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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_correlation.wasp
Title produced by softwarePearson Correlation
Date of computationWed, 07 Aug 2024 16:56:29 +0200
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2024/Aug/07/t1723042708oz1mn27p094yzta.htm/, Retrieved Sat, 06 Jun 2026 08:44:43 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=320111, Retrieved Sat, 06 Jun 2026 08:44:43 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact292

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Pearson Correlation] [מחקר] [2024-08-07 14:56:29] [7ce0b7a4ddace779e8df3ab88528977a] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
4.68
3.32
3.4
3.12
4.08
4.4
4.08
4.08
2.96
3.8
4.28
3.52
3.52
3.92
1.88
4.72
4.24
4.24
3.48
2.48
4.92
3.96
4.16
5
3.88
3.08
4.04
2.84
3.88
3.56
3.88
3.52
4.16
3.12
4.52
3.44
2.96
4.64
3.44
4.4
3.72
Dataseries Y:
Download CSV
Histogram 
4
2.15
1.75
2.75
4
3.8
2.95
3.45
2.45
3.25
3.45
3.25
4
4.05
2.4
4.25
4.3
3.95
4
2.3
3.95
4.4
3.75
3.85
3.05
3.35
3.25
2.7
4.3
3.45
3.65
1.4
3.95
2.65
3.65
3.8
2.25
4.2
2.9
3.5
2.05

Tables (Output of Computation)





Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R ServerBig 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 time1 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=320111&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]1 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=320111&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=320111&T=0

As an alternative you can also use a QR Code:  
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 Outputview raw output of R engine
Computing time1 seconds
R ServerBig Analytics Cloud Computing Center






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean3.788292682926833.33048780487805
Biased Variance0.4326434265318260.585472932778108
Biased Standard Deviation0.6577563580322320.76516203040801
Covariance0.333065853658537
Correlation0.645636061329489
Determination0.416845923689055
T-Test5.27993316456571
p-value (2 sided)5.15982793301975e-06
p-value (1 sided)2.57991396650987e-06
95% CI of Correlation[0.421759873928886, 0.795313257508177]
Degrees of Freedom39
Number of Observations41

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 3.78829268292683 & 3.33048780487805 \tabularnewline
Biased Variance & 0.432643426531826 & 0.585472932778108 \tabularnewline
Biased Standard Deviation & 0.657756358032232 & 0.76516203040801 \tabularnewline
Covariance & 0.333065853658537 \tabularnewline
Correlation & 0.645636061329489 \tabularnewline
Determination & 0.416845923689055 \tabularnewline
T-Test & 5.27993316456571 \tabularnewline
p-value (2 sided) & 5.15982793301975e-06 \tabularnewline
p-value (1 sided) & 2.57991396650987e-06 \tabularnewline
95% CI of Correlation & [0.421759873928886, 0.795313257508177] \tabularnewline
Degrees of Freedom & 39 \tabularnewline
Number of Observations & 41 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=320111&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]3.78829268292683[/C][C]3.33048780487805[/C][/ROW]
[ROW][C]Biased Variance[/C][C]0.432643426531826[/C][C]0.585472932778108[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]0.657756358032232[/C][C]0.76516203040801[/C][/ROW]
[ROW][C]Covariance[/C][C]0.333065853658537[/C][/ROW]
[ROW][C]Correlation[/C][C]0.645636061329489[/C][/ROW]
[ROW][C]Determination[/C][C]0.416845923689055[/C][/ROW]
[ROW][C]T-Test[/C][C]5.27993316456571[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]5.15982793301975e-06[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]2.57991396650987e-06[/C][/ROW]
[ROW][C]95% CI of Correlation[/C][C][0.421759873928886, 0.795313257508177][/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]39[/C][/ROW]
[ROW][C]Number of Observations[/C][C]41[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=320111&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=320111&T=1

As an alternative you can also use a QR Code:  
QR Code


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

Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean3.788292682926833.33048780487805
Biased Variance0.4326434265318260.585472932778108
Biased Standard Deviation0.6577563580322320.76516203040801
Covariance0.333065853658537
Correlation0.645636061329489
Determination0.416845923689055
T-Test5.27993316456571
p-value (2 sided)5.15982793301975e-06
p-value (1 sided)2.57991396650987e-06
95% CI of Correlation[0.421759873928886, 0.795313257508177]
Degrees of Freedom39
Number of Observations41






Normality Tests
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 1.8004, p-value = 0.4065
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 3.5218, p-value = 0.1719
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 0.23597, p-value = 0.7748

> ad.y
	Anderson-Darling normality test
data:  y
A = 0.93181, p-value = 0.01635


\begin{tabular}{lllllllll}
\hline
Normality Tests \tabularnewline

> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 1.8004, p-value = 0.4065
alternative hypothesis: greater

 \tabularnewline

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 3.5218, p-value = 0.1719
alternative hypothesis: greater

 \tabularnewline

> ad.x
	Anderson-Darling normality test
data:  x
A = 0.23597, p-value = 0.7748

 \tabularnewline

> ad.y
	Anderson-Darling normality test
data:  y
A = 0.93181, p-value = 0.01635

 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=320111&T=2

[TABLE]
[ROW][C]Normality Tests[/C][/ROW]
[ROW][C]
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 1.8004, p-value = 0.4065
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 3.5218, p-value = 0.1719
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> ad.x
	Anderson-Darling normality test
data:  x
A = 0.23597, p-value = 0.7748

[/C][/ROW]
[ROW][C]
> ad.y
	Anderson-Darling normality test
data:  y
A = 0.93181, p-value = 0.01635

[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=320111&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=320111&T=2

As an alternative you can also use a QR Code:  
QR Code


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

Normality Tests
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 1.8004, p-value = 0.4065
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 3.5218, p-value = 0.1719
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 0.23597, p-value = 0.7748

> ad.y
	Anderson-Darling normality test
data:  y
A = 0.93181, p-value = 0.01635


Figures (Output of Computation)

Input Parameters & R Code

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('<pre>',RC.texteval('jarque.x'),'</pre>',sep=''))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,paste('<pre>',RC.texteval('jarque.y'),'</pre>',sep=''))
a<-table.row.end(a)
if(lx>7) {
a<-table.row.start(a)
a<-table.element(a,paste('<pre>',RC.texteval('ad.x'),'</pre>',sep=''))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,paste('<pre>',RC.texteval('ad.y'),'</pre>',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()