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*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

Tue, 11 Dec 2012 13:51:34 -0500

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/2012/Dec/11/t1355251911pu9ualcml66w84n.htm/, Retrieved Thu, 25 Apr 2024 17:15:40 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=198622, Retrieved Thu, 25 Apr 2024 17:15:40 +0000

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Estimated Impact

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] [WS10] [2012-12-11 18:51:34] [eef9f4a55a40721b371cf4577ce601c1] [Current]

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Dataseries X:

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Histogram

Boxplots

521	18308	185	4,041	79,6	7,2
367	1148	600	0,55	1	8,5
443	18068	372	3,665	32,3	5,7
365	7729	142	2,351	45,1	7,3
614	100484	432	29,76	190,8	7,5
385	16728	290	3,294	31,8	5
286	14630	346	3,287	678,4	6,7
397	4008	328	0,666	340,8	6,2
764	38927	354	12,938	239,6	7,3
427	22322	266	6,478	111,9	5
153	3711	320	1,108	172,5	2,8
231	3136	197	1,007	12,2	6,1
524	50508	266	11,431	205,6	7,1
328	28886	173	5,544	154,6	5,9
240	16996	190	2,777	49,7	4,6
286	13035	239	2,478	30,3	4,4
285	12973	190	3,685	92,8	7,4
569	16309	241	4,22	96,9	7,1
96	5227	189	1,228	39,8	7,5
498	19235	358	4,781	489,2	5,9
481	44487	315	6,016	767,6	9
468	44213	303	9,295	163,6	9,2
177	23619	228	4,375	55	5,1
198	9106	134	2,573	54,9	8,6
458	24917	189	5,117	74,3	6,6
108	3872	196	0,799	5,5	6,9
246	8945	183	1,578	20,5	2,7
291	2373	417	1,202	10,9	5,5
68	7128	233	1,109	123,7	7,2
311	23624	349	7,73	1042	6,6
606	5242	284	1,515	12,5	6,9
512	92629	499	17,99	381	7,2
426	28795	231	6,629	136,1	5,8
47	4487	143	0,639	9,3	4,1
265	48799	249	10,847	264,9	6,4
370	14067	195	3,146	45,8	6,7
312	12693	288	2,842	29,6	6
222	62184	229	11,882	265,1	6,9
280	9153	287	1,003	960,3	8,5
759	14250	224	3,487	115,8	6,2
114	3680	161	0,696	9,2	3,4
419	18063	221	4,877	118,3	6,6
435	65112	237	16,987	64,9	6,6
186	11340	220	1,723	21	4,9
87	4553	185	0,563	60,8	6,4
188	28960	260	6,187	156,3	5,8
303	19201	261	4,867	73,1	6,3
102	7533	118	1,793	74,5	10,5
127	26343	268	4,892	90,1	5,4
251	1641	300	0,454	4,7	5,1
205	145360	237	10,379	889	6,8
453	9066420	240	82,422	609	5,6
320	1038933	185	16,491	1259	3,8
405	2739420	201	60,876	289	8,2
89	61620	193	0,474	475	4,1
74	827530	254	7,523	490	2,8
101	534100	230	5,45	333	6,3
321	328755	197	10,605	300	11,4
315	1413895	248	40,397	210	19,4
229	2909136	258	60,607	650	5,8
302	3604246	206	58,133	512	6,9
216	917504	199	8,192	256	3,5

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	'Sir Ronald Aylmer Fisher' @ fisher.wessa.net

\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 & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=198622&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]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=198622&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=198622&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	'Sir Ronald Aylmer Fisher' @ fisher.wessa.net

Correlations for all pairs of data series (method=pearson)
	Assaults	BachDegrees	PoliceExp	Population	Density	Unemployment
Assaults	1	0.062	0.387	0.19	0.024	0.205
BachDegrees	0.062	1	-0.08	0.878	0.312	0.038
PoliceExp	0.387	-0.08	1	0.013	0.13	0.067
Population	0.19	0.878	0.013	1	0.338	0.229
Density	0.024	0.312	0.13	0.338	1	0.024
Unemployment	0.205	0.038	0.067	0.229	0.024	1

\begin{tabular}{lllllllll}
\hline
Correlations for all pairs of data series (method=pearson) \tabularnewline
  & Assaults & BachDegrees & PoliceExp & Population & Density & Unemployment \tabularnewline
Assaults & 1 & 0.062 & 0.387 & 0.19 & 0.024 & 0.205 \tabularnewline
BachDegrees & 0.062 & 1 & -0.08 & 0.878 & 0.312 & 0.038 \tabularnewline
PoliceExp & 0.387 & -0.08 & 1 & 0.013 & 0.13 & 0.067 \tabularnewline
Population & 0.19 & 0.878 & 0.013 & 1 & 0.338 & 0.229 \tabularnewline
Density & 0.024 & 0.312 & 0.13 & 0.338 & 1 & 0.024 \tabularnewline
Unemployment & 0.205 & 0.038 & 0.067 & 0.229 & 0.024 & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=198622&T=1

