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Author*The author of this computation has been verified*
R Software Modulerwasp_pairs.wasp
Title produced by softwareKendall tau Correlation Matrix
Date of computationTue, 06 Dec 2016 18:32:09 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Dec/06/t1481045815k7cs7gu8lqf0gh8.htm/, Retrieved Sat, 04 May 2024 08:15:23 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=297885, Retrieved Sat, 04 May 2024 08:15:23 +0000
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-       [Kendall tau Correlation Matrix] [Correlation Matrices] [2016-12-06 17:32:09] [3c8d1d1050061614560bf423eb580e6a] [Current]
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Dataseries X:
4	5	5	4	14
5	5	5	4	19
5	5	4	4	17
3	4	4	4	17
5	5	5	4	15
5	5	5	4	20
5	4	5	5	15
4	4	4	4	19
5	5	4	4	15
5	5	5	5	15
4	3	4	3	19
3	5	4	3	15
4	5	5	4	20
5	5	5	4	18
5	4	5	4	14
4	5	5	4	20
5	4	4	4	16
5	4	5	5	16
5	5	5	4	16
3	5	5	4	10
4	5	5	4	19
4	4	4	4	19
5	5	5	5	16
3	4	3	3	15
5	5	4	5	18
4	4	4	3	17
4	5	4	4	19
4	5	4	4	17
5	4	5	3	19
5	5	5	4	19
5	5	5	5	16
4	4	4	4	15
5	4	4	4	16
4	4	4	4	18
4	4	4	4	17
4	3	4	3	14
5	5	4	3	20
5	4	5	4	19
4	4	4	4	7
4	4	4	4	13
4	4	4	1	16
4	4	4	4	16
5	5	5	4	18
4	4	4	4	18
5	5	5	4	17
4	5	4	4	19
4	5	4	4	16
5	4	3	4	13
4	4	4	4	16
5	4	4	3	13
4	5	4	4	12
4	5	5	4	17
4	5	5	4	17
5	5	5	3	17
5	5	5	4	16
4	2	4	3	14
4	4	4	3	16
4	5	5	4	20
5	5	5	4	13
5	5	4	3	14
5	5	5	4	19
4	5	5	5	18
5	5	5	4	18
4	5	5	4	19
4	4	4	4	14
4	3	4	4	17
5	5	5	5	19
4	4	4	4	19
5	5	5	5	18
5	5	5	5	20
4	5	5	4	15
5	4	2	4	15
4	3	4	3	15
4	4	4	4	20
3	4	3	4	15
4	5	5	4	19
5	5	5	5	18
5	5	5	5	18
4	5	5	4	15
5	5	5	5	20
3	4	4	3	17
4	5	4	4	18
3	4	4	3	20
5	5	5	5	17
4	5	4	5	16
4	5	4	4	18
4	5	4	4	18
5	4	5	5	14
4	4	4	4	18
5	5	5	5	17
5	5	5	5	20
5	5	5	3	16
4	5	4	4	14
5	4	5	5	15
4	5	5	4	18
5	5	5	4	20
5	4	3	5	17
5	5	4	4	17
4	5	4	4	17
4	4	4	4	17
5	5	4	4	17
4	5	4	4	18
5	5	4	4	17
5	5	5	5	15
4	3	4	3	16
4	5	4	4	15
3	3	2	5	18
4	5	4	4	15
4	5	5	4	18
4	4	4	4	20
5	5	5	4	14
3	5	5	4	15
4	5	4	3	17
4	5	4	4	18
5	5	4	3	20
4	5	4	4	17
5	5	5	5	18
3	4	4	3	15
5	5	5	5	16
3	5	5	3	15
5	5	5	4	18
4	5	4	4	17
5	5	5	4	18
4	5	4	3	15
5	4	5	4	17
5	4	2	5	19
4	5	4	4	18
4	5	5	4	19
4	4	5	3	16
4	5	4	4	16
4	4	4	3	16
5	5	5	3	14




Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R ServerBig Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time1 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=297885&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]1 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=297885&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=297885&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 Outputview raw output of R engine
Computing time1 seconds
R ServerBig Analytics Cloud Computing Center







