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Bonus - Pearson Correlation

*The author of this computation has been verified*

R Software Module: Patrick.Wessa/rwasp_pairs.wasp (opens new window with default values)

Title produced by software: Kendall tau Correlation Matrix

Date of computation: Mon, 13 Dec 2010 19:37:37 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/13/t1292268941hm32nq939fdjn1k.htm/, Retrieved Mon, 20 May 2013 17:02:56 +0000

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

System-generated keywords (parent):

t1291984038blfe7gfcemxkbye (pk = 107606)

Estimated Impact

Dataseries X:

» Textfile « » CSV « » Correlation Matrix « » Notched Boxplots «

6,30	2,00	4,50	0,000	0,82	1,62	3	1	3
2,10	1,80	69,00	3,406	3,66	2,80	3	5	4
9,10	0,70	27,00	1,023	2,25	2,26	4	4	4
15,80	3,90	19,00	-4,638	-3,52	1,54	1	1	1
5,20	1,00	30,40	2,204	2,23	2,59	4	5	4
10,90	3,60	28,00	0,519	1,41	1,80	1	2	1
8,30	1,40	50,00	1,717	2,64	2,36	1	1	1
11,00	1,50	7,00	-3,372	0,81	2,05	5	4	4
3,20	0,70	30,00	2,667	2,63	2,45	5	5	5
6,30	2,10	3,50	-4,125	0,08	1,62	1	1	1
8,60	0,00	50,00	0,477	1,40	1,45	2	2	2
6,60	4,10	6,00	-3,105	0,54	1,62	2	2	2
9,50	1,20	10,40	-3,699	0,70	2,08	2	2	2
3,30	0,50	20,00	1,442	2,06	2,17	5	5	5
11,00	3,40	3,90	-3,921	0,00	1,20	3	1	2
4,70	1,50	41,00	1,929	2,51	2,49	1	3	1
10,40	3,40	9,00	-3,996	0,60	1,45	5	1	3
7,40	0,80	7,60	0,017	0,74	1,83	5	3	4
2,10	0,80	46,00	2,717	2,82	2,53	5	5	5
7,70	1,40	2,60	-5,301	-3,85	1,33	5	2	4
17,90	2,00	24,00	-5,000	-3,60	1,70	1	1	1
6,10	1,90	100,00	1,792	3,12	2,43	1	1	1
11,90	1,30	3,20	-4,638	-3,40	1,28	4	1	3
10,80	2,00	2,00	-4,319	-3,48	1,48	4	1	3
13,80	5,60	5,00	0,230	0,80	1,08	2	1	1
14,30	3,10	6,50	0,544	1,03	2,08	2	1	1
15,20	1,80	12,00	-3,319	1,19	2,15	2	2	2
10,00	0,90	20,20	1,000	2,06	2,23	4	4	4
11,90	1,80	13,00	0,210	1,06	1,23	2	1	2
6,50	1,90	27,00	2,283	2,26	2,06	4	4	4
7,50	0,90	18,00	0,398	1,08	1,49	5	5	5
10,60	2,60	4,70	-3,553	0,28	1,32	3	1	3
7,40	2,40	9,80	0,627	1,70	1,72	1	1	1
8,40	1,20	29,00	0,833	2,25	2,21	2	3	2
5,70	0,90	7,00	-3,125	1,09	2,35	2	2	2
4,90	0,50	6,00	0,556	1,32	2,35	3	2	3
3,20	0,60	20,00	1,744	2,24	2,18	5	5	5
11,00	2,30	4,50	-3,046	0,41	1,78	2	1	2
4,90	0,50	7,50	0,301	1,09	2,30	3	1	3
13,20	2,60	2,30	-3,983	0,40	1,66	3	2	2
9,70	0,60	24,00	0,622	1,76	2,32	4	3	4
12,80	6,60	3,00	0,544	0,59	1,15	2	1	1

Output produced by software:

Enter (or paste) a matrix (table) containing all data (time) series. Every column represents a different variable and must be delimited by a space or Tab. Every row represents a period in time (or category) and must be delimited by hard returns. The easiest way to enter data is to copy and paste a block of spreadsheet cells. Please, do not use commas or spaces to seperate groups of digits!

