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R Software Module

rwasp_correlation.wasp

Title produced by software

Pearson Correlation

Date of computation

Wed, 13 Dec 2017 14:20:45 +0100

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2017/Dec/13/t1513171277obbk5w82kfy014o.htm/, Retrieved Wed, 15 May 2024 13:43:38 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=309288, Retrieved Wed, 15 May 2024 13:43:38 +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)

-       [Pearson Correlation] [Pearson Correlation] [2017-12-13 13:20:45] [64452737148143cd44d8cd15ff28c062] [Current]

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Dataseries X:

Download CSV

Histogram

Boxplots

16,5
9,2
6,2
5,8
15
5,7
6,4
4,3
15,1
0,5
3,7
11,8
0,5
8,6
7,2
1,1
1,9
3,1
27,9
15,6
9,5
1,9
8,4
3,8
9,1
7,6
6
5,3
3,8
3,3
7,4
2,9
7,4
8,3
12,8
11,6
3,3
9
8,4
7,1
6,3
9,4
10,3
12,9
4,6
20,4
2
6,1
9,2
11,4
4,3
5,1
5,1
5,5
10,7
9,2
3,3
11
9,1
3,8
6,7
10,8
5,4
23,8
4,1
27,2
3,1
2,4
6,1
5,2
5,3
3,9
6,1
7,2
17,8
22,2
0,8
23,3
5,8
3,1
4,4
4,7
2
4,4
5,9
6
10,8
7,1
6
2,4
6,6
7,4
15,5
4
1,7
7,9
30,3
3,4
6,7
23,7
4,5
1,9
0,7
3,3
3,3
3,2
2,7
9,9
5,7
4,7
13,1

Dataseries Y:

Download CSV

Histogram

16,1
19,7
7,1
7,7
18,7
5,8
5,8
5,9
15,6
4,3
4,7
10,9
0,5
7,9
16,5
0,9
3,1
4,5
22,3
21,4
14
2,2
7,5
2,1
12,7
6,4
7,3
3,7
3
2,1
13,1
4,4
11,5
11
14,2
11,9
5
22,2
23,9
6,7
11,1
8,5
9,6
10
4
28,5
3
7
15,7
15,1
9,7
5,3
6,3
5,8
12,7
18,2
2,9
23,9
13,2
3,4
9,1
8,9
11
31,8
3,9
26
3,6
4,3
11,4
5,5
11,5
4,2
3,8
6,1
17,1
26,2
0,9
28
6
1,5
5,8
7,6
3
5,6
5,8
6,4
11,5
5,5
5,5
2,6
8,6
12,5
17,9
1,9
1,9
9,6
32,8
8,5
15,5
27,7
4,7
3,4
0,6
5,6
6,9
4,7
1,9
7,8
11,2
6,2
28,4

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	5 seconds
R Server	Big Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time5 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=309288&T=0

[TABLE]
[ROW]

Summary of computational transaction[/C][/ROW] [ROW]

Raw Input[/C]

view raw input (R code) [/C][/ROW] [ROW]

Raw Output[/C]

view raw output of R engine [/C][/ROW] [ROW]

Computing time[/C]

5 seconds[/C][/ROW] [ROW]

R Server[/C]

Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=309288&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=309288&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	5 seconds
R Server	Big Analytics Cloud Computing Center

Pearson Product Moment Correlation - Ungrouped Data
Statistic	Variable X	Variable Y
Mean	7.80990990990991	9.87927927927928
Biased Variance	36.5691810729649	57.0104715526337
Biased Standard Deviation	6.0472457427299	7.55052789893751
Covariance	40.3469344799345
Correlation	0.875679767248747
Determination	0.76681505476882
T-Test	18.9325150264662
p-value (2 sided)	3.00871607422228e-36
p-value (1 sided)	1.50435803711114e-36
95% CI of Correlation	[0.8237377454463, 0.913045012654866]
Degrees of Freedom	109
Number of Observations	111

