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*Unverified author*

R Software Module

rwasp_pairs.wasp

Title produced by software

Kendall tau Correlation Matrix

Date of computation

Thu, 06 Nov 2008 08:21:18 -0700

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/2008/Nov/06/t1225984951huw06qujmf0crpb.htm/, Retrieved Mon, 20 May 2024 03:01:39 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=22260, Retrieved Mon, 20 May 2024 03:01:39 +0000

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Estimated Impact

148

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

F     [Notched Boxplots] [hypothesis testin...] [2008-11-05 17:58:44] [ad0ba236827d3670a23de17d480bce47]
F RMPD    [Kendall tau Correlation Matrix] [Hypothesis testin...] [2008-11-06 15:21:18] [c8dc05b1cdf5010d9a4f2d773adefb82] [Current]

Feedback Forum

2008-11-10 14:41:43 [Jasmine Hendrikx] [reply] 
Evaluatie Q2: 
 
De student heeft deze vraag met de verkeerde module opgelost. Het moet niet opgelost worden met de ‘Kendall tau Correlation’, maar met de ‘star plot’. Hieronder heb ik een link gezet waarin je deze star plot kunt terugvinden: 
http://www.freestatistics.org/blog/index.php?v=date/2008/Nov/04/t122582811151u3lslre47kabs.htm 
Bij een star plot stelt elke ster een enkele observatie voor. De grootte van elk lijntje van de star geeft de relatieve waarde van de betrokken variabele voor. Star plots worden gebruikt om gelijkenissen en verschillen tussen verschillende observaties te ontdekken. De star plot is wel een beperkte manier als je met teveel variabelen zou werken.  
Op basis van deze star plot, kunnen we zien dat er auto’s zijn die veel gelijkenissen vertonen en kunnen we bijgevolg enkele categorieën definiëren. Zo zou je bijvoorbeeld de auto’s 18 (Fiat128), 19 (HondaCivic), 20 (ToyotaCorolla) en 26 (FiatX1-9) kunnen samennemen. Qua ‘drat’ zitten zij verder boven het gemiddelde, qua qsec zitten zij algemeen boven het gemiddelde. Wat de variabelen ‘disp’, ‘hp’, ‘wt’ en ‘cyl’ betreft, zitten zij ver onder het gemiddelde ten opzichte van de andere auto’s. Wat ‘mpg’ betreft, zitten ze dan weer goed boven het gemiddelde. Je zou ook de auto’s 15, 16 en 17 kunnen samennemen. Zij scoren ongeveer hetzelfde over de verschillende variabelen. Ook de auto's 3 en 21 kunnen in 1 categorie geplaatst worden. Je ziet dus dat er toch heel wat gelijkenissen zijn tussen de auto’s en dat je deze dus bijgevolg in verschillende categorieën kunt plaatsen. 
2008-11-12 09:40:24 [Kelly Deckx] [reply] 
Je hebt de verkeerde methode gebruikt. Je moest hier de Starplot gebruiken. Het antwoord was dan: wanneer de verschillende sterretjes op elkaar lijken dan vertonen ze dezelfde karakteristieken.  
2008-11-12 11:18:14 [Bénédicte Soens] [reply] 
Deze vraag werd op een totaal foutieve manier opgelost. Er moest gebruik gemaakt worden van een starplot, die zo alle eigenschappen van de auto's kan weergeven. De grootte van iedere onderdeel van de ster zou dan de mate weergeven waarin de eigenschap aanwezig is in de auto. Op deze manier kon men de ongeveer gelijke sterren in groepen plaatsen van wagens die ongeveer dezelfde eigenschappen hebben.

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Dataseries X:

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Histogram

Boxplots

21	6	160	110	3,9	2,62	16,46
21	6	160	110	3,9	2,875	17,02
22,8	4	108	93	3,85	2,32	18,61
21,4	6	258	110	3,08	3,215	19,44
18,7	8	360	175	3,15	3,44	17,02
18,1	6	225	105	2,76	3,46	20,22
14,3	8	360	245	3,21	3,57	15,84
24,4	4	146,7	62	3,69	3,19	20
22,8	4	140,8	95	3,92	3,15	22,9
19,2	6	167,6	123	3,92	3,44	18,3
17,8	6	167,6	123	3,92	3,44	18,9
16,4	8	275,8	180	3,07	4,07	17,4
17,3	8	275,8	180	3,07	3,73	17,6
15,2	8	275,8	180	3,07	3,78	18
10,4	8	472	205	2,93	5,25	17,98
10,4	8	460	215	3	5,424	17,82
14,7	8	440	230	3,23	5,345	17,42
32,4	4	78,7	66	4,08	2,2	19,47
30,4	4	75,7	52	4,93	1,615	18,52
33,9	4	71,1	65	4,22	1,835	19,9
21,5	4	120,1	97	3,7	2,465	20,01
15,5	8	318	150	2,76	3,52	16,87
15,2	8	304	150	3,15	3,435	17,3
13,3	8	350	245	3,73	3,84	15,41
19,2	8	400	175	3,08	3,845	17,05
27,3	4	79	66	4,08	1,935	18,9
26	4	120,3	91	4,43	2,14	16,7
30,4	4	95,1	113	3,77	1,513	16,9
15,8	8	351	264	4,22	3,17	14,5
19,7	6	145	175	3,62	2,77	15,5
15	8	301	335	3,54	3,57	14,6
21,4	4	121	109	4,11	2,78	18,6

