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Author

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R Software Module

rwasp_correlation.wasp

Title produced by software

Pearson Correlation

Date of computation

Wed, 09 Dec 2015 11:56:41 +0000

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/2015/Dec/09/t1449662336q67mzmqvow751aa.htm/, Retrieved Thu, 16 May 2024 15:41:39 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=285636, Retrieved Thu, 16 May 2024 15:41:39 +0000

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User-defined keywords

Estimated Impact

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

-       [Pearson Correlation] [pearson correlati...] [2015-12-09 11:56:41] [aff7c5b01bb5e691e5ecdf00b98aae53] [Current]

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Dataseries X:

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Histogram

Boxplots

6.5
6.8
6.8
6.5
6.2
6.2
6.6
6.7
6.5
6.4
6.5
6.8
7.1
7.2
7.1
7
6.9
6.9
7.4
7.3
7
6.8
6.5
6.4
6.3
6
5.9
5.7
5.7
5.7
6.2
6.4
6.2
6.2
6.1
6.1
6.2
6.1
6.1
6.2
6.2
6.2
6.4
6.4
6.4
6.7
6.9
7.1
7.3
7.2
7.1
6.9
6.8
6.7
7.2
7.2
7.1
7.1
7
7.1
7.3
7.2
7.1
7
6.9
7
7.5
7.6
7.5
7.3
7.3
7.4
7.7
7.8
7.7
7.5
7.3
7.3
7.6
7.6

Dataseries Y:

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Histogram

2.3
1.9
0.6
0.6
-0.4
-1.1
-1.7
-0.8
-1.2
-1
-0.1
0.3
0.6
0.7
1.7
1.8
2.3
2.5
2.6
2.3
2.9
3
2.9
3.1
3.2
3.4
3.5
3.4
3.4
3.7
3.8
3.6
3.6
3.6
3.9
3.5
3.7
3.7
3.4
3.2
2.8
2.3
2.3
2.9
2.8
2.8
2.3
2.2
1.5
1.2
1.1
1
1.2
1.6
1.5
1
0.9
0.6
0.8
1
1.1
1
0.9
0.6
0.4
0.3
0.3
0
-0.1
0.1
-0.1
-0.4
-0.7
-0.4
-0.4
0.3
0.6
0.6
0.5
0.9

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	4 seconds
R Server	'Gwilym Jenkins' @ jenkins.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 & 4 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=285636&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]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=285636&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=285636&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	4 seconds
R Server	'Gwilym Jenkins' @ jenkins.wessa.net

Pearson Product Moment Correlation - Ungrouped Data
Statistic	Variable X	Variable Y
Mean	6.7975	1.52125
Biased Variance	0.27824375	2.1741734375
Biased Standard Deviation	0.5274881515257	1.4745078628139
Covariance	-0.470579113924051
Correlation	-0.597461534877055
Determination	0.356960285657647
T-Test	-6.58018878448525
p-value (2 sided)	4.89971457782899e-09
p-value (1 sided)	2.44985728891449e-09
95% CI of Correlation	[-0.722353374278768, -0.434825181221908]
Degrees of Freedom	78
Number of Observations	80

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 6.7975 & 1.52125 \tabularnewline
Biased Variance & 0.27824375 & 2.1741734375 \tabularnewline
Biased Standard Deviation & 0.5274881515257 & 1.4745078628139 \tabularnewline
Covariance & -0.470579113924051 \tabularnewline
Correlation & -0.597461534877055 \tabularnewline
Determination & 0.356960285657647 \tabularnewline
T-Test & -6.58018878448525 \tabularnewline
p-value (2 sided) & 4.89971457782899e-09 \tabularnewline
p-value (1 sided) & 2.44985728891449e-09 \tabularnewline
95% CI of Correlation & [-0.722353374278768, -0.434825181221908] \tabularnewline
Degrees of Freedom & 78 \tabularnewline
Number of Observations & 80 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=285636&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]6.7975[/C][C]1.52125[/C][/ROW]
[ROW][C]Biased Variance[/C][C]0.27824375[/C][C]2.1741734375[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]0.5274881515257[/C][C]1.4745078628139[/C][/ROW]
[ROW][C]Covariance[/C][C]-0.470579113924051[/C][/ROW]
[ROW][C]Correlation[/C][C]-0.597461534877055[/C][/ROW]
[ROW][C]Determination[/C][C]0.356960285657647[/C][/ROW]
[ROW][C]T-Test[/C][C]-6.58018878448525[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]4.89971457782899e-09[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]2.44985728891449e-09[/C][/ROW]
[ROW][C]95% CI of Correlation[/C][C][-0.722353374278768, -0.434825181221908][/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]78[/C][/ROW]
[ROW][C]Number of Observations[/C][C]80[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=285636&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=285636&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	6.7975	1.52125
Biased Variance	0.27824375	2.1741734375
Biased Standard Deviation	0.5274881515257	1.4745078628139
Covariance	-0.470579113924051
Correlation	-0.597461534877055
Determination	0.356960285657647
T-Test	-6.58018878448525
p-value (2 sided)	4.89971457782899e-09
p-value (1 sided)	2.44985728891449e-09
95% CI of Correlation	[-0.722353374278768, -0.434825181221908]
Degrees of Freedom	78
Number of Observations	80

