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Author

*The author of this computation has been verified*

R Software Module

rwasp_correlation.wasp

Title produced by software

Pearson Correlation

Date of computation

Fri, 09 Dec 2016 12:45:15 +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/2016/Dec/09/t1481283953zfj491aznlrxur6.htm/, Retrieved Fri, 17 May 2024 00:47:51 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=298473, Retrieved Fri, 17 May 2024 00:47:51 +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] [] [2016-12-09 11:45:15] [c6ea875f0603e0876d03f43aca979571] [Current]

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Dataseries X:

Download CSV

Histogram

Boxplots

2.75
2.25
3.00
3.00
2.75
3.00
3.00
3.75
3.25
3.00
2.75
2.75
3.00
3.00
3.00
3.50
3.00
2.25
3.25
3.25
3.00
3.00
3.00
3.00
3.00
2.75
3.25
3.25
3.25
2.50
3.25
1.25
2.50
3.75
3.25
3.00
3.25
3.25
2.75
3.00
3.00
3.25
3.50
3.00
3.00
2.50
3.00
3.00
3.25
3.50
2.50
3.00
3.25
2.75
3.00
3.00
3.00
2.25
3.00
2.75
3.00
3.00
2.25
3.25
2.50
3.50
2.50
3.00
2.75
3.50
3.25
2.50
3.00
3.00
3.75
3.00
3.00
3.00
3.00
2.75
3.25
3.25
2.75
2.50
2.25
3.00
3.25
2.50
3.25
3.00
3.00

Dataseries Y:

Download CSV

Histogram

3.25
4.00
4.25
4.00
4.25
4.25
3.75
4.00
3.50
4.00
4.25
4.00
4.00
4.00
3.75
4.00
3.25
3.75
4.25
3.25
4.25
3.50
3.50
4.50
4.25
3.25
4.00
3.75
3.75
3.25
4.25
2.75
3.25
4.25
4.00
4.25
4.00
4.00
4.00
4.25
3.50
3.50
4.00
3.75
4.00
3.50
3.75
4.25
4.25
5.00
4.25
4.50
4.25
3.50
4.25
4.25
4.00
4.50
4.00
3.25
4.00
3.00
4.00
4.00
4.00
3.50
3.75
3.50
3.75
3.75
4.00
2.75
4.50
2.75
4.50
4.75
4.25
3.50
4.25
3.50
4.75
4.00
4.00
3.75
3.00
4.25
4.50
3.75
4.50
4.00
4.00

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	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 time4 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298473&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]

4 seconds[/C][/ROW] [ROW]

R Server[/C]

Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=298473&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298473&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	Big Analytics Cloud Computing Center

Pearson Product Moment Correlation - Ungrouped Data
Statistic	Variable X	Variable Y
Mean	2.96428571428571	3.90659340659341
Biased Variance	0.140894819466248	0.202813669846637
Biased Standard Deviation	0.375359586884694	0.450348387192224
Covariance	0.0653769841269841
Correlation	0.382498622428223
Determination	0.146305196159488
T-Test	3.90547228038332
p-value (2 sided)	0.000182778527600273
p-value (1 sided)	9.13892638001363e-05
95% CI of Correlation	[0.191650801797091, 0.545474471495549]
Degrees of Freedom	89
Number of Observations	91

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 2.96428571428571 & 3.90659340659341 \tabularnewline
Biased Variance & 0.140894819466248 & 0.202813669846637 \tabularnewline
Biased Standard Deviation & 0.375359586884694 & 0.450348387192224 \tabularnewline
Covariance & 0.0653769841269841 \tabularnewline
Correlation & 0.382498622428223 \tabularnewline
Determination & 0.146305196159488 \tabularnewline
T-Test & 3.90547228038332 \tabularnewline
p-value (2 sided) & 0.000182778527600273 \tabularnewline
p-value (1 sided) & 9.13892638001363e-05 \tabularnewline
95% CI of Correlation & [0.191650801797091, 0.545474471495549] \tabularnewline
Degrees of Freedom & 89 \tabularnewline
Number of Observations & 91 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298473&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]2.96428571428571[/C][C]3.90659340659341[/C][/ROW]
[ROW][C]Biased Variance[/C][C]0.140894819466248[/C][C]0.202813669846637[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]0.375359586884694[/C][C]0.450348387192224[/C][/ROW]
[ROW][C]Covariance[/C][C]0.0653769841269841[/C][/ROW]
[ROW][C]Correlation[/C][C]0.382498622428223[/C][/ROW]
[ROW][C]Determination[/C][C]0.146305196159488[/C][/ROW]
[ROW][C]T-Test[/C][C]3.90547228038332[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0.000182778527600273[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]9.13892638001363e-05[/C][/ROW]
[ROW][C]95% CI of Correlation[/C][C][0.191650801797091, 0.545474471495549][/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]89[/C][/ROW]
[ROW][C]Number of Observations[/C][C]91[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298473&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298473&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	2.96428571428571	3.90659340659341
Biased Variance	0.140894819466248	0.202813669846637
Biased Standard Deviation	0.375359586884694	0.450348387192224
Covariance	0.0653769841269841
Correlation	0.382498622428223
Determination	0.146305196159488
T-Test	3.90547228038332
p-value (2 sided)	0.000182778527600273
p-value (1 sided)	9.13892638001363e-05
95% CI of Correlation	[0.191650801797091, 0.545474471495549]
Degrees of Freedom	89
Number of Observations	91

Normality Tests
> jarque.x Jarque-Bera Normality Test data: x JB = 68.963, p-value = 1.11e-15 alternative hypothesis: greater
> jarque.y Jarque-Bera Normality Test data: y JB = 3.8148, p-value = 0.1485 alternative hypothesis: greater
> ad.x Anderson-Darling normality test data: x A = 3.6536, p-value = 3.433e-09
> ad.y Anderson-Darling normality test data: y A = 2.086, p-value = 2.408e-05

\begin{tabular}{lllllllll}
\hline
Normality Tests \tabularnewline
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 68.963, p-value = 1.11e-15
alternative hypothesis: greater
 \tabularnewline
> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 3.8148, p-value = 0.1485
alternative hypothesis: greater
 \tabularnewline
> ad.x
	Anderson-Darling normality test
data:  x
A = 3.6536, p-value = 3.433e-09
 \tabularnewline
> ad.y
	Anderson-Darling normality test
data:  y
A = 2.086, p-value = 2.408e-05
 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298473&T=2

[TABLE]
[ROW][C]Normality Tests[/C][/ROW]
[ROW][C]> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 68.963, p-value = 1.11e-15
alternative hypothesis: greater
[/C][/ROW]
[ROW][C]> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 3.8148, p-value = 0.1485
alternative hypothesis: greater
[/C][/ROW]
[ROW][C]> ad.x
	Anderson-Darling normality test
data:  x
A = 3.6536, p-value = 3.433e-09
[/C][/ROW]
[ROW][C]> ad.y
	Anderson-Darling normality test
data:  y
A = 2.086, p-value = 2.408e-05
[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298473&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298473&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 = 68.963, p-value = 1.11e-15 alternative hypothesis: greater
> jarque.y Jarque-Bera Normality Test data: y JB = 3.8148, p-value = 0.1485 alternative hypothesis: greater
> ad.x Anderson-Darling normality test data: x A = 3.6536, p-value = 3.433e-09
> ad.y Anderson-Darling normality test data: y A = 2.086, p-value = 2.408e-05

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):

par2 = greygreygreygreygrey ; par3 = FALSEFALSEFALSEFALSEFALSE ; par4 = UnknownUnknownUnknownUnknownUnknown ;

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()

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code