[TABLE]
[ROW][C]Correlations for all pairs of data series (method=pearson)[/C][/ROW]
[ROW][C] [/C][C]Assaults[/C][C]BachDegrees[/C][C]PoliceExp[/C][C]Population[/C][C]Density[/C][C]Unemployment[/C][/ROW]
[ROW][C]Assaults[/C][C]1[/C][C]0.062[/C][C]0.387[/C][C]0.19[/C][C]0.024[/C][C]0.205[/C][/ROW]
[ROW][C]BachDegrees[/C][C]0.062[/C][C]1[/C][C]-0.08[/C][C]0.878[/C][C]0.312[/C][C]0.038[/C][/ROW]
[ROW][C]PoliceExp[/C][C]0.387[/C][C]-0.08[/C][C]1[/C][C]0.013[/C][C]0.13[/C][C]0.067[/C][/ROW]
[ROW][C]Population[/C][C]0.19[/C][C]0.878[/C][C]0.013[/C][C]1[/C][C]0.338[/C][C]0.229[/C][/ROW]
[ROW][C]Density[/C][C]0.024[/C][C]0.312[/C][C]0.13[/C][C]0.338[/C][C]1[/C][C]0.024[/C][/ROW]
[ROW][C]Unemployment[/C][C]0.205[/C][C]0.038[/C][C]0.067[/C][C]0.229[/C][C]0.024[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=198622&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=198622&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)
	Assaults	BachDegrees	PoliceExp	Population	Density	Unemployment
Assaults	1	0.062	0.387	0.19	0.024	0.205
BachDegrees	0.062	1	-0.08	0.878	0.312	0.038
PoliceExp	0.387	-0.08	1	0.013	0.13	0.067
Population	0.19	0.878	0.013	1	0.338	0.229
Density	0.024	0.312	0.13	0.338	1	0.024
Unemployment	0.205	0.038	0.067	0.229	0.024	1

Correlations for all pairs of data series with p-values
pair	Pearson r	Spearman rho	Kendall tau
Assaults;BachDegrees	0.0621	0.2381	0.1693
p-value	(0.6314)	(0.0624)	(0.0519)
Assaults;PoliceExp	0.3867	0.4011	0.2788
p-value	(0.0019)	(0.0012)	(0.0014)
Assaults;Population	0.1896	0.413	0.2888
p-value	(0.1399)	(8e-04)	(9e-04)
Assaults;Density	0.0244	0.1427	0.0942
p-value	(0.8504)	(0.2684)	(0.2796)
Assaults;Unemployment	0.2047	0.3252	0.2203
p-value	(0.1105)	(0.0099)	(0.0121)
BachDegrees;PoliceExp	-0.0797	0.0815	0.0546
p-value	(0.5383)	(0.5289)	(0.5315)
BachDegrees;Population	0.8779	0.9087	0.7916
p-value	(0)	(0)	(0)
BachDegrees;Density	0.3123	0.7231	0.5759
p-value	(0.0135)	(0)	(0)
BachDegrees;Unemployment	0.0375	0.0775	0.0597
p-value	(0.7723)	(0.5495)	(0.496)
PoliceExp;Population	0.0129	0.1748	0.1171
p-value	(0.9205)	(0.1741)	(0.1794)
PoliceExp;Density	0.1297	0.2353	0.1691
p-value	(0.3151)	(0.0656)	(0.0526)
PoliceExp;Unemployment	0.0666	0.0574	0.0395
p-value	(0.607)	(0.6577)	(0.6528)
Population;Density	0.3378	0.6246	0.5029
p-value	(0.0072)	(0)	(0)
Population;Unemployment	0.2289	0.2045	0.1429
p-value	(0.0736)	(0.1109)	(0.1033)
Density;Unemployment	0.0242	0.1737	0.1226
p-value	(0.8518)	(0.177)	(0.1621)

