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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_pairs.wasp
Title produced by softwareKendall tau Correlation Matrix
Date of computationFri, 16 Dec 2016 11:27:32 +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/16/t14818840675d7vn7z5bdt1dhz.htm/, Retrieved Thu, 02 May 2024 17:44:50 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=300169, Retrieved Thu, 02 May 2024 17:44:50 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact66

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Kendall tau Correlation Matrix] [] [2016-12-16 10:27:32] [ab21f94b493a02d0f1353f0a7f852860] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
22	4	5	5	4
24	5	5	5	4
21	5	5	4	4
21	3	4	4	4
24	5	5	5	4
20	5	5	5	4
22	5	4	5	5
20	4	NA	4	4
19	5	5	4	4
23	5	5	5	5
21	4	3	4	3
19	3	5	4	3
19	4	5	5	4
21	5	5	5	4
21	4	4	4	4
22	5	4	5	4
22	4	5	5	4
19	NA	NA	NA	NA
21	5	4	4	4
21	5	4	5	5
21	5	5	5	4
20	3	5	5	4
22	4	5	5	4
22	4	4	4	4
24	5	5	5	5
21	3	4	3	3
19	5	5	4	5
19	4	4	4	3
23	4	5	4	4
21	4	5	4	4
21	4	3	5	4
19	5	4	5	3
21	5	5	5	4
19	4	4	5	5
21	5	5	5	4
21	5	5	5	5
23	4	4	4	4
19	5	4	4	4
19	4	4	4	4
19	4	5	4	3
18	4	4	4	4
22	4	4	4	4
18	4	3	4	3
22	5	5	4	3
18	5	4	5	4
22	4	4	4	4
22	4	4	4	4
19	4	NA	4	1
22	4	4	4	4
25	4	4	4	3
19	5	5	5	4
19	4	4	4	4
19	4	5	4	4
19	5	5	5	4
21	4	5	4	4
21	4	5	4	4
20	4	4	4	3
19	5	4	3	4
19	4	4	4	4
22	5	4	4	3
26	4	5	4	4
19	4	5	5	4
21	4	5	5	4
21	5	5	5	3
20	5	5	5	4
23	4	4	3	3
22	4	2	4	3
22	4	5	5	4
22	4	4	4	4
21	4	4	4	3
21	4	5	5	4
22	4	5	5	4
23	2	5	4	5
18	5	5	5	4
24	4	5	4	4
22	5	5	4	3
21	5	5	5	4
21	4	5	5	5
21	5	5	5	5
23	5	5	5	4
21	4	5	5	4
23	4	4	4	4
21	4	4	4	4
19	4	3	4	4
21	5	5	5	5
21	4	5	4	3
21	4	4	4	4
23	5	5	5	5
23	5	5	5	5
20	4	5	5	4
20	5	4	2	4
19	4	3	4	3
23	4	4	4	4
22	3	4	3	4
19	4	5	5	4
23	5	5	5	5
22	5	5	5	5
22	4	5	5	4
21	5	5	5	5
21	3	4	4	3
21	5	5	5	5
21	4	5	4	4
22	5	5	5	5
25	3	4	4	3
21	4	4	4	4
23	5	5	5	5
19	5	5	5	4
22	4	5	4	5
20	4	5	4	4
21	4	5	4	4
25	5	4	5	5
21	4	4	4	3
19	5	4	5	4
23	4	3	4	4
22	4	4	4	4
21	4	4	4	4
24	5	5	5	5
21	5	5	4	4
19	5	5	5	5
18	5	5	5	3
19	4	5	4	4
20	5	4	5	5
19	4	5	5	4
22	5	5	5	4
21	5	4	3	5
22	5	5	4	4
24	4	5	4	4
28	4	4	4	4
19	5	5	5	4
18	5	5	4	4
23	4	5	4	4
19	5	5	4	4
23	4	4	4	4
19	5	5	5	5
22	4	3	4	3
21	4	5	4	4
19	3	3	2	5
22	2	3	4	4
21	4	5	4	4
23	4	5	5	4
22	4	4	4	4
19	4	5	NA	4
19	5	5	5	4
21	5	5	4	NA
22	3	5	5	4
21	4	5	4	3
20	4	5	4	4
23	5	5	4	3
22	4	5	4	4
23	5	5	5	5
22	3	4	4	3
21	5	5	5	5
20	5	5	5	4
18	3	5	5	3
18	5	5	5	4
20	4	5	4	4
19	5	5	5	4
21	5	5	5	5
24	5	4	5	5
19	5	5	5	4
20	4	5	4	3
19	5	4	5	4
23	5	4	2	5
22	4	5	4	4
21	4	5	5	4
24	4	4	5	3
21	4	5	4	4
21	4	4	4	3
22	5	5	5	3