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 7.80990990990991 & 9.87927927927928 \tabularnewline
Biased Variance & 36.5691810729649 & 57.0104715526337 \tabularnewline
Biased Standard Deviation & 6.0472457427299 & 7.55052789893751 \tabularnewline
Covariance & 40.3469344799345 \tabularnewline
Correlation & 0.875679767248747 \tabularnewline
Determination & 0.76681505476882 \tabularnewline
T-Test & 18.9325150264662 \tabularnewline
p-value (2 sided) & 3.00871607422228e-36 \tabularnewline
p-value (1 sided) & 1.50435803711114e-36 \tabularnewline
95% CI of Correlation & [0.8237377454463, 0.913045012654866] \tabularnewline
Degrees of Freedom & 109 \tabularnewline
Number of Observations & 111 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=309288&T=1

[TABLE]
[ROW][C]Pearson Product Moment Correlation - Ungrouped Data[/C][/ROW]
[ROW][C]Statistic[/C][C]Variable X[/C][C]Variable Y[/C][/ROW]
[ROW][C]Mean[/C][C]7.80990990990991[/C][C]9.87927927927928[/C][/ROW]
[ROW][C]Biased Variance[/C][C]36.5691810729649[/C][C]57.0104715526337[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]6.0472457427299[/C][C]7.55052789893751[/C][/ROW]
[ROW][C]Covariance[/C][C]40.3469344799345[/C][/ROW]
[ROW][C]Correlation[/C][C]0.875679767248747[/C][/ROW]
[ROW][C]Determination[/C][C]0.76681505476882[/C][/ROW]
[ROW][C]T-Test[/C][C]18.9325150264662[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]3.00871607422228e-36[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]1.50435803711114e-36[/C][/ROW]
[ROW][C]95% CI of Correlation[/C][C][0.8237377454463, 0.913045012654866][/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]109[/C][/ROW]
[ROW][C]Number of Observations[/C][C]111[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=309288&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=309288&T=1

As an alternative you can also use a QR Code:

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

Pearson Product Moment Correlation - Ungrouped Data
Statistic	Variable X	Variable Y
Mean	7.80990990990991	9.87927927927928
Biased Variance	36.5691810729649	57.0104715526337
Biased Standard Deviation	6.0472457427299	7.55052789893751
Covariance	40.3469344799345
Correlation	0.875679767248747
Determination	0.76681505476882
T-Test	18.9325150264662
p-value (2 sided)	3.00871607422228e-36
p-value (1 sided)	1.50435803711114e-36
95% CI of Correlation	[0.8237377454463, 0.913045012654866]
Degrees of Freedom	109
Number of Observations	111

Normality Tests
> jarque.x Jarque-Bera Normality Test data: x JB = 93.631, p-value < 2.2e-16 alternative hypothesis: greater
> jarque.y Jarque-Bera Normality Test data: y JB = 30.034, p-value = 3.008e-07 alternative hypothesis: greater
> ad.x Anderson-Darling normality test data: x A = 5.6817, p-value = 4.379e-14
> ad.y Anderson-Darling normality test data: y A = 4.5207, p-value = 2.773e-11

\begin{tabular}{lllllllll}
\hline
Normality Tests \tabularnewline
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 93.631, p-value < 2.2e-16
alternative hypothesis: greater
 \tabularnewline
> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 30.034, p-value = 3.008e-07
alternative hypothesis: greater
 \tabularnewline
> ad.x
	Anderson-Darling normality test
data:  x
A = 5.6817, p-value = 4.379e-14
 \tabularnewline
> ad.y
	Anderson-Darling normality test
data:  y
A = 4.5207, p-value = 2.773e-11
 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=309288&T=2

[TABLE]
[ROW][C]Normality Tests[/C][/ROW]
[ROW][C]> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 93.631, p-value < 2.2e-16
alternative hypothesis: greater
[/C][/ROW]
[ROW][C]> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 30.034, p-value = 3.008e-07
alternative hypothesis: greater
[/C][/ROW]
[ROW][C]> ad.x
	Anderson-Darling normality test
data:  x
A = 5.6817, p-value = 4.379e-14
[/C][/ROW]
[ROW][C]> ad.y
	Anderson-Darling normality test
data:  y
A = 4.5207, p-value = 2.773e-11
[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=309288&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=309288&T=2

As an alternative you can also use a QR Code:

