 if(adjust.median==T){
	cat("\n","Adjusting medians...","\n",sep="")
	data$x[data$y==0]=data$x[data$y==0]-(median(data$x[data$y==0]))
	data$x[data$y==1]=data$x[data$y==1]-(median(data$x[data$y==1]))
 }
 cat("\n","Median of group 1 = ",median(data$x[data$y==0]),"\n",sep="")
 cat("Median of group 2 = ",median(data$x[data$y==1]),"\n","\n",sep="")
 cat("Testing median differences...","\n")
 print(wilcox.test(data$x[data$y==0],data$x[data$y==1]))
 

 cat("Performing Siegel-Tukey rank transformation...","\n","\n")

sort.x<-sort(data$x)
sort.id<-data$y[order(data$x)]

data.matrix<-data.frame(sort.x,sort.id)

base1<-c(1,4)
iterator1<-matrix(seq(from=1,to=length(x),by=4))-1
rank1<-apply(iterator1,1,function(x) x+base)

iterator2<-matrix(seq(from=2,to=length(x),by=4))
base2<-c(0,1)
rank2<-apply(iterator2,1,function(x) x+base2)

#print(rank1)
#print(rank2)

if(length(rank1)==length(rank2)){
	rank<-c(rank1[1:floor(length(x)/2)],rev(rank2[1:ceiling(length(x)/2)]))
	} else{
	rank<-c(rank1[1:ceiling(length(x)/2)],rev(rank2[1:floor(length(x)/2)]))
}
	

unique.ranks<-tapply(rank,sort.x,mean)
unique.x<-as.numeric(as.character(names(unique.ranks)))

rank.matrix<-data.frame(unique.x,unique.ranks)

ST.matrix<-merge(data.matrix,rank.matrix,by.x="sort.x",by.y="unique.x")

print(ST.matrix)

cat("\n","Performing Siegel-Tukey test...","\n",sep="")

ranks0<-ST.matrix$unique.ranks[ST.matrix$sort.id==0]
ranks1<-ST.matrix$unique.ranks[ST.matrix$sort.id==1]

cat("\n","Mean rank of group 0: ",mean(ranks0),"\n",sep="")
cat("Mean rank of group 1: ",mean(ranks1),"\n",sep="")

print(wilcox.test(ranks0,ranks1,alternative=alternative,mu=mu,paired=paired,exact=exact,correct=correct,conf.int=conf.int,conf.level=conf.level))
}

Examples:

x <- c(33, 62, 84, 85, 88, 93, 97, 4, 16, 48, 51, 66, 98)
id <- c(0,0,0,0,0,0,0,1,1,1,1,1,1)

siegel.tukey(x,id,adjust.median=F,exact=T)

x<-c(0,0,1,4,4,5,5,6,6,9,10,10)
id<-c(0,0,0,1,1,1,1,1,1,0,0,0)

siegel.tukey(x,id)

x <- c(85,106,96, 105, 104, 108, 86)
id<-c(0,0,1,1,1,1,1)

siegel.tukey(x,id)

x<-c(177,200,227,230,232,268,272,297,47,105,126,142,158,172,197,220,225,230,262,270)
id<-c(rep(0,8),rep(1,12))

siegel.tukey(x,id,adjust.median=T)



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