Tables (Output of Computation)





Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time0 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 time0 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300169&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]0 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=300169&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300169&T=0

As an alternative you can also use a QR Code:  
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 time0 seconds
R ServerBig Analytics Cloud Computing Center






Correlations for all pairs of data series (method=pearson)
abcde
a1-0.093-0.034-0.0520.116
b-0.09310.2980.380.325
c-0.0340.29810.4360.242
d-0.0520.380.43610.255
e0.1160.3250.2420.2551

\begin{tabular}{lllllllll}
\hline
Correlations for all pairs of data series (method=pearson) \tabularnewline
  & a & b & c & d & e \tabularnewline
a & 1 & -0.093 & -0.034 & -0.052 & 0.116 \tabularnewline
b & -0.093 & 1 & 0.298 & 0.38 & 0.325 \tabularnewline
c & -0.034 & 0.298 & 1 & 0.436 & 0.242 \tabularnewline
d & -0.052 & 0.38 & 0.436 & 1 & 0.255 \tabularnewline
e & 0.116 & 0.325 & 0.242 & 0.255 & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300169&T=1

[TABLE]
[ROW][C]Correlations for all pairs of data series (method=pearson)[/C][/ROW]
[ROW][C] [/C][C]a[/C][C]b[/C][C]c[/C][C]d[/C][C]e[/C][/ROW]
[ROW][C]a[/C][C]1[/C][C]-0.093[/C][C]-0.034[/C][C]-0.052[/C][C]0.116[/C][/ROW]
[ROW][C]b[/C][C]-0.093[/C][C]1[/C][C]0.298[/C][C]0.38[/C][C]0.325[/C][/ROW]
[ROW][C]c[/C][C]-0.034[/C][C]0.298[/C][C]1[/C][C]0.436[/C][C]0.242[/C][/ROW]
[ROW][C]d[/C][C]-0.052[/C][C]0.38[/C][C]0.436[/C][C]1[/C][C]0.255[/C][/ROW]
[ROW][C]e[/C][C]0.116[/C][C]0.325[/C][C]0.242[/C][C]0.255[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300169&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300169&T=1

As an alternative you can also use a QR Code:  
QR Code


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

Correlations for all pairs of data series (method=pearson)
abcde
a1-0.093-0.034-0.0520.116
b-0.09310.2980.380.325
c-0.0340.29810.4360.242
d-0.0520.380.43610.255
e0.1160.3250.2420.2551