\begin{tabular}{lllllllll}
\hline
Correlations for all pairs of data series with p-values \tabularnewline
pair & Pearson r & Spearman rho & Kendall tau \tabularnewline
Assaults;BachDegrees & 0.0621 & 0.2381 & 0.1693 \tabularnewline
p-value & (0.6314) & (0.0624) & (0.0519) \tabularnewline
Assaults;PoliceExp & 0.3867 & 0.4011 & 0.2788 \tabularnewline
p-value & (0.0019) & (0.0012) & (0.0014) \tabularnewline
Assaults;Population & 0.1896 & 0.413 & 0.2888 \tabularnewline
p-value & (0.1399) & (8e-04) & (9e-04) \tabularnewline
Assaults;Density & 0.0244 & 0.1427 & 0.0942 \tabularnewline
p-value & (0.8504) & (0.2684) & (0.2796) \tabularnewline
Assaults;Unemployment & 0.2047 & 0.3252 & 0.2203 \tabularnewline
p-value & (0.1105) & (0.0099) & (0.0121) \tabularnewline
BachDegrees;PoliceExp & -0.0797 & 0.0815 & 0.0546 \tabularnewline
p-value & (0.5383) & (0.5289) & (0.5315) \tabularnewline
BachDegrees;Population & 0.8779 & 0.9087 & 0.7916 \tabularnewline
p-value & (0) & (0) & (0) \tabularnewline
BachDegrees;Density & 0.3123 & 0.7231 & 0.5759 \tabularnewline
p-value & (0.0135) & (0) & (0) \tabularnewline
BachDegrees;Unemployment & 0.0375 & 0.0775 & 0.0597 \tabularnewline
p-value & (0.7723) & (0.5495) & (0.496) \tabularnewline
PoliceExp;Population & 0.0129 & 0.1748 & 0.1171 \tabularnewline
p-value & (0.9205) & (0.1741) & (0.1794) \tabularnewline
PoliceExp;Density & 0.1297 & 0.2353 & 0.1691 \tabularnewline
p-value & (0.3151) & (0.0656) & (0.0526) \tabularnewline
PoliceExp;Unemployment & 0.0666 & 0.0574 & 0.0395 \tabularnewline
p-value & (0.607) & (0.6577) & (0.6528) \tabularnewline
Population;Density & 0.3378 & 0.6246 & 0.5029 \tabularnewline
p-value & (0.0072) & (0) & (0) \tabularnewline
Population;Unemployment & 0.2289 & 0.2045 & 0.1429 \tabularnewline
p-value & (0.0736) & (0.1109) & (0.1033) \tabularnewline
Density;Unemployment & 0.0242 & 0.1737 & 0.1226 \tabularnewline
p-value & (0.8518) & (0.177) & (0.1621) \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=198622&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]Assaults;BachDegrees[/C][C]0.0621[/C][C]0.2381[/C][C]0.1693[/C][/ROW]
[ROW][C]p-value[/C][C](0.6314)[/C][C](0.0624)[/C][C](0.0519)[/C][/ROW]
[ROW][C]Assaults;PoliceExp[/C][C]0.3867[/C][C]0.4011[/C][C]0.2788[/C][/ROW]
[ROW][C]p-value[/C][C](0.0019)[/C][C](0.0012)[/C][C](0.0014)[/C][/ROW]
[ROW][C]Assaults;Population[/C][C]0.1896[/C][C]0.413[/C][C]0.2888[/C][/ROW]
[ROW][C]p-value[/C][C](0.1399)[/C][C](8e-04)[/C][C](9e-04)[/C][/ROW]
[ROW][C]Assaults;Density[/C][C]0.0244[/C][C]0.1427[/C][C]0.0942[/C][/ROW]
[ROW][C]p-value[/C][C](0.8504)[/C][C](0.2684)[/C][C](0.2796)[/C][/ROW]
[ROW][C]Assaults;Unemployment[/C][C]0.2047[/C][C]0.3252[/C][C]0.2203[/C][/ROW]
[ROW][C]p-value[/C][C](0.1105)[/C][C](0.0099)[/C][C](0.0121)[/C][/ROW]