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	'Gwilym Jenkins' @ 72.249.127.135

Correlations for all pairs of data series (method=pearson)
	SWS	PS	L	Wb	Wbr	Tg	P	S	D
SWS	1	0.518	-0.372	-0.584	-0.578	-0.575	-0.353	-0.58	-0.535
PS	0.518	1	-0.268	-0.257	-0.247	-0.572	-0.398	-0.504	-0.572
L	-0.372	-0.268	1	0.584	0.521	0.562	-0.17	0.316	0.015
Wb	-0.584	-0.257	0.584	1	0.818	0.584	0.109	0.557	0.292
Wbr	-0.578	-0.247	0.521	0.818	1	0.641	0.035	0.509	0.209
Tg	-0.575	-0.572	0.562	0.584	0.641	1	0.091	0.583	0.31
P	-0.353	-0.398	-0.17	0.109	0.035	0.091	1	0.626	0.927
S	-0.58	-0.504	0.316	0.557	0.509	0.583	0.626	1	0.79
D	-0.535	-0.572	0.015	0.292	0.209	0.31	0.927	0.79	1

Correlations for all pairs of data series with p-values
pair	Pearson r	Spearman rho	Kendall tau
SWS;PS	0.5182	0.5641	0.3924
p-value	(4e-04)	(1e-04)	(3e-04)
SWS;L	-0.3722	-0.4014	-0.2778
p-value	(0.0152)	(0.0084)	(0.0101)
SWS;Wb	-0.5835	-0.6189	-0.4465
p-value	(0)	(0)	(0)
SWS;Wbr	-0.5784	-0.622	-0.4573
p-value	(1e-04)	(0)	(0)
SWS;Tg	-0.5749	-0.6298	-0.4628
p-value	(1e-04)	(0)	(0)
SWS;P	-0.3527	-0.2896	-0.224
p-value	(0.022)	(0.0629)	(0.0545)
SWS;S	-0.5803	-0.5428	-0.4242
p-value	(1e-04)	(2e-04)	(3e-04)
SWS;D	-0.5346	-0.4751	-0.3771
p-value	(3e-04)	(0.0015)	(0.0012)
PS;L	-0.2683	-0.4118	-0.2562
p-value	(0.0858)	(0.0067)	(0.0185)
PS;Wb	-0.2574	-0.4041	-0.2472
p-value	(0.0998)	(0.0079)	(0.0227)
PS;Wbr	-0.2473	-0.4911	-0.2957
p-value	(0.1143)	(0.001)	(0.0064)
PS;Tg	-0.5717	-0.5528	-0.387
p-value	(1e-04)	(1e-04)	(4e-04)
PS;P	-0.398	-0.4703	-0.3417
p-value	(0.0091)	(0.0017)	(0.0036)
PS;S	-0.5036	-0.6061	-0.4586
p-value	(7e-04)	(0)	(1e-04)
PS;D	-0.5719	-0.6303	-0.4859
p-value	(1e-04)	(0)	(0)
L;Wb	0.5844	0.7214	0.5417
p-value	(0)	(0)	(0)
L;Wbr	0.5207	0.8153	0.66
p-value	(4e-04)	(0)	(0)
L;Tg	0.5617	0.6602	0.4915
p-value	(1e-04)	(0)	(0)
L;P	-0.1697	-0.0932	-0.0841
p-value	(0.2825)	(0.557)	(0.4701)
L;S	0.3157	0.5042	0.3844
p-value	(0.0417)	(7e-04)	(0.0012)
L;D	0.0147	0.1247	0.0922
p-value	(0.9265)	(0.4313)	(0.4292)
Wb;Wbr	0.8178	0.9383	0.8107
p-value	(0)	(0)	(0)
Wb;Tg	0.5844	0.7036	0.5169
p-value	(0)	(0)	(0)
Wb;P	0.1086	0.1083	0.0761
p-value	(0.4936)	(0.495)	(0.5122)
Wb;S	0.557	0.5768	0.463
p-value	(1e-04)	(1e-04)	(1e-04)
Wb;D	0.2919	0.2842	0.2007
p-value	(0.0607)	(0.0682)	(0.0844)
Wbr;Tg	0.641	0.7847	0.5791
p-value	(0)	(0)	(0)
Wbr;P	0.0354	0.0653	0.0426
p-value	(0.8239)	(0.6812)	(0.7139)
Wbr;S	0.5086	0.5852	0.4754
p-value	(6e-04)	(0)	(1e-04)
Wbr;D	0.2089	0.2657	0.1983
p-value	(0.1842)	(0.0889)	(0.0885)
Tg;P	0.0906	0.0579	0.0349
p-value	(0.5683)	(0.7156)	(0.7641)
Tg;S	0.5832	0.5693	0.4532
p-value	(1e-04)	(1e-04)	(1e-04)
Tg;D	0.31	0.268	0.1947
p-value	(0.0457)	(0.0862)	(0.0949)
P;S	0.6257	0.5701	0.4755
p-value	(0)	(1e-04)	(2e-04)
P;D	0.9273	0.9304	0.8709
p-value	(0)	(0)	(0)
S;D	0.7898	0.7239	0.6292
p-value	(0)	(0)	(0)

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/13/t1292268941hm32nq939fdjn1k/1d1h41292269054.png (opens in new window)

http://www.freestatistics.org/blog/date/2010/Dec/13/t1292268941hm32nq939fdjn1k/1d1h41292269054.ps (opens in new window)

Click here to open pdf file.

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')