Correlations for all pairs of data series with p-values
pairPearson rSpearman rhoKendall tau
a;b-0.0927-0.0844-0.0729
p-value(0.238)(0.2826)(0.2781)
a;c-0.034-0.0481-0.0419
p-value(0.6653)(0.5406)(0.5355)
a;d-0.0522-0.0642-0.0557
p-value(0.5067)(0.4138)(0.4118)
a;e0.11580.12490.1068
p-value(0.1399)(0.111)(0.1076)
b;c0.29830.29260.2767
p-value(1e-04)(1e-04)(2e-04)
b;d0.38040.46340.4459
p-value(0)(0)(0)
b;e0.3250.3680.3476
p-value(0)(0)(0)
c;d0.43550.45240.4309
p-value(0)(0)(0)
c;e0.24210.22550.2112
p-value(0.0018)(0.0037)(0.0039)
d;e0.25510.34630.3271
p-value(0.001)(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
a;b & -0.0927 & -0.0844 & -0.0729 \tabularnewline
p-value & (0.238) & (0.2826) & (0.2781) \tabularnewline
a;c & -0.034 & -0.0481 & -0.0419 \tabularnewline
p-value & (0.6653) & (0.5406) & (0.5355) \tabularnewline
a;d & -0.0522 & -0.0642 & -0.0557 \tabularnewline
p-value & (0.5067) & (0.4138) & (0.4118) \tabularnewline
a;e & 0.1158 & 0.1249 & 0.1068 \tabularnewline
p-value & (0.1399) & (0.111) & (0.1076) \tabularnewline
b;c & 0.2983 & 0.2926 & 0.2767 \tabularnewline
p-value & (1e-04) & (1e-04) & (2e-04) \tabularnewline
b;d & 0.3804 & 0.4634 & 0.4459 \tabularnewline
p-value & (0) & (0) & (0) \tabularnewline
b;e & 0.325 & 0.368 & 0.3476 \tabularnewline
p-value & (0) & (0) & (0) \tabularnewline
c;d & 0.4355 & 0.4524 & 0.4309 \tabularnewline
p-value & (0) & (0) & (0) \tabularnewline
c;e & 0.2421 & 0.2255 & 0.2112 \tabularnewline
p-value & (0.0018) & (0.0037) & (0.0039) \tabularnewline
d;e & 0.2551 & 0.3463 & 0.3271 \tabularnewline
p-value & (0.001) & (0) & (0) \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300169&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]a;b[/C][C]-0.0927[/C][C]-0.0844[/C][C]-0.0729[/C][/ROW]
[ROW][C]p-value[/C][C](0.238)[/C][C](0.2826)[/C][C](0.2781)[/C][/ROW]
[ROW][C]a;c[/C][C]-0.034[/C][C]-0.0481[/C][C]-0.0419[/C][/ROW]
[ROW][C]p-value[/C][C](0.6653)[/C][C](0.5406)[/C][C](0.5355)[/C][/ROW]
[ROW][C]a;d[/C][C]-0.0522[/C][C]-0.0642[/C][C]-0.0557[/C][/ROW]
[ROW][C]p-value[/C][C](0.5067)[/C][C](0.4138)[/C][C](0.4118)[/C][/ROW]
[ROW][C]a;e[/C][C]0.1158[/C][C]0.1249[/C][C]0.1068[/C][/ROW]
[ROW][C]p-value[/C][C](0.1399)[/C][C](0.111)[/C][C](0.1076)[/C][/ROW]
[ROW][C]b;c[/C][C]0.2983[/C][C]0.2926[/C][C]0.2767[/C][/ROW]
[ROW][C]p-value[/C][C](1e-04)[/C][C](1e-04)[/C][C](2e-04)[/C][/ROW]
[ROW][C]b;d[/C][C]0.3804[/C][C]0.4634[/C][C]0.4459[/C][/ROW]
[ROW][C]p-value[/C][C](0)[/C][C](0)[/C][C](0)[/C][/ROW]
[ROW][C]b;e[/C][C]0.325[/C][C]0.368[/C][C]0.3476[/C][/ROW]
[ROW][C]p-value[/C][C](0)[/C][C](0)[/C][C](0)[/C][/ROW]
[ROW][C]c;d[/C][C]0.4355[/C][C]0.4524[/C][C]0.4309[/C][/ROW]
[ROW][C]p-value[/C][C](0)[/C][C](0)[/C][C](0)[/C][/ROW]
[ROW][C]c;e[/C][C]0.2421[/C][C]0.2255[/C][C]0.2112[/C][/ROW]
[ROW][C]p-value[/C][C](0.0018)[/C][C](0.0037)[/C][C](0.0039)[/C][/ROW]
[ROW][C]d;e[/C][C]0.2551[/C][C]0.3463[/C][C]0.3271[/C][/ROW]
[ROW][C]p-value[/C][C](0.001)[/C][C](0)[/C][C](0)[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300169&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300169&T=2

