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*The author of this computation has been verified*

R Software Module

rwasp_pairs.wasp

Title produced by software

Kendall tau Correlation Matrix

Date of computation

Fri, 08 Jan 2016 15:01:17 +0000

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Jan/08/t14522652891nup8d5rpt0udif.htm/, Retrieved Sun, 28 Apr 2024 02:08:01 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=287427, Retrieved Sun, 28 Apr 2024 02:08:01 +0000

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Estimated Impact

128

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-       [Kendall tau Correlation Matrix] [kendall tau] [2016-01-08 15:01:17] [d474e8108ba0b0c845f49e9b6dcf374b] [Current]

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Dataseries X:

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Histogram

Boxplots

68.5 46.4 392 0.4
87.8 45.7 118 0.61
115.8 45.3 44 0.53
106.8 38.6 158 0.53
71.6 37.2 81 0.53
60.2 35 374 0.37
118.7 34 187 0.3
33.7 28.3 993 0.19
27.2 24.7 1723 0.12
62 24.7 287 0.2
24.9 24.4 970 0.19
22.9 22.7 885 0.12
65.7 22.3 200 0.53
21.6 21.7 575 0.14
32.4 21.6 688 0.34
108.7 21.3 48 0.69
38.6 21.2 572 0.49
46.7 20.8 239 0.42
56.5 20.3 244 0.48
44.4 18.9 472 0.25
47.4 18.8 134 0.52
21.7 18.6 633 0.19
55.7 18 295 0.44
27.1 17.6 906 0.24
28.5 17 1045 0.16
41.6 16.7 775 0.1
44.6 15.9 619 0.15
26.1 15.3 901 0.05
18.7 15 910 0.24
49.1 14.8 556 0.22

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	'Sir Maurice George Kendall' @ kendall.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=287427&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=287427&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=287427&T=0

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

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	'Sir Maurice George Kendall' @ kendall.wessa.net

Correlations for all pairs of data series (method=kendall)
	Homicides	HIV_Risk	Per_Capita_Income	Prop_Population_on_Farms
Homicides	1	0.359	-0.646	0.54
HIV_Risk	0.359	1	-0.29	0.329
Per_Capita_Income	-0.646	-0.29	1	-0.652
Prop_Population_on_Farms	0.54	0.329	-0.652	1

\begin{tabular}{lllllllll}
\hline
Correlations for all pairs of data series (method=kendall) \tabularnewline
  & Homicides & HIV_Risk & Per_Capita_Income & Prop_Population_on_Farms \tabularnewline
Homicides & 1 & 0.359 & -0.646 & 0.54 \tabularnewline
HIV_Risk & 0.359 & 1 & -0.29 & 0.329 \tabularnewline
Per_Capita_Income & -0.646 & -0.29 & 1 & -0.652 \tabularnewline
Prop_Population_on_Farms & 0.54 & 0.329 & -0.652 & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=287427&T=1

[TABLE]
[ROW][C]Correlations for all pairs of data series (method=kendall)[/C][/ROW]
[ROW][C] [/C][C]Homicides[/C][C]HIV_Risk[/C][C]Per_Capita_Income[/C][C]Prop_Population_on_Farms[/C][/ROW]
[ROW][C]Homicides[/C][C]1[/C][C]0.359[/C][C]-0.646[/C][C]0.54[/C][/ROW]
[ROW][C]HIV_Risk[/C][C]0.359[/C][C]1[/C][C]-0.29[/C][C]0.329[/C][/ROW]
[ROW][C]Per_Capita_Income[/C][C]-0.646[/C][C]-0.29[/C][C]1[/C][C]-0.652[/C][/ROW]
[ROW][C]Prop_Population_on_Farms[/C][C]0.54[/C][C]0.329[/C][C]-0.652[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=287427&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=287427&T=1

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Correlations for all pairs of data series (method=kendall)
	Homicides	HIV_Risk	Per_Capita_Income	Prop_Population_on_Farms
Homicides	1	0.359	-0.646	0.54
HIV_Risk	0.359	1	-0.29	0.329
Per_Capita_Income	-0.646	-0.29	1	-0.652
Prop_Population_on_Farms	0.54	0.329	-0.652	1

