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Author

*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, 24 Dec 2010 17:12:52 +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/2010/Dec/24/t1293210661k239kvvwd02s00g.htm/, Retrieved Tue, 30 Apr 2024 05:53:12 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=115219, Retrieved Tue, 30 Apr 2024 05:53:12 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

186

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-     [Kendall tau Correlation Matrix] [] [2010-12-05 17:44:33] [b98453cac15ba1066b407e146608df68]
- RMPD  [Kendall tau Correlation Matrix] [Pearson Correlati...] [2010-12-21 19:02:22] [253127ae8da904b75450fbd69fe4eb21]
-         [Kendall tau Correlation Matrix] [De pearson correl...] [2010-12-24 10:33:01] [ca50229b6b451ac8f5a30a9e3154d674]
-    D      [Kendall tau Correlation Matrix] [correlation Pearson] [2010-12-24 16:47:37] [8e42c8cdf50f15ce85eb45a67cf771d0]
F    D          [Kendall tau Correlation Matrix] [Pearson corr.] [2010-12-24 17:12:52] [5876f3b3a8c6f0cebdbe74121f58174b] [Current]
-                 [Kendall tau Correlation Matrix] [] [2010-12-25 09:28:49] [64a7ae6044525e7ca71ecb546c042c9e] 
- R               [Kendall tau Correlation Matrix] [] [2010-12-29 18:59:33] [46e2473aa7b3b1358cef648d2cdd04a9] 

Feedback Forum

2010-12-30 07:23:45 [17057d7538d25ae6e90d657dd6ae3201] [reply] 
Het is misschien iets gemakkelijker om de tabellen te interpreteren als je voor 'Names of X columns' de benamingen: Popularity, Finding Friends... gebruikt ipv X1,X2...
2010-12-30 07:43:19 [17057d7538d25ae6e90d657dd6ae3201] [reply] 
We kunnen hier volgens mij zien dat X1-X3, X1-X4, X1-X5, X3-X4, X4-X5 het sterkst gecorreleerd zijn en deze zijn allemaal ongeveer even sterk gecorreleerd (correlatie is ongeveer 0.6). Bij een perfecte correlatie is de coëfficiënt gelijk aan 1. Hoe dicht bij de 1, hoe sterker twee variabelen zijn gecorreleerd. 
 
Er is dus een correlatie is tussen Popularity en Knowing People, Liked en Celebrity. Daarnaast is Knowing People en Liked ook gecorreleerd en Liked en Celebrity.
2010-12-30 08:21:15 [17057d7538d25ae6e90d657dd6ae3201] [reply] 
Bij het gebruik van de Pearson Correlation matrix moet echter rekening gehouden worden met verdelingsassumpties voordat er definitieve besluiten worden genomen. In de scatterplots en de histogrammen is te zien dat de variabelen niet normaal verdeeld zijn. Er mag dus geen correlatie getoetst worden.  
 
Vergeet dus maar mijn bovenstaande opmerking.

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Dataseries X:

