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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 computationTue, 03 Aug 2021 09:55:04 +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/2021/Aug/03/t16279777907n0xlgd2pm2uy4g.htm/, Retrieved Mon, 06 May 2024 08:09:17 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=319487, Retrieved Mon, 06 May 2024 08:09:17 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact73

Tree of Dependent Computations

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

Dataseries X:
Download CSV
Histogram
Boxplots 
748396.56
889044.78
728045.77
767267.79
717781.78
865883.56
738321.23
792075.08
769515.56
899430.49
738808.61
739280.87
742091.29
887764.39
738911.82
770741.21
715822.75
882949.52
746344.98
737833.67
671772.56
828055.71
733460.62
717984.32
682792.65
810859.01
695016.33
708100.72
650805.72
816237.90
680088.65
731441.69
661109.37
832420.20
681021.32
740489.56
636640.80
864734.45
713142.36
717202.15
636750.55
Dataseries Y:
Download CSV
Histogram 
-1.4
3.3
3.6
6.1
5.6
2.9
4.1
0.5
-2.5
-6.5
-4.6
-6.4
-7.1
-7.7
-7.7
-7.7
-7.6
-3.6
-2.2
-6.3
-7.9
-9.0
-8.7
-4.3
6.7
9.2
7.2
7.0
1.0
-2.6
2.5
-0.9
2.3
4.7
-0.1
6.0
6.1
-7.0
-7.0
-2.2
6.6

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=319487&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=319487&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=319487&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
Mean751864.35-0.868292682926829
Biased Variance4992289044.6274831.0455800118977
Biased Standard Deviation70656.1323922245.57185606525309
Covariance-100543.684825
Correlation-0.249161640767536
Determination0.0620815232299707
T-Test-1.6066857427412
p-value (2 sided)0.116190814304332
p-value (1 sided)0.058095407152166
95% CI of Correlation[-0.517168680589843, 0.0633444530820802]
Degrees of Freedom39
Number of Observations41

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 751864.35 & -0.868292682926829 \tabularnewline
Biased Variance & 4992289044.62748 & 31.0455800118977 \tabularnewline
Biased Standard Deviation & 70656.132392224 & 5.57185606525309 \tabularnewline
Covariance & -100543.684825 \tabularnewline
Correlation & -0.249161640767536 \tabularnewline
Determination & 0.0620815232299707 \tabularnewline
T-Test & -1.6066857427412 \tabularnewline
p-value (2 sided) & 0.116190814304332 \tabularnewline
p-value (1 sided) & 0.058095407152166 \tabularnewline
95% CI of Correlation & [-0.517168680589843, 0.0633444530820802] \tabularnewline
Degrees of Freedom & 39 \tabularnewline
Number of Observations & 41 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=319487&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]751864.35[/C][C]-0.868292682926829[/C][/ROW]
[ROW][C]Biased Variance[/C][C]4992289044.62748[/C][C]31.0455800118977[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]70656.132392224[/C][C]5.57185606525309[/C][/ROW]
[ROW][C]Covariance[/C][C]-100543.684825[/C][/ROW]
[ROW][C]Correlation[/C][C]-0.249161640767536[/C][/ROW]
[ROW][C]Determination[/C][C]0.0620815232299707[/C][/ROW]
[ROW][C]T-Test[/C][C]-1.6066857427412[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0.116190814304332[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0.058095407152166[/C][/ROW]
[ROW][C]95% CI of Correlation[/C][C][-0.517168680589843, 0.0633444530820802][/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=319487&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=319487&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
Mean751864.35-0.868292682926829
Biased Variance4992289044.6274831.0455800118977
Biased Standard Deviation70656.1323922245.57185606525309
Covariance-100543.684825
Correlation-0.249161640767536
Determination0.0620815232299707
T-Test-1.6066857427412
p-value (2 sided)0.116190814304332
p-value (1 sided)0.058095407152166
95% CI of Correlation[-0.517168680589843, 0.0633444530820802]
Degrees of Freedom39
Number of Observations41






Normality Tests
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 2.5282, p-value = 0.2825
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 3.4735, p-value = 0.1761
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 1.0098, p-value = 0.01041

> ad.y
	Anderson-Darling normality test
data:  y
A = 1.1025, p-value = 0.006092


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

> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 2.5282, p-value = 0.2825
alternative hypothesis: greater

 \tabularnewline

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 3.4735, p-value = 0.1761
alternative hypothesis: greater

 \tabularnewline

> ad.x
	Anderson-Darling normality test
data:  x
A = 1.0098, p-value = 0.01041

 \tabularnewline

> ad.y
	Anderson-Darling normality test
data:  y
A = 1.1025, p-value = 0.006092

 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=319487&T=2

[TABLE]
[ROW][C]Normality Tests[/C][/ROW]
[ROW][C]
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 2.5282, p-value = 0.2825
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 3.4735, p-value = 0.1761
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> ad.x
	Anderson-Darling normality test
data:  x
A = 1.0098, p-value = 0.01041

[/C][/ROW]
[ROW][C]
> ad.y
	Anderson-Darling normality test
data:  y
