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Kendall's Tau correlation matrix

*The author of this computation has been verified*

R Software Module: /rwasp_pairs.wasp (opens new window with default values)

Title produced by software: Kendall tau Correlation Matrix

Date of computation: Sun, 26 Dec 2010 11:22:08 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/26/t12933626992blkrsrh9fwxhdm.htm/, Retrieved Sun, 26 Dec 2010 12:25:00 +0100

BibTeX entries for LaTeX users:

@Manual{KEY,
    author = {{YOUR NAME}},
    publisher = {Office for Research Development and Education},
    title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2010/Dec/26/t12933626992blkrsrh9fwxhdm.htm/},
    year = {2010},
}
@Manual{R,
    title = {R: A Language and Environment for Statistical Computing},
    author = {{R Development Core Team}},
    organization = {R Foundation for Statistical Computing},
    address = {Vienna, Austria},
    year = {2010},
    note = {{ISBN} 3-900051-07-0},
    url = {http://www.R-project.org},
}

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

14450609152 9119000 15369578496 9166000 16440317952 9218000 17674829824 9283000 19782035456 9367000 21531359232 9448000 23118405632 9508000 24779487232 9557000 26495297536 9590000 29388689408 9613000 32676600000 9638000 35799700000 9673000 40077000000 9709000 45536800000 9738000 53409700000 9768000 59108700000 9795000 67180700000 9811000 72656600000 9822000 78026600000 9830000 83450800000 9837000 90756100000 9847000 95153800000 9852000 102966000000 9856000 109085000000 9856000 117854000000 9853000 125345000000 9858000 131200000000 9862000 136486000000 9870000 146033000000 9902000 158348000000 9938000 167909000000 9967400 175906000000 10004500 184714000000 10045000 190243000000 10084500 200495000000 10115600 207782000000 10136800 211399000000 10157000 221184000000 10181000 229572000000 10203000 238248000000 10226000 251741000000 10252000 258883000000 10287000 267652000000 10333000 274726000000 10376080.14 290825000000 10421120.61 302845000000 10478650 318193000000 etc...

Output produced by software:

Enter (or paste) a matrix (table) containing all data (time) series. Every column represents a different variable and must be delimited by a space or Tab. Every row represents a period in time (or category) and must be delimited by hard returns. The easiest way to enter data is to copy and paste a block of spreadsheet cells. Please, do not use commas or spaces to seperate groups of digits!

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	'RServer@AstonUniversity' @ vre.aston.ac.uk
R Framework error message	The field 'Names of X columns' contains a hard return which cannot be interpreted. Please, resubmit your request without hard returns in the 'Names of X columns'.

Correlations for all pairs of data series (method=kendall)
	GDP	Population
GDP	1	0.995
Population	0.995	1

Correlations for all pairs of data series with p-values
pair	Pearson r	Spearman rho	Kendall tau
GDP;Population	0.9552	0.9996	0.9947
p-value	(0)	(0)	(0)

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/26/t12933626992blkrsrh9fwxhdm/1jgs91293362526.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/26/t12933626992blkrsrh9fwxhdm/1jgs91293362526.ps (open in new window)

Parameters (Session):

par1 = kendall ;

Parameters (R input):

par1 = kendall ;

R code (references can be found in the software module):

panel.tau <- function(x, y, digits=2, prefix='', cex.cor)

{

usr <- par('usr'); on.exit(par(usr))

par(usr = c(0, 1, 0, 1))

rr <- cor.test(x, y, method=par1)

r <- round(rr$p.value,2)

txt <- format(c(r, 0.123456789), digits=digits)[1]

txt <- paste(prefix, txt, sep='')

if(missing(cex.cor)) cex <- 0.5/strwidth(txt)

text(0.5, 0.5, txt, cex = cex)

}

panel.hist <- function(x, ...)

{

usr <- par('usr'); on.exit(par(usr))

par(usr = c(usr[1:2], 0, 1.5) )

h <- hist(x, plot = FALSE)

breaks <- h$breaks; nB <- length(breaks)

y <- h$counts; y <- y/max(y)

rect(breaks[-nB], 0, breaks[-1], y, col='grey', ...)

}

bitmap(file='test1.png')

pairs(t(y),diag.panel=panel.hist, upper.panel=panel.smooth, lower.panel=panel.tau, main=main)

dev.off()

load(file='createtable')

n <- length(y[,1])

n

a<-table.start()

a<-table.row.start(a)

a<-table.element(a,paste('Correlations for all pairs of data series (method=',par1,')',sep=''),n+1,TRUE)

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a,' ',header=TRUE)

for (i in 1:n) {

a<-table.element(a,dimnames(t(x))[[2]][i],header=TRUE)

}

a<-table.row.end(a)

for (i in 1:n) {

a<-table.row.start(a)

a<-table.element(a,dimnames(t(x))[[2]][i],header=TRUE)

for (j in 1:n) {

r <- cor.test(y[i,],y[j,],method=par1)

a<-table.element(a,round(r$estimate,3))

}

a<-table.row.end(a)

}

a<-table.end(a)

table.save(a,file='mytable.tab')

a<-table.start()

a<-table.row.start(a)

a<-table.element(a,'Correlations for all pairs of data series with p-values',4,TRUE)

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a,'pair',1,TRUE)

a<-table.element(a,'Pearson r',1,TRUE)

a<-table.element(a,'Spearman rho',1,TRUE)

a<-table.element(a,'Kendall tau',1,TRUE)

a<-table.row.end(a)

cor.test(y[1,],y[2,],method=par1)

for (i in 1:(n-1))

{

for (j in (i+1):n)

{

a<-table.row.start(a)

dum <- paste(dimnames(t(x))[[2]][i],';',dimnames(t(x))[[2]][j],sep='')

a<-table.element(a,dum,header=TRUE)

rp <- cor.test(y[i,],y[j,],method='pearson')

a<-table.element(a,round(rp$estimate,4))

rs <- cor.test(y[i,],y[j,],method='spearman')

a<-table.element(a,round(rs$estimate,4))

rk <- cor.test(y[i,],y[j,],method='kendall')

a<-table.element(a,round(rk$estimate,4))

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a,'p-value',header=T)

a<-table.element(a,paste('(',round(rp$p.value,4),')',sep=''))

a<-table.element(a,paste('(',round(rs$p.value,4),')',sep=''))

a<-table.element(a,paste('(',round(rk$p.value,4),')',sep=''))

a<-table.row.end(a)

}

}

a<-table.end(a)

table.save(a,file='mytable1.tab')

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa

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