Download CSV

Histogram

Boxplots

13	13	14	13	3
12	12	8	13	5
15	10	12	16	6
12	9	7	12	6
10	10	10	11	5
12	12	7	12	3
15	13	16	18	8
9	12	11	11	4
12	12	14	14	4
11	6	6	9	4
11	5	16	14	6
11	12	11	12	6
15	11	16	11	5
7	14	12	12	4
11	14	7	13	6
11	12	13	11	4
10	12	11	12	6
14	11	15	16	6
10	11	7	9	4
6	7	9	11	4
11	9	7	13	2
15	11	14	15	7
11	11	15	10	5
12	12	7	11	4
14	12	15	13	6
15	11	17	16	6
9	11	15	15	7
13	8	14	14	5
13	9	14	14	6
16	12	8	14	4
13	10	8	8	4
12	10	14	13	7
14	12	14	15	7
11	8	8	13	4
9	12	11	11	4
16	11	16	15	6
12	12	10	15	6
10	7	8	9	5
13	11	14	13	6
16	11	16	16	7
14	12	13	13	6
15	9	5	11	3
5	15	8	12	3
8	11	10	12	4
11	11	8	12	6
16	11	13	14	7
17	11	15	14	5
9	15	6	8	4
9	11	12	13	5
13	12	16	16	6
10	12	5	13	6
6	9	15	11	6
12	12	12	14	5
8	12	8	13	4
14	13	13	13	5
12	11	14	13	5
11	9	12	12	4
16	9	16	16	6
8	11	10	15	2
15	11	15	15	8
7	12	8	12	3
16	12	16	14	6
14	9	19	12	6
16	11	14	15	6
9	9	6	12	5
14	12	13	13	5
11	12	15	12	6
13	12	7	12	5
15	12	13	13	6
5	14	4	5	2
15	11	14	13	5
13	12	13	13	5
11	11	11	14	5
11	6	14	17	6
12	10	12	13	6
12	12	15	13	6
12	13	14	12	5
12	8	13	13	5
14	12	8	14	4
6	12	6	11	2
7	12	7	12	4
14	6	13	12	6
14	11	13	16	6
10	10	11	12	5
13	12	5	12	3
12	13	12	12	6
9	11	8	10	4
12	7	11	15	5
16	11	14	15	8
10	11	9	12	4
14	11	10	16	6
10	11	13	15	6
16	12	16	16	7
15	10	16	13	6
12	11	11	12	5
10	12	8	11	4
8	7	4	13	6
8	13	7	10	3
11	8	14	15	5
13	12	11	13	6
16	11	17	16	7
16	12	15	15	7
14	14	17	18	6
11	10	5	13	3
4	10	4	10	2
14	13	10	16	8
9	10	11	13	3
14	11	15	15	8
8	10	10	14	3
8	7	9	15	4
11	10	12	14	5
12	8	15	13	7
11	12	7	13	6
14	12	13	15	6
15	12	12	16	7
16	11	14	14	6
16	12	14	14	6
11	12	8	16	6
14	12	15	14	6
14	11	12	12	4
12	12	12	13	4
14	11	16	12	5
8	11	9	12	4
13	13	15	14	6
16	12	15	14	6
12	12	6	14	5
16	12	14	16	8
12	12	15	13	6
11	8	10	14	5
4	8	6	4	4
16	12	14	16	8
15	11	12	13	6
10	12	8	16	4
13	13	11	15	6
15	12	13	14	6
12	12	9	13	4
14	11	15	14	6
7	12	13	12	3
19	12	15	15	6
12	10	14	14	5
12	11	16	13	4
13	12	14	14	6
15	12	14	16	4
8	10	10	6	4
12	12	10	13	4
10	13	4	13	6
8	12	8	14	5
10	15	15	15	6
15	11	16	14	6
16	12	12	15	8
13	11	12	13	7
16	12	15	16	7
9	11	9	12	4
14	10	12	15	6
14	11	14	12	6
12	11	11	14	2

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 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'.

\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 & 2 seconds \tabularnewline
R Server & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
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'. \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115219&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[ROW][C]R Framework error message[/C][C]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'.[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115219&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115219&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	2 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=pearson)
	X1	X2	X3	X4	X5
X1	1	0.094	0.584	0.567	0.6
X2	0.094	1	0.017	0.089	0.031
X3	0.584	0.017	1	0.497	0.558
X4	0.567	0.089	0.497	1	0.538
X5	0.6	0.031	0.558	0.538	1

\begin{tabular}{lllllllll}
\hline
Correlations for all pairs of data series (method=pearson) \tabularnewline
  & X1 & X2 & X3 & X4 & X5
 \tabularnewline
X1 & 1 & 0.094 & 0.584 & 0.567 & 0.6 \tabularnewline
X2 & 0.094 & 1 & 0.017 & 0.089 & 0.031 \tabularnewline
X3 & 0.584 & 0.017 & 1 & 0.497 & 0.558 \tabularnewline
X4 & 0.567 & 0.089 & 0.497 & 1 & 0.538 \tabularnewline
X5
 & 0.6 & 0.031 & 0.558 & 0.538 & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115219&T=1

[TABLE]
[ROW][C]Correlations for all pairs of data series (method=pearson)[/C][/ROW]
[ROW][C] [/C][C]X1[/C][C]X2[/C][C]X3[/C][C]X4[/C][C]X5
[/C][/ROW]
[ROW][C]X1[/C][C]1[/C][C]0.094[/C][C]0.584[/C][C]0.567[/C][C]0.6[/C][/ROW]
[ROW][C]X2[/C][C]0.094[/C][C]1[/C][C]0.017[/C][C]0.089[/C][C]0.031[/C][/ROW]
[ROW][C]X3[/C][C]0.584[/C][C]0.017[/C][C]1[/C][C]0.497[/C][C]0.558[/C][/ROW]
[ROW][C]X4[/C][C]0.567[/C][C]0.089[/C][C]0.497[/C][C]1[/C][C]0.538[/C][/ROW]
[ROW][C]X5
[/C][C]0.6[/C][C]0.031[/C][C]0.558[/C][C]0.538[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115219&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115219&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=pearson)
	X1	X2	X3	X4	X5
X1	1	0.094	0.584	0.567	0.6
X2	0.094	1	0.017	0.089	0.031
X3	0.584	0.017	1	0.497	0.558
X4	0.567	0.089	0.497	1	0.538
X5	0.6	0.031	0.558	0.538	1