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

Normality Tests
> jarque.x Jarque-Bera Normality Test data: x JB = 93.631, p-value < 2.2e-16 alternative hypothesis: greater
> jarque.y Jarque-Bera Normality Test data: y JB = 30.034, p-value = 3.008e-07 alternative hypothesis: greater
> ad.x Anderson-Darling normality test data: x A = 5.6817, p-value = 4.379e-14
> ad.y Anderson-Darling normality test data: y A = 4.5207, p-value = 2.773e-11

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

Parameters (R input):

R code (references can be found in the software module):

library(psychometric)
x <- x[!is.na(y)]
y <- y[!is.na(y)]
y <- y[!is.na(x)]
x <- x[!is.na(x)]
bitmap(file='test1.png')
histx <- hist(x, plot=FALSE)
histy <- hist(y, plot=FALSE)
maxcounts <- max(c(histx$counts, histx$counts))
xrange <- c(min(x),max(x))
yrange <- c(min(y),max(y))
nf <- layout(matrix(c(2,0,1,3),2,2,byrow=TRUE), c(3,1), c(1,3), TRUE)
par(mar=c(4,4,1,1))
plot(x, y, xlim=xrange, ylim=yrange, xlab=xlab, ylab=ylab, sub=main)
par(mar=c(0,4,1,1))
barplot(histx$counts, axes=FALSE, ylim=c(0, maxcounts), space=0)
par(mar=c(4,0,1,1))
barplot(histy$counts, axes=FALSE, xlim=c(0, maxcounts), space=0, horiz=TRUE)
dev.off()
lx = length(x)
makebiased = (lx-1)/lx
varx = var(x)*makebiased
vary = var(y)*makebiased
corxy <- cor.test(x,y,method='pearson', na.rm = T)
cxy <- as.matrix(corxy$estimate)[1,1]
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Pearson Product Moment Correlation - Ungrouped Data',3,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Statistic',1,TRUE)
a<-table.element(a,'Variable X',1,TRUE)
a<-table.element(a,'Variable Y',1,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Mean',header=TRUE)
a<-table.element(a,mean(x))
a<-table.element(a,mean(y))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Biased Variance',header=TRUE)
a<-table.element(a,varx)
a<-table.element(a,vary)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Biased Standard Deviation',header=TRUE)
a<-table.element(a,sqrt(varx))
a<-table.element(a,sqrt(vary))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Covariance',header=TRUE)
a<-table.element(a,cov(x,y),2)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Correlation',header=TRUE)
a<-table.element(a,cxy,2)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Determination',header=TRUE)
a<-table.element(a,cxy*cxy,2)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'T-Test',header=TRUE)
a<-table.element(a,as.matrix(corxy$statistic)[1,1],2)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'p-value (2 sided)',header=TRUE)
a<-table.element(a,(p2 <- as.matrix(corxy$p.value)[1,1]),2)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'p-value (1 sided)',header=TRUE)
a<-table.element(a,p2/2,2)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'95% CI of Correlation',header=TRUE)
a<-table.element(a,paste('[',CIr(r=cxy, n = lx, level = .95)[1],', ', CIr(r=cxy, n = lx, level = .95)[2],']',sep=''),2)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Degrees of Freedom',header=TRUE)
a<-table.element(a,lx-2,2)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Number of Observations',header=TRUE)
a<-table.element(a,lx,2)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
library(moments)
library(nortest)
jarque.x <- jarque.test(x)
jarque.y <- jarque.test(y)
if(lx>7) {
ad.x <- ad.test(x)
ad.y <- ad.test(y)
}
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Normality Tests',1,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,paste('',RC.texteval('jarque.x'),'
',sep=''))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,paste('',RC.texteval('jarque.y'),'
',sep=''))
a<-table.row.end(a)
if(lx>7) {
a<-table.row.start(a)
a<-table.element(a,paste('',RC.texteval('ad.x'),'
',sep=''))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,paste('',RC.texteval('ad.y'),'
',sep=''))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
library(car)
bitmap(file='test2.png')
qqPlot(x,main='QQplot of variable x')
dev.off()
bitmap(file='test3.png')
qqPlot(y,main='QQplot of variable y')
dev.off()

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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code