As an alternative you can also use a QR Code:  
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
a;b-0.0927-0.0844-0.0729
p-value(0.238)(0.2826)(0.2781)
a;c-0.034-0.0481-0.0419
p-value(0.6653)(0.5406)(0.5355)
a;d-0.0522-0.0642-0.0557
p-value(0.5067)(0.4138)(0.4118)
a;e0.11580.12490.1068
p-value(0.1399)(0.111)(0.1076)
b;c0.29830.29260.2767
p-value(1e-04)(1e-04)(2e-04)
b;d0.38040.46340.4459
p-value(0)(0)(0)
b;e0.3250.3680.3476
p-value(0)(0)(0)
c;d0.43550.45240.4309
p-value(0)(0)(0)
c;e0.24210.22550.2112
p-value(0.0018)(0.0037)(0.0039)
d;e0.25510.34630.3271
p-value(0.001)(0)(0)






Meta Analysis of Correlation Tests
Number of significant by total number of Correlations
Type I errorPearson rSpearman rhoKendall tau
0.010.60.60.6
0.020.60.60.6
0.030.60.60.6
0.040.60.60.6
0.050.60.60.6
0.060.60.60.6
0.070.60.60.6
0.080.60.60.6
0.090.60.60.6
0.10.60.60.6

\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 & 0.6 & 0.6 & 0.6 \tabularnewline
0.02 & 0.6 & 0.6 & 0.6 \tabularnewline
0.03 & 0.6 & 0.6 & 0.6 \tabularnewline
0.04 & 0.6 & 0.6 & 0.6 \tabularnewline
0.05 & 0.6 & 0.6 & 0.6 \tabularnewline
0.06 & 0.6 & 0.6 & 0.6 \tabularnewline
0.07 & 0.6 & 0.6 & 0.6 \tabularnewline
0.08 & 0.6 & 0.6 & 0.6 \tabularnewline
0.09 & 0.6 & 0.6 & 0.6 \tabularnewline
0.1 & 0.6 & 0.6 & 0.6 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300169&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]0.6[/C][C]0.6[/C][C]0.6[/C][/ROW]
[ROW][C]0.02[/C][C]0.6[/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]0.6[/C][C]0.6[/C][/ROW]
[ROW][C]0.05[/C][C]0.6[/C][C]0.6[/C][C]0.6[/C][/ROW]
[ROW][C]0.06[/C][C]0.6[/C][C]0.6[/C][C]0.6[/C][/ROW]
[ROW][C]0.07[/C][C]0.6[/C][C]0.6[/C][C]0.6[/C][/ROW]
[ROW][C]0.08[/C][C]0.6[/C][C]0.6[/C][C]0.6[/C][/ROW]
[ROW][C]0.09[/C][C]0.6[/C][C]0.6[/C][C]0.6[/C][/ROW]
[ROW][C]0.1[/C][C]0.6[/C][C]0.6[/C][C]0.6[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300169&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300169&T=3

As an alternative you can also use a QR Code:  
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
0.010.60.60.6
0.020.60.60.6
0.030.60.60.6
0.040.60.60.6
0.050.60.60.6
0.060.60.60.6
0.070.60.60.6
0.080.60.60.6
0.090.60.60.6
0.10.60.60.6


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = pearson ;
Parameters (R input):
par1 = pearson ;
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$counts; y <- y/max(y)
rect(breaks[-nB], 0, breaks[-1], y, col='grey', ...)
}
x <- na.omit(x)
y <- t(na.omit(t(y)))
bitmap(file='test1.png')
pairs(t(y),diag.panel=panel.hist, upper.panel=panel.smooth, lower.panel=panel.tau, main=main)
dev.off()
load(file='createtable')
n <- length(y[,1])
print(n)
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,paste('Correlations for all pairs of data series (method=',par1,')',sep=''),n+1,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,' ',header=TRUE)
for (i in 1:n) {
a<-table.element(a,dimnames(t(x))[[2]][i],header=TRUE)
}
a<-table.row.end(a)
for (i in 1:n) {
a<-table.row.start(a)
a<-table.element(a,dimnames(t(x))[[2]][i],header=TRUE)
for (j in 1:n) {
r <- cor.test(y[i,],y[j,],method=par1)
a<-table.element(a,round(r$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')