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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 computationSat, 01 Nov 2008 08:54:43 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Nov/01/t1225551319k4r5br82g9f45cv.htm/, Retrieved Sun, 19 May 2024 08:52:25 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=20418, Retrieved Sun, 19 May 2024 08:52:25 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact191

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Notched Boxplots] [workshop 3] [2007-10-26 13:31:48] [e9ffc5de6f8a7be62f22b142b5b6b1a8]
F RMPD  [Mean Plot] [workshop 4 deel 1...] [2008-10-31 09:40:26] [077ffec662d24c06be4c491541a44245]
F         [Mean Plot] [] [2008-11-01 13:19:15] [4c8dfb519edec2da3492d7e6be9a5685]
F RM D        [Kendall tau Correlation Matrix] [] [2008-11-01 14:54:43] [6d40a467de0f28bd2350f82ac9522c51] [Current]
F RM D          [Star Plot] [] [2008-11-01 15:07:20] [4c8dfb519edec2da3492d7e6be9a5685]
F RM D            [Notched Boxplots] [] [2008-11-01 15:20:06] [4c8dfb519edec2da3492d7e6be9a5685]
F   P               [Notched Boxplots] [] [2008-11-02 21:57:12] [077ffec662d24c06be4c491541a44245]
F   P             [Star Plot] [] [2008-11-02 21:55:44] [077ffec662d24c06be4c491541a44245]
F   PD          [Kendall tau Correlation Matrix] [] [2008-11-02 21:54:30] [077ffec662d24c06be4c491541a44245]
Feedback Forum
2008-11-08 12:40:12 [Astrid Sniekers] [reply] 
Het antwoord van de student is correct, maar had concreter gekund.

Het probleem van de dataset is dat de variabelen links en de jaren vanboven staan. Dit moet juist andersom zijn. Dus we gaan transponeren.

De Kendall tau Correlation Plot is robuust voor outliers en is een goede maatstaf om correlatie te berekenen.

Boven de diagonaal in de Kendall tau Correlation Plot zien we scatter plots met rode correlatielijnen door. Aan de hand van deze lijn kunnen we al zien dat er een zeer positieve relatie is tussen RNR en RCF.

Onder de diagonaal in de Kendall tau Correlation Plot staan getallen. Deze getallen zeggen iets over de correlatie, maar het zijn geen correlatiecoëfficiënten. De getallen zeggen iets over de betrouwbaarheid. Hoe kleiner het getal, hoe groter de betrouwbaarheid. RNR is het meest gecorreleerd met RCF, want hier is het getal het laagste, namelijk 0,01.

Tabel:
Tau staat voor de correlatiecoëfficiënt en p-value staat voor de betrouwbaarheid. De correlatie tussen RNR en RCF is 0.80952380952381. Dus we hebben te maken met een zeer positieve correlatie.
2008-11-09 13:25:17 [2df1bcd103d52957f4a39bd4617794c8] [reply] 
De transformatie van de gegevens gebeurt correct, de waardoor de kolommen rijen worden en de rijen kolommen. We verwisselen dus de assen.

De conclusie van de student is ook correct.

Grafisch geeft de diagonaal de verdeling van elke variabele weer. De getallen hebben betrekking op de betrouwbaarheid van uw correlatie en zeggen dus niet wat de correlatie is. Voorts nemen we ook correlatielijnen waar op de scatterplots.

De kleinste betrouwbaarheid vinden we bij RCF. Bij de correlatie tussen RNR en RCF kan het minst gesproken worden over toeval.
2008-11-09 14:49:06 [Roland Feldman] [reply] 
Het antwoord van de student is correct maar men kan iets aanpassen.
Jaren moeten links staan en de variablen vanboven.

De tabel geeft aan de p- waarde het kleinst is tussen rnr en rcf. Dit komt neer dat de correlatie niet toevallig is. Namelijk hoe hoger de p-waarde hoe groter het toeval. De p-waarde geeft niet weer hoe groot de correlatie is enkel de betrouwbaarheid van de correlatie.

Op de kleine grafieken kan je ook de correlatielijn zien en bij rnr en rcf liggen deze op of nabij de lijn.

Post a new message

Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
4,2	4,8	20,8	0,9	39,6
2,6	-4,2	17,1	0,85	36,1
3	1,6	22,3	0,83	34,4
3,8	5,2	25,1	0,84	22,4
4	9,2	27,7	0,85	34,8
3,5	4,6	24,9	0,83	33,7
4,1	10,6	29,5	0,83	36,3

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\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 & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=20418&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]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=20418&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=20418&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 Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001