Correlations for all pairs of data series (method=kendall)
IK1IK2IK3IK4ITH
IK110.2350.4010.3560.065
IK20.23510.4540.2270.154
IK30.4010.45410.2810.121
IK40.3560.2270.28110.129
ITH0.0650.1540.1210.1291

\begin{tabular}{lllllllll}
\hline
Correlations for all pairs of data series (method=kendall) \tabularnewline
  & IK1 & IK2 & IK3 & IK4 & ITH \tabularnewline
IK1 & 1 & 0.235 & 0.401 & 0.356 & 0.065 \tabularnewline
IK2 & 0.235 & 1 & 0.454 & 0.227 & 0.154 \tabularnewline
IK3 & 0.401 & 0.454 & 1 & 0.281 & 0.121 \tabularnewline
IK4 & 0.356 & 0.227 & 0.281 & 1 & 0.129 \tabularnewline
ITH & 0.065 & 0.154 & 0.121 & 0.129 & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=297885&T=1

[TABLE]
[ROW][C]Correlations for all pairs of data series (method=kendall)[/C][/ROW]
[ROW][C] [/C][C]IK1[/C][C]IK2[/C][C]IK3[/C][C]IK4[/C][C]ITH[/C][/ROW]
[ROW][C]IK1[/C][C]1[/C][C]0.235[/C][C]0.401[/C][C]0.356[/C][C]0.065[/C][/ROW]
[ROW][C]IK2[/C][C]0.235[/C][C]1[/C][C]0.454[/C][C]0.227[/C][C]0.154[/C][/ROW]
[ROW][C]IK3[/C][C]0.401[/C][C]0.454[/C][C]1[/C][C]0.281[/C][C]0.121[/C][/ROW]
[ROW][C]IK4[/C][C]0.356[/C][C]0.227[/C][C]0.281[/C][C]1[/C][C]0.129[/C][/ROW]
[ROW][C]ITH[/C][C]0.065[/C][C]0.154[/C][C]0.121[/C][C]0.129[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=297885&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=297885&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)
IK1IK2IK3IK4ITH
IK110.2350.4010.3560.065
IK20.23510.4540.2270.154
IK30.4010.45410.2810.121
IK40.3560.2270.28110.129
ITH0.0650.1540.1210.1291







Correlations for all pairs of data series with p-values
pairPearson rSpearman rhoKendall tau
IK1;IK20.25910.24920.2347
p-value(0.0027)(0.004)(0.0046)
IK1;IK30.34430.41510.4011
p-value(1e-04)(0)(0)
IK1;IK40.36160.37610.3557
p-value(0)(0)(0)
IK1;ITH0.11610.07670.0652
p-value(0.1848)(0.3821)(0.3762)
IK2;IK30.46570.47560.4536
p-value(0)(0)(0)
IK2;IK40.26980.24270.2274
p-value(0.0018)(0.005)(0.0053)
IK2;ITH0.17780.18080.154
p-value(0.0414)(0.038)(0.0384)
IK3;IK40.1920.29890.2805
p-value(0.0274)(5e-04)(6e-04)
IK3;ITH0.11590.1410.1205
p-value(0.1858)(0.1067)(0.1047)
IK4;ITH0.13670.15920.1291
p-value(0.118)(0.0682)(0.0755)