Correlations for all pairs of data series with p-values
pair	Pearson r	Spearman rho	Kendall tau
Homicides;HIV_Risk	0.6643	0.5293	0.359
p-value	(1e-04)	(0.0026)	(0.0054)
Homicides;Per_Capita_Income	-0.7455	-0.8541	-0.646
p-value	(0)	(0)	(0)
Homicides;Prop_Population_on_Farms	0.6964	0.737	0.5402
p-value	(0)	(0)	(0)
HIV_Risk;Per_Capita_Income	-0.4191	-0.4232	-0.29
p-value	(0.0212)	(0.0198)	(0.0246)
HIV_Risk;Prop_Population_on_Farms	0.4804	0.4216	0.3287
p-value	(0.0072)	(0.0203)	(0.0117)
Per_Capita_Income;Prop_Population_on_Farms	-0.7755	-0.8293	-0.652
p-value	(0)	(0)	(0)

\begin{tabular}{lllllllll}
\hline
Correlations for all pairs of data series with p-values \tabularnewline
pair & Pearson r & Spearman rho & Kendall tau \tabularnewline
Homicides;HIV_Risk & 0.6643 & 0.5293 & 0.359 \tabularnewline
p-value & (1e-04) & (0.0026) & (0.0054) \tabularnewline
Homicides;Per_Capita_Income & -0.7455 & -0.8541 & -0.646 \tabularnewline
p-value & (0) & (0) & (0) \tabularnewline
Homicides;Prop_Population_on_Farms & 0.6964 & 0.737 & 0.5402 \tabularnewline
p-value & (0) & (0) & (0) \tabularnewline
HIV_Risk;Per_Capita_Income & -0.4191 & -0.4232 & -0.29 \tabularnewline
p-value & (0.0212) & (0.0198) & (0.0246) \tabularnewline
HIV_Risk;Prop_Population_on_Farms & 0.4804 & 0.4216 & 0.3287 \tabularnewline
p-value & (0.0072) & (0.0203) & (0.0117) \tabularnewline
Per_Capita_Income;Prop_Population_on_Farms & -0.7755 & -0.8293 & -0.652 \tabularnewline
p-value & (0) & (0) & (0) \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=287427&T=2

[TABLE]
[ROW][C]Correlations for all pairs of data series with p-values[/C][/ROW]
[ROW][C]pair[/C][C]Pearson r[/C][C]Spearman rho[/C][C]Kendall tau[/C][/ROW]
[ROW][C]Homicides;HIV_Risk[/C][C]0.6643[/C][C]0.5293[/C][C]0.359[/C][/ROW]
[ROW][C]p-value[/C][C](1e-04)[/C][C](0.0026)[/C][C](0.0054)[/C][/ROW]
[ROW][C]Homicides;Per_Capita_Income[/C][C]-0.7455[/C][C]-0.8541[/C][C]-0.646[/C][/ROW]
[ROW][C]p-value[/C][C](0)[/C][C](0)[/C][C](0)[/C][/ROW]
[ROW][C]Homicides;Prop_Population_on_Farms[/C][C]0.6964[/C][C]0.737[/C][C]0.5402[/C][/ROW]
[ROW][C]p-value[/C][C](0)[/C][C](0)[/C][C](0)[/C][/ROW]
[ROW][C]HIV_Risk;Per_Capita_Income[/C][C]-0.4191[/C][C]-0.4232[/C][C]-0.29[/C][/ROW]
[ROW][C]p-value[/C][C](0.0212)[/C][C](0.0198)[/C][C](0.0246)[/C][/ROW]
[ROW][C]HIV_Risk;Prop_Population_on_Farms[/C][C]0.4804[/C][C]0.4216[/C][C]0.3287[/C][/ROW]
[ROW][C]p-value[/C][C](0.0072)[/C][C](0.0203)[/C][C](0.0117)[/C][/ROW]
[ROW][C]Per_Capita_Income;Prop_Population_on_Farms[/C][C]-0.7755[/C][C]-0.8293[/C][C]-0.652[/C][/ROW]
[ROW][C]p-value[/C][C](0)[/C][C](0)[/C][C](0)[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=287427&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=287427&T=2

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Correlations for all pairs of data series with p-values
pair	Pearson r	Spearman rho	Kendall tau
Homicides;HIV_Risk	0.6643	0.5293	0.359
p-value	(1e-04)	(0.0026)	(0.0054)
Homicides;Per_Capita_Income	-0.7455	-0.8541	-0.646
p-value	(0)	(0)	(0)
Homicides;Prop_Population_on_Farms	0.6964	0.737	0.5402
p-value	(0)	(0)	(0)
HIV_Risk;Per_Capita_Income	-0.4191	-0.4232	-0.29
p-value	(0.0212)	(0.0198)	(0.0246)
HIV_Risk;Prop_Population_on_Farms	0.4804	0.4216	0.3287
p-value	(0.0072)	(0.0203)	(0.0117)
Per_Capita_Income;Prop_Population_on_Farms	-0.7755	-0.8293	-0.652
p-value	(0)	(0)	(0)