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	3 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24
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 & 3 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \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=22260&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/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=22260&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=22260&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	3 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24
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'.

Kendall tau rank correlations for all pairs of data series
pair	tau	p-value
tau( mpg , cyl )	-0.795313408619535	2.25362043202028e-08
tau( mpg , disp )	-0.768131146377997	1.00695006483270e-09
tau( mpg , hp )	-0.742812506088673	4.33160494891487e-09
tau( mpg , drat )	0.464548785236484	0.000238153299719546
tau( mpg , wt )	-0.727832149528431	6.70577040559586e-09
tau( mpg , qsec )	0.315365218988041	0.0118519955124592
tau( cyl , disp )	0.814426251098896	9.95652738033925e-09
tau( cyl , hp )	0.785186498532206	3.99666648664976e-08
tau( cyl , drat )	-0.551317846419971	0.000113971491179788
tau( cyl , wt )	0.728261112109847	2.8291139386738e-07
tau( cyl , qsec )	-0.448969823063678	0.00151975754259582
tau( disp , hp )	0.665998735836933	1.37128917110374e-07
tau( disp , drat )	-0.498982773649946	7.7849413883775e-05
tau( disp , wt )	0.74338239716769	3.07005865174403e-09
tau( disp , qsec )	-0.300815493561507	0.0162715491077270
tau( hp , drat )	-0.382626885048903	0.00260253883990014
tau( hp , wt )	0.611308095732059	1.26623978791152e-06
tau( hp , qsec )	-0.47290612619145	0.000173773709093133
tau( drat , wt )	-0.547149528309556	1.42468808580507e-05
tau( drat , qsec )	0.0327215469575162	0.794874350624461
tau( wt , qsec )	-0.141988121712634	0.255895606449493