\begin{tabular}{lllllllll}
\hline
Correlations for all pairs of data series with p-values \tabularnewline
pair & Pearson r & Spearman rho & Kendall tau \tabularnewline
IK1;IK2 & 0.2591 & 0.2492 & 0.2347 \tabularnewline
p-value & (0.0027) & (0.004) & (0.0046) \tabularnewline
IK1;IK3 & 0.3443 & 0.4151 & 0.4011 \tabularnewline
p-value & (1e-04) & (0) & (0) \tabularnewline
IK1;IK4 & 0.3616 & 0.3761 & 0.3557 \tabularnewline
p-value & (0) & (0) & (0) \tabularnewline
IK1;ITH & 0.1161 & 0.0767 & 0.0652 \tabularnewline
p-value & (0.1848) & (0.3821) & (0.3762) \tabularnewline
IK2;IK3 & 0.4657 & 0.4756 & 0.4536 \tabularnewline
p-value & (0) & (0) & (0) \tabularnewline
IK2;IK4 & 0.2698 & 0.2427 & 0.2274 \tabularnewline
p-value & (0.0018) & (0.005) & (0.0053) \tabularnewline
IK2;ITH & 0.1778 & 0.1808 & 0.154 \tabularnewline
p-value & (0.0414) & (0.038) & (0.0384) \tabularnewline
IK3;IK4 & 0.192 & 0.2989 & 0.2805 \tabularnewline
p-value & (0.0274) & (5e-04) & (6e-04) \tabularnewline
IK3;ITH & 0.1159 & 0.141 & 0.1205 \tabularnewline
p-value & (0.1858) & (0.1067) & (0.1047) \tabularnewline
IK4;ITH & 0.1367 & 0.1592 & 0.1291 \tabularnewline
p-value & (0.118) & (0.0682) & (0.0755) \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=297885&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]IK1;IK2[/C][C]0.2591[/C][C]0.2492[/C][C]0.2347[/C][/ROW]
[ROW][C]p-value[/C][C](0.0027)[/C][C](0.004)[/C][C](0.0046)[/C][/ROW]
[ROW][C]IK1;IK3[/C][C]0.3443[/C][C]0.4151[/C][C]0.4011[/C][/ROW]
[ROW][C]p-value[/C][C](1e-04)[/C][C](0)[/C][C](0)[/C][/ROW]
[ROW][C]IK1;IK4[/C][C]0.3616[/C][C]0.3761[/C][C]0.3557[/C][/ROW]
[ROW][C]p-value[/C][C](0)[/C][C](0)[/C][C](0)[/C][/ROW]
[ROW][C]IK1;ITH[/C][C]0.1161[/C][C]0.0767[/C][C]0.0652[/C][/ROW]
[ROW][C]p-value[/C][C](0.1848)[/C][C](0.3821)[/C][C](0.3762)[/C][/ROW]
[ROW][C]IK2;IK3[/C][C]0.4657[/C][C]0.4756[/C][C]0.4536[/C][/ROW]
[ROW][C]p-value[/C][C](0)[/C][C](0)[/C][C](0)[/C][/ROW]
[ROW][C]IK2;IK4[/C][C]0.2698[/C][C]0.2427[/C][C]0.2274[/C][/ROW]
[ROW][C]p-value[/C][C](0.0018)[/C][C](0.005)[/C][C](0.0053)[/C][/ROW]
[ROW][C]IK2;ITH[/C][C]0.1778[/C][C]0.1808[/C][C]0.154[/C][/ROW]
[ROW][C]p-value[/C][C](0.0414)[/C][C](0.038)[/C][C](0.0384)[/C][/ROW]
[ROW][C]IK3;IK4[/C][C]0.192[/C][C]0.2989[/C][C]0.2805[/C][/ROW]
[ROW][C]p-value[/C][C](0.0274)[/C][C](5e-04)[/C][C](6e-04)[/C][/ROW]
[ROW][C]IK3;ITH[/C][C]0.1159[/C][C]0.141[/C][C]0.1205[/C][/ROW]
[ROW][C]p-value[/C][C](0.1858)[/C][C](0.1067)[/C][C](0.1047)[/C][/ROW]
[ROW][C]IK4;ITH[/C][C]0.1367[/C][C]0.1592[/C][C]0.1291[/C][/ROW]
[ROW][C]p-value[/C][C](0.118)[/C][C](0.0682)[/C][C](0.0755)[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=297885&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=297885&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
pairPearson rSpearman rhoKendall tau
IK1;IK20.25910.24920.2347
p-value(0.0027)(0.004)(0.0046)
IK1;IK30.34430.41510.4011
p-value(1e-04)(0)(0)
IK1;IK40.36160.37610.3557
p-value(0)(0)(0)
IK1;ITH0.11610.07670.0652
p-value(0.1848)(0.3821)(0.3762)
IK2;IK30.46570.47560.4536
p-value(0)(0)(0)
IK2;IK40.26980.24270.2274
p-value(0.0018)(0.005)(0.0053)
IK2;ITH0.17780.18080.154
p-value(0.0414)(0.038)(0.0384)
IK3;IK40.1920.29890.2805
p-value(0.0274)(5e-04)(6e-04)
IK3;ITH0.11590.1410.1205
p-value(0.1858)(0.1067)(0.1047)
IK4;ITH0.13670.15920.1291
p-value(0.118)(0.0682)(0.0755)