Meta Analysis of Correlation Tests
Number of significant by total number of Correlations
Type I error	Pearson r	Spearman rho	Kendall tau
0.01	0.83	0.67	0.67
0.02	0.83	0.83	0.83
0.03	1	1	1
0.04	1	1	1
0.05	1	1	1
0.06	1	1	1
0.07	1	1	1
0.08	1	1	1
0.09	1	1	1
0.1	1	1	1

\begin{tabular}{lllllllll}
\hline
Meta Analysis of Correlation Tests \tabularnewline
Number of significant by total number of Correlations \tabularnewline
Type I error & Pearson r & Spearman rho & Kendall tau \tabularnewline
0.01 & 0.83 & 0.67 & 0.67 \tabularnewline
0.02 & 0.83 & 0.83 & 0.83 \tabularnewline
0.03 & 1 & 1 & 1 \tabularnewline
0.04 & 1 & 1 & 1 \tabularnewline
0.05 & 1 & 1 & 1 \tabularnewline
0.06 & 1 & 1 & 1 \tabularnewline
0.07 & 1 & 1 & 1 \tabularnewline
0.08 & 1 & 1 & 1 \tabularnewline
0.09 & 1 & 1 & 1 \tabularnewline
0.1 & 1 & 1 & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=287427&T=3

[TABLE]
[ROW][C]Meta Analysis of Correlation Tests[/C][/ROW]
[ROW][C]Number of significant by total number of Correlations[/C][/ROW]
[ROW][C]Type I error[/C][C]Pearson r[/C][C]Spearman rho[/C][C]Kendall tau[/C][/ROW]
[ROW][C]0.01[/C][C]0.83[/C][C]0.67[/C][C]0.67[/C][/ROW]
[ROW][C]0.02[/C][C]0.83[/C][C]0.83[/C][C]0.83[/C][/ROW]
[ROW][C]0.03[/C][C]1[/C][C]1[/C][C]1[/C][/ROW]
[ROW][C]0.04[/C][C]1[/C][C]1[/C][C]1[/C][/ROW]
[ROW][C]0.05[/C][C]1[/C][C]1[/C][C]1[/C][/ROW]
[ROW][C]0.06[/C][C]1[/C][C]1[/C][C]1[/C][/ROW]
[ROW][C]0.07[/C][C]1[/C][C]1[/C][C]1[/C][/ROW]
[ROW][C]0.08[/C][C]1[/C][C]1[/C][C]1[/C][/ROW]
[ROW][C]0.09[/C][C]1[/C][C]1[/C][C]1[/C][/ROW]
[ROW][C]0.1[/C][C]1[/C][C]1[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=287427&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=287427&T=3

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Meta Analysis of Correlation Tests
Number of significant by total number of Correlations
Type I error	Pearson r	Spearman rho	Kendall tau
0.01	0.83	0.67	0.67
0.02	0.83	0.83	0.83
0.03	1	1	1
0.04	1	1	1
0.05	1	1	1
0.06	1	1	1
0.07	1	1	1
0.08	1	1	1
0.09	1	1	1
0.1	1	1	1

Figure 1

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 1 ; par2 = 2 ; par3 = 0,99 ; par4 = two.sided ; par5 = paired ; par6 = 0 ;

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$counts; y <- y/max(y)
rect(breaks[-nB], 0, breaks[-1], y, col='grey', ...)
}
x <- na.omit(x)
y <- t(na.omit(t(y)))
bitmap(file='test1.png')
pairs(t(y),diag.panel=panel.hist, upper.panel=panel.smooth, lower.panel=panel.tau, main=main)
dev.off()
load(file='createtable')
n <- length(y[,1])
n
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,paste('Correlations for all pairs of data series (method=',par1,')',sep=''),n+1,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,' ',header=TRUE)
for (i in 1:n) {
a<-table.element(a,dimnames(t(x))[[2]][i],header=TRUE)
}
a<-table.row.end(a)
for (i in 1:n) {
a<-table.row.start(a)
a<-table.element(a,dimnames(t(x))[[2]][i],header=TRUE)
for (j in 1:n) {
r <- cor.test(y[i,],y[j,],method=par1)
a<-table.element(a,round(r$estimate,3))
}
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable.tab')
ncorrs <- (n*n -n)/2
mycorrs <- array(0, dim=c(10,3))
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)
for (iii in 1:10) {
iiid100 <- iii / 100
if (rp$p.value < iiid100) mycorrs[iii, 1] = mycorrs[iii, 1] + 1
if (rs$p.value < iiid100) mycorrs[iii, 2] = mycorrs[iii, 2] + 1
if (rk$p.value < iiid100) mycorrs[iii, 3] = mycorrs[iii, 3] + 1
}
}
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Meta Analysis of Correlation Tests',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Number of significant by total number of Correlations',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Type I error',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)
for (iii in 1:10) {
iiid100 <- iii / 100
a<-table.row.start(a)
a<-table.element(a,round(iiid100,2),header=T)
a<-table.element(a,round(mycorrs[iii,1]/ncorrs,2))
a<-table.element(a,round(mycorrs[iii,2]/ncorrs,2))
a<-table.element(a,round(mycorrs[iii,3]/ncorrs,2))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code