\begin{tabular}{lllllllll}
\hline
Kendall tau rank correlations for all pairs of data series \tabularnewline
pair & tau & p-value \tabularnewline
tau( mpg , cyl ) & -0.795313408619535 & 2.25362043202028e-08 \tabularnewline
tau( mpg , disp ) & -0.768131146377997 & 1.00695006483270e-09 \tabularnewline
tau( mpg , hp ) & -0.742812506088673 & 4.33160494891487e-09 \tabularnewline
tau( mpg , drat ) & 0.464548785236484 & 0.000238153299719546 \tabularnewline
tau( mpg , wt ) & -0.727832149528431 & 6.70577040559586e-09 \tabularnewline
tau( mpg , qsec
 ) & 0.315365218988041 & 0.0118519955124592 \tabularnewline
tau( cyl , disp ) & 0.814426251098896 & 9.95652738033925e-09 \tabularnewline
tau( cyl , hp ) & 0.785186498532206 & 3.99666648664976e-08 \tabularnewline
tau( cyl , drat ) & -0.551317846419971 & 0.000113971491179788 \tabularnewline
tau( cyl , wt ) & 0.728261112109847 & 2.8291139386738e-07 \tabularnewline
tau( cyl , qsec
 ) & -0.448969823063678 & 0.00151975754259582 \tabularnewline
tau( disp , hp ) & 0.665998735836933 & 1.37128917110374e-07 \tabularnewline
tau( disp , drat ) & -0.498982773649946 & 7.7849413883775e-05 \tabularnewline
tau( disp , wt ) & 0.74338239716769 & 3.07005865174403e-09 \tabularnewline
tau( disp , qsec
 ) & -0.300815493561507 & 0.0162715491077270 \tabularnewline
tau( hp , drat ) & -0.382626885048903 & 0.00260253883990014 \tabularnewline
tau( hp , wt ) & 0.611308095732059 & 1.26623978791152e-06 \tabularnewline
tau( hp , qsec
 ) & -0.47290612619145 & 0.000173773709093133 \tabularnewline
tau( drat , wt ) & -0.547149528309556 & 1.42468808580507e-05 \tabularnewline
tau( drat , qsec
 ) & 0.0327215469575162 & 0.794874350624461 \tabularnewline
tau( wt , qsec
 ) & -0.141988121712634 & 0.255895606449493 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=22260&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( mpg , cyl )[/C][C]-0.795313408619535[/C][C]2.25362043202028e-08[/C][/ROW]
[ROW][C]tau( mpg , disp )[/C][C]-0.768131146377997[/C][C]1.00695006483270e-09[/C][/ROW]
[ROW][C]tau( mpg , hp )[/C][C]-0.742812506088673[/C][C]4.33160494891487e-09[/C][/ROW]
[ROW][C]tau( mpg , drat )[/C][C]0.464548785236484[/C][C]0.000238153299719546[/C][/ROW]
[ROW][C]tau( mpg , wt )[/C][C]-0.727832149528431[/C][C]6.70577040559586e-09[/C][/ROW]
[ROW][C]tau( mpg , qsec
 )[/C][C]0.315365218988041[/C][C]0.0118519955124592[/C][/ROW]
[ROW][C]tau( cyl , disp )[/C][C]0.814426251098896[/C][C]9.95652738033925e-09[/C][/ROW]
[ROW][C]tau( cyl , hp )[/C][C]0.785186498532206[/C][C]3.99666648664976e-08[/C][/ROW]
[ROW][C]tau( cyl , drat )[/C][C]-0.551317846419971[/C][C]0.000113971491179788[/C][/ROW]
[ROW][C]tau( cyl , wt )[/C][C]0.728261112109847[/C][C]2.8291139386738e-07[/C][/ROW]
[ROW][C]tau( cyl , qsec
 )[/C][C]-0.448969823063678[/C][C]0.00151975754259582[/C][/ROW]
[ROW][C]tau( disp , hp )[/C][C]0.665998735836933[/C][C]1.37128917110374e-07[/C][/ROW]
[ROW][C]tau( disp , drat )[/C][C]-0.498982773649946[/C][C]7.7849413883775e-05[/C][/ROW]
[ROW][C]tau( disp , wt )[/C][C]0.74338239716769[/C][C]3.07005865174403e-09[/C][/ROW]
[ROW][C]tau( disp , qsec
 )[/C][C]-0.300815493561507[/C][C]0.0162715491077270[/C][/ROW]
[ROW][C]tau( hp , drat )[/C][C]-0.382626885048903[/C][C]0.00260253883990014[/C][/ROW]
[ROW][C]tau( hp , wt )[/C][C]0.611308095732059[/C][C]1.26623978791152e-06[/C][/ROW]
[ROW][C]tau( hp , qsec
 )[/C][C]-0.47290612619145[/C][C]0.000173773709093133[/C][/ROW]
[ROW][C]tau( drat , wt )[/C][C]-0.547149528309556[/C][C]1.42468808580507e-05[/C][/ROW]
[ROW][C]tau( drat , qsec
 )[/C][C]0.0327215469575162[/C][C]0.794874350624461[/C][/ROW]
[ROW][C]tau( wt , qsec
 )[/C][C]-0.141988121712634[/C][C]0.255895606449493[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=22260&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=22260&T=1

As an alternative you can also use a QR Code:

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

Kendall tau rank correlations for all pairs of data series
pair	tau	p-value
tau( mpg , cyl )	-0.795313408619535	2.25362043202028e-08
tau( mpg , disp )	-0.768131146377997	1.00695006483270e-09
tau( mpg , hp )	-0.742812506088673	4.33160494891487e-09
tau( mpg , drat )	0.464548785236484	0.000238153299719546
tau( mpg , wt )	-0.727832149528431	6.70577040559586e-09
tau( mpg , qsec )	0.315365218988041	0.0118519955124592
tau( cyl , disp )	0.814426251098896	9.95652738033925e-09
tau( cyl , hp )	0.785186498532206	3.99666648664976e-08
tau( cyl , drat )	-0.551317846419971	0.000113971491179788
tau( cyl , wt )	0.728261112109847	2.8291139386738e-07
tau( cyl , qsec )	-0.448969823063678	0.00151975754259582
tau( disp , hp )	0.665998735836933	1.37128917110374e-07
tau( disp , drat )	-0.498982773649946	7.7849413883775e-05
tau( disp , wt )	0.74338239716769	3.07005865174403e-09
tau( disp , qsec )	-0.300815493561507	0.0162715491077270
tau( hp , drat )	-0.382626885048903	0.00260253883990014
tau( hp , wt )	0.611308095732059	1.26623978791152e-06
tau( hp , qsec )	-0.47290612619145	0.000173773709093133
tau( drat , wt )	-0.547149528309556	1.42468808580507e-05
tau( drat , qsec )	0.0327215469575162	0.794874350624461
tau( wt , qsec )	-0.141988121712634	0.255895606449493

Figure 1

PNG link

Postscript link

PDF link

Parameters (Session):

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')

Free Statistics

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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code