Meta Analysis of Correlation Tests
Number of significant by total number of Correlations
Type I errorPearson rSpearman rhoKendall tau
0.010.50.60.6
0.020.50.60.6
0.030.60.60.6
0.040.60.70.7
0.050.70.70.7
0.060.70.70.7
0.070.70.80.7
0.080.70.80.8
0.090.70.80.8
0.10.70.80.8

\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 & 0.5 & 0.6 & 0.6 \tabularnewline
0.02 & 0.5 & 0.6 & 0.6 \tabularnewline
0.03 & 0.6 & 0.6 & 0.6 \tabularnewline
0.04 & 0.6 & 0.7 & 0.7 \tabularnewline
0.05 & 0.7 & 0.7 & 0.7 \tabularnewline
0.06 & 0.7 & 0.7 & 0.7 \tabularnewline
0.07 & 0.7 & 0.8 & 0.7 \tabularnewline
0.08 & 0.7 & 0.8 & 0.8 \tabularnewline
0.09 & 0.7 & 0.8 & 0.8 \tabularnewline
0.1 & 0.7 & 0.8 & 0.8 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=297885&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]0.5[/C][C]0.6[/C][C]0.6[/C][/ROW]
[ROW][C]0.02[/C][C]0.5[/C][C]0.6[/C][C]0.6[/C][/ROW]
[ROW][C]0.03[/C][C]0.6[/C][C]0.6[/C][C]0.6[/C][/ROW]
[ROW][C]0.04[/C][C]0.6[/C][C]0.7[/C][C]0.7[/C][/ROW]
[ROW][C]0.05[/C][C]0.7[/C][C]0.7[/C][C]0.7[/C][/ROW]
[ROW][C]0.06[/C][C]0.7[/C][C]0.7[/C][C]0.7[/C][/ROW]
[ROW][C]0.07[/C][C]0.7[/C][C]0.8[/C][C]0.7[/C][/ROW]
[ROW][C]0.08[/C][C]0.7[/C][C]0.8[/C][C]0.8[/C][/ROW]
[ROW][C]0.09[/C][C]0.7[/C][C]0.8[/C][C]0.8[/C][/ROW]
[ROW][C]0.1[/C][C]0.7[/C][C]0.8[/C][C]0.8[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=297885&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=297885&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 errorPearson rSpearman rhoKendall tau
0.010.50.60.6
0.020.50.60.6
0.030.60.60.6
0.040.60.70.7
0.050.70.70.7
0.060.70.70.7
0.070.70.80.7
0.080.70.80.8
0.090.70.80.8
0.10.70.80.8



Parameters (Session):
par1 = 5 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ; par4 = 0 ; par5 = 0 ;
Parameters (R input):
par1 = kendall ;
R code (references can be found in the software module):
par1 <- 'kendall'
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$counts; y <- y/max(y)
rect(breaks[-nB], 0, breaks[-1], y, col='grey', ...)
}
x <- na.omit(x)
y <- t(na.omit(t(y)))
bitmap(file='test1.png')
pairs(t(y),diag.panel=panel.hist, upper.panel=panel.smooth, lower.panel=panel.tau, main=main)
dev.off()
load(file='createtable')
n <- length(y[,1])
print(n)
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,paste('Correlations for all pairs of data series (method=',par1,')',sep=''),n+1,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,' ',header=TRUE)
for (i in 1:n) {
a<-table.element(a,dimnames(t(x))[[2]][i],header=TRUE)
}
a<-table.row.end(a)
for (i in 1:n) {
a<-table.row.start(a)
a<-table.element(a,dimnames(t(x))[[2]][i],header=TRUE)
for (j in 1:n) {
r <- cor.test(y[i,],y[j,],method=par1)
a<-table.element(a,round(r$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')