[ROW][C]BachDegrees;PoliceExp[/C][C]-0.0797[/C][C]0.0815[/C][C]0.0546[/C][/ROW]
[ROW][C]p-value[/C][C](0.5383)[/C][C](0.5289)[/C][C](0.5315)[/C][/ROW]
[ROW][C]BachDegrees;Population[/C][C]0.8779[/C][C]0.9087[/C][C]0.7916[/C][/ROW]
[ROW][C]p-value[/C][C](0)[/C][C](0)[/C][C](0)[/C][/ROW]
[ROW][C]BachDegrees;Density[/C][C]0.3123[/C][C]0.7231[/C][C]0.5759[/C][/ROW]
[ROW][C]p-value[/C][C](0.0135)[/C][C](0)[/C][C](0)[/C][/ROW]
[ROW][C]BachDegrees;Unemployment[/C][C]0.0375[/C][C]0.0775[/C][C]0.0597[/C][/ROW]
[ROW][C]p-value[/C][C](0.7723)[/C][C](0.5495)[/C][C](0.496)[/C][/ROW]
[ROW][C]PoliceExp;Population[/C][C]0.0129[/C][C]0.1748[/C][C]0.1171[/C][/ROW]
[ROW][C]p-value[/C][C](0.9205)[/C][C](0.1741)[/C][C](0.1794)[/C][/ROW]
[ROW][C]PoliceExp;Density[/C][C]0.1297[/C][C]0.2353[/C][C]0.1691[/C][/ROW]
[ROW][C]p-value[/C][C](0.3151)[/C][C](0.0656)[/C][C](0.0526)[/C][/ROW]
[ROW][C]PoliceExp;Unemployment[/C][C]0.0666[/C][C]0.0574[/C][C]0.0395[/C][/ROW]
[ROW][C]p-value[/C][C](0.607)[/C][C](0.6577)[/C][C](0.6528)[/C][/ROW]
[ROW][C]Population;Density[/C][C]0.3378[/C][C]0.6246[/C][C]0.5029[/C][/ROW]
[ROW][C]p-value[/C][C](0.0072)[/C][C](0)[/C][C](0)[/C][/ROW]
[ROW][C]Population;Unemployment[/C][C]0.2289[/C][C]0.2045[/C][C]0.1429[/C][/ROW]
[ROW][C]p-value[/C][C](0.0736)[/C][C](0.1109)[/C][C](0.1033)[/C][/ROW]
[ROW][C]Density;Unemployment[/C][C]0.0242[/C][C]0.1737[/C][C]0.1226[/C][/ROW]
[ROW][C]p-value[/C][C](0.8518)[/C][C](0.177)[/C][C](0.1621)[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=198622&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=198622&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
Assaults;BachDegrees	0.0621	0.2381	0.1693
p-value	(0.6314)	(0.0624)	(0.0519)
Assaults;PoliceExp	0.3867	0.4011	0.2788
p-value	(0.0019)	(0.0012)	(0.0014)
Assaults;Population	0.1896	0.413	0.2888
p-value	(0.1399)	(8e-04)	(9e-04)
Assaults;Density	0.0244	0.1427	0.0942
p-value	(0.8504)	(0.2684)	(0.2796)
Assaults;Unemployment	0.2047	0.3252	0.2203
p-value	(0.1105)	(0.0099)	(0.0121)
BachDegrees;PoliceExp	-0.0797	0.0815	0.0546
p-value	(0.5383)	(0.5289)	(0.5315)
BachDegrees;Population	0.8779	0.9087	0.7916
p-value	(0)	(0)	(0)
BachDegrees;Density	0.3123	0.7231	0.5759
p-value	(0.0135)	(0)	(0)
BachDegrees;Unemployment	0.0375	0.0775	0.0597
p-value	(0.7723)	(0.5495)	(0.496)
PoliceExp;Population	0.0129	0.1748	0.1171
p-value	(0.9205)	(0.1741)	(0.1794)
PoliceExp;Density	0.1297	0.2353	0.1691
p-value	(0.3151)	(0.0656)	(0.0526)
PoliceExp;Unemployment	0.0666	0.0574	0.0395
p-value	(0.607)	(0.6577)	(0.6528)
Population;Density	0.3378	0.6246	0.5029
p-value	(0.0072)	(0)	(0)
Population;Unemployment	0.2289	0.2045	0.1429
p-value	(0.0736)	(0.1109)	(0.1033)
Density;Unemployment	0.0242	0.1737	0.1226
p-value	(0.8518)	(0.177)	(0.1621)

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