Normality Tests
> jarque.x Jarque-Bera Normality Test data: x JB = 3.1628, p-value = 0.2057 alternative hypothesis: greater
> jarque.y Jarque-Bera Normality Test data: y JB = 4.0512, p-value = 0.1319 alternative hypothesis: greater
> ad.x Anderson-Darling normality test data: x A = 0.92409, p-value = 0.01801
> ad.y Anderson-Darling normality test data: y A = 1.2323, p-value = 0.003086

\begin{tabular}{lllllllll}
\hline
Normality Tests \tabularnewline
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 3.1628, p-value = 0.2057
alternative hypothesis: greater
 \tabularnewline
> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 4.0512, p-value = 0.1319
alternative hypothesis: greater
 \tabularnewline
> ad.x
	Anderson-Darling normality test
data:  x
A = 0.92409, p-value = 0.01801
 \tabularnewline
> ad.y
	Anderson-Darling normality test
data:  y
A = 1.2323, p-value = 0.003086
 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=285636&T=2

[TABLE]
[ROW][C]Normality Tests[/C][/ROW]
[ROW][C]> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 3.1628, p-value = 0.2057
alternative hypothesis: greater
[/C][/ROW]
[ROW][C]> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 4.0512, p-value = 0.1319
alternative hypothesis: greater
[/C][/ROW]
[ROW][C]> ad.x
	Anderson-Darling normality test
data:  x
A = 0.92409, p-value = 0.01801
[/C][/ROW]
[ROW][C]> ad.y
	Anderson-Darling normality test
data:  y
A = 1.2323, p-value = 0.003086
[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=285636&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=285636&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 = 3.1628, p-value = 0.2057 alternative hypothesis: greater
> jarque.y Jarque-Bera Normality Test data: y JB = 4.0512, p-value = 0.1319 alternative hypothesis: greater
> ad.x Anderson-Darling normality test data: x A = 0.92409, p-value = 0.01801
> ad.y Anderson-Darling normality test data: y A = 1.2323, p-value = 0.003086

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$estimate)[1,1]
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Pearson Product Moment Correlation - Ungrouped Data',3,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Statistic',1,TRUE)
a<-table.element(a,'Variable X',1,TRUE)
a<-table.element(a,'Variable Y',1,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('arithmetic_mean.htm','Mean',''),header=TRUE)
a<-table.element(a,mean(x))
a<-table.element(a,mean(y))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('biased.htm','Biased Variance',''),header=TRUE)
a<-table.element(a,varx)
a<-table.element(a,vary)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('biased1.htm','Biased Standard Deviation',''),header=TRUE)
a<-table.element(a,sqrt(varx))
a<-table.element(a,sqrt(vary))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('covariance.htm','Covariance',''),header=TRUE)
a<-table.element(a,cov(x,y),2)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('pearson_correlation.htm','Correlation',''),header=TRUE)
a<-table.element(a,cxy,2)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('coeff_of_determination.htm','Determination',''),header=TRUE)
a<-table.element(a,cxy*cxy,2)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('ttest_statistic.htm','T-Test',''),header=TRUE)
a<-table.element(a,as.matrix(corxy$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')
qq.plot(x,main='QQplot of variable x')
dev.off()
bitmap(file='test3.png')
qq.plot(y,main='QQplot of variable y')
dev.off()

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code