Correlations for all pairs of data series with p-values
pair	Pearson r	Spearman rho	Kendall tau
X1;X2	0.094	0.0891	0.0671
p-value	(0.2432)	(0.2688)	(0.2772)
X1;X3	0.5837	0.5916	0.4504
p-value	(0)	(0)	(0)
X1;X4	0.5672	0.5512	0.433
p-value	(0)	(0)	(0)
X1;X5	0.6001	0.588	0.4814
p-value	(0)	(0)	(0)
X2;X3	0.0172	-0.0171	-0.015
p-value	(0.8308)	(0.8318)	(0.8069)
X2;X4	0.0886	0.0775	0.0612
p-value	(0.2714)	(0.3361)	(0.3316)
X2;X5	0.0305	0.048	0.0382
p-value	(0.7052)	(0.5522)	(0.5541)
X3;X4	0.4973	0.4753	0.3704
p-value	(0)	(0)	(0)
X3;X5	0.5577	0.5692	0.4502
p-value	(0)	(0)	(0)
X4;X5	0.5376	0.5699	0.4651
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
X1;X2 & 0.094 & 0.0891 & 0.0671 \tabularnewline
p-value & (0.2432) & (0.2688) & (0.2772) \tabularnewline
X1;X3 & 0.5837 & 0.5916 & 0.4504 \tabularnewline
p-value & (0) & (0) & (0) \tabularnewline
X1;X4 & 0.5672 & 0.5512 & 0.433 \tabularnewline
p-value & (0) & (0) & (0) \tabularnewline
X1;X5
 & 0.6001 & 0.588 & 0.4814 \tabularnewline
p-value & (0) & (0) & (0) \tabularnewline
X2;X3 & 0.0172 & -0.0171 & -0.015 \tabularnewline
p-value & (0.8308) & (0.8318) & (0.8069) \tabularnewline
X2;X4 & 0.0886 & 0.0775 & 0.0612 \tabularnewline
p-value & (0.2714) & (0.3361) & (0.3316) \tabularnewline
X2;X5
 & 0.0305 & 0.048 & 0.0382 \tabularnewline
p-value & (0.7052) & (0.5522) & (0.5541) \tabularnewline
X3;X4 & 0.4973 & 0.4753 & 0.3704 \tabularnewline
p-value & (0) & (0) & (0) \tabularnewline
X3;X5
 & 0.5577 & 0.5692 & 0.4502 \tabularnewline
p-value & (0) & (0) & (0) \tabularnewline
X4;X5
 & 0.5376 & 0.5699 & 0.4651 \tabularnewline
p-value & (0) & (0) & (0) \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115219&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]X1;X2[/C][C]0.094[/C][C]0.0891[/C][C]0.0671[/C][/ROW]
[ROW][C]p-value[/C][C](0.2432)[/C][C](0.2688)[/C][C](0.2772)[/C][/ROW]
[ROW][C]X1;X3[/C][C]0.5837[/C][C]0.5916[/C][C]0.4504[/C][/ROW]
[ROW][C]p-value[/C][C](0)[/C][C](0)[/C][C](0)[/C][/ROW]
[ROW][C]X1;X4[/C][C]0.5672[/C][C]0.5512[/C][C]0.433[/C][/ROW]
[ROW][C]p-value[/C][C](0)[/C][C](0)[/C][C](0)[/C][/ROW]
[ROW][C]X1;X5
[/C][C]0.6001[/C][C]0.588[/C][C]0.4814[/C][/ROW]
[ROW][C]p-value[/C][C](0)[/C][C](0)[/C][C](0)[/C][/ROW]
[ROW][C]X2;X3[/C][C]0.0172[/C][C]-0.0171[/C][C]-0.015[/C][/ROW]
[ROW][C]p-value[/C][C](0.8308)[/C][C](0.8318)[/C][C](0.8069)[/C][/ROW]
[ROW][C]X2;X4[/C][C]0.0886[/C][C]0.0775[/C][C]0.0612[/C][/ROW]
[ROW][C]p-value[/C][C](0.2714)[/C][C](0.3361)[/C][C](0.3316)[/C][/ROW]
[ROW][C]X2;X5
[/C][C]0.0305[/C][C]0.048[/C][C]0.0382[/C][/ROW]
[ROW][C]p-value[/C][C](0.7052)[/C][C](0.5522)[/C][C](0.5541)[/C][/ROW]
[ROW][C]X3;X4[/C][C]0.4973[/C][C]0.4753[/C][C]0.3704[/C][/ROW]
[ROW][C]p-value[/C][C](0)[/C][C](0)[/C][C](0)[/C][/ROW]
[ROW][C]X3;X5
[/C][C]0.5577[/C][C]0.5692[/C][C]0.4502[/C][/ROW]
[ROW][C]p-value[/C][C](0)[/C][C](0)[/C][C](0)[/C][/ROW]
[ROW][C]X4;X5
[/C][C]0.5376[/C][C]0.5699[/C][C]0.4651[/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=115219&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115219&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
X1;X2	0.094	0.0891	0.0671
p-value	(0.2432)	(0.2688)	(0.2772)
X1;X3	0.5837	0.5916	0.4504
p-value	(0)	(0)	(0)
X1;X4	0.5672	0.5512	0.433
p-value	(0)	(0)	(0)
X1;X5	0.6001	0.588	0.4814
p-value	(0)	(0)	(0)
X2;X3	0.0172	-0.0171	-0.015
p-value	(0.8308)	(0.8318)	(0.8069)
X2;X4	0.0886	0.0775	0.0612
p-value	(0.2714)	(0.3361)	(0.3316)
X2;X5	0.0305	0.048	0.0382
p-value	(0.7052)	(0.5522)	(0.5541)
X3;X4	0.4973	0.4753	0.3704
p-value	(0)	(0)	(0)
X3;X5	0.5577	0.5692	0.4502
p-value	(0)	(0)	(0)
X4;X5	0.5376	0.5699	0.4651
p-value	(0)	(0)	(0)

Figure 1

PNG link

Postscript link

PDF link

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

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code