Kendall tau rank correlations for all pairs of data series
pairtaup-value
tau( RNVM , RNR )0.7142857142857140.0301587301587301
tau( RNVM , RCF )0.5238095238095240.136111111111111
tau( RNVM , RLEZ )0.2646280620124820.427262856745706
tau( RNVM , REV )0.3333333333333330.381349206349206
tau( RNR , RCF )0.809523809523810.0107142857142857
tau( RNR , RLEZ )-0.05292561240249630.873844698517373
tau( RNR , REV )0.04761904761904761
tau( RCF , RLEZ )-0.2646280620124820.427262856745706
tau( RCF , REV )-0.1428571428571430.772619047619048
tau( RLEZ , REV )0.3704792868174740.266379923342483

\begin{tabular}{lllllllll}
\hline
Kendall tau rank correlations for all pairs of data series \tabularnewline
pair & tau & p-value \tabularnewline
tau( RNVM , RNR ) & 0.714285714285714 & 0.0301587301587301 \tabularnewline
tau( RNVM , RCF ) & 0.523809523809524 & 0.136111111111111 \tabularnewline
tau( RNVM , RLEZ ) & 0.264628062012482 & 0.427262856745706 \tabularnewline
tau( RNVM , REV ) & 0.333333333333333 & 0.381349206349206 \tabularnewline
tau( RNR , RCF ) & 0.80952380952381 & 0.0107142857142857 \tabularnewline
tau( RNR , RLEZ ) & -0.0529256124024963 & 0.873844698517373 \tabularnewline
tau( RNR , REV ) & 0.0476190476190476 & 1 \tabularnewline
tau( RCF , RLEZ ) & -0.264628062012482 & 0.427262856745706 \tabularnewline
tau( RCF , REV ) & -0.142857142857143 & 0.772619047619048 \tabularnewline
tau( RLEZ , REV ) & 0.370479286817474 & 0.266379923342483 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=20418&T=1

[TABLE]
[ROW][C]Kendall tau rank correlations for all pairs of data series[/C][/ROW]
[ROW][C]pair[/C][C]tau[/C][C]p-value[/C][/ROW]
[ROW][C]tau( RNVM , RNR )[/C][C]0.714285714285714[/C][C]0.0301587301587301[/C][/ROW]
[ROW][C]tau( RNVM , RCF )[/C][C]0.523809523809524[/C][C]0.136111111111111[/C][/ROW]
[ROW][C]tau( RNVM , RLEZ )[/C][C]0.264628062012482[/C][C]0.427262856745706[/C][/ROW]
[ROW][C]tau( RNVM , REV )[/C][C]0.333333333333333[/C][C]0.381349206349206[/C][/ROW]
[ROW][C]tau( RNR , RCF )[/C][C]0.80952380952381[/C][C]0.0107142857142857[/C][/ROW]
[ROW][C]tau( RNR , RLEZ )[/C][C]-0.0529256124024963[/C][C]0.873844698517373[/C][/ROW]
[ROW][C]tau( RNR , REV )[/C][C]0.0476190476190476[/C][C]1[/C][/ROW]
[ROW][C]tau( RCF , RLEZ )[/C][C]-0.264628062012482[/C][C]0.427262856745706[/C][/ROW]
[ROW][C]tau( RCF , REV )[/C][C]-0.142857142857143[/C][C]0.772619047619048[/C][/ROW]
[ROW][C]tau( RLEZ , REV )[/C][C]0.370479286817474[/C][C]0.266379923342483[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=20418&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=20418&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:

Kendall tau rank correlations for all pairs of data series
pairtaup-value
tau( RNVM , RNR )0.7142857142857140.0301587301587301
tau( RNVM , RCF )0.5238095238095240.136111111111111
tau( RNVM , RLEZ )0.2646280620124820.427262856745706
tau( RNVM , REV )0.3333333333333330.381349206349206
tau( RNR , RCF )0.809523809523810.0107142857142857
tau( RNR , RLEZ )-0.05292561240249630.873844698517373
tau( RNR , REV )0.04761904761904761
tau( RCF , RLEZ )-0.2646280620124820.427262856745706
tau( RCF , REV )-0.1428571428571430.772619047619048
tau( RLEZ , REV )0.3704792868174740.266379923342483


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 12 ;
Parameters (R input):
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='kendall')
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$counts; y <- y/max(y)
rect(breaks[-nB], 0, breaks[-1], y, col='grey', ...)
}
bitmap(file='test1.png')
pairs(t(y),diag.panel=panel.hist, upper.panel=panel.smooth, lower.panel=panel.tau, main=main)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Kendall tau rank correlations for all pairs of data series',3,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'pair',1,TRUE)
a<-table.element(a,'tau',1,TRUE)
a<-table.element(a,'p-value',1,TRUE)
a<-table.row.end(a)
n <- length(y[,1])
n
cor.test(y[1,],y[2,],method='kendall')
for (i in 1:(n-1))
{
for (j in (i+1):n)
{
a<-table.row.start(a)
dum <- paste('tau(',dimnames(t(x))[[2]][i])
dum <- paste(dum,',')
dum <- paste(dum,dimnames(t(x))[[2]][j])
dum <- paste(dum,')')
a<-table.element(a,dum,header=TRUE)
r <- cor.test(y[i,],y[j,],method='kendall')
a<-table.element(a,r$estimate)
a<-table.element(a,r$p.value)
a<-table.row.end(a)
}
}
a<-table.end(a)
table.save(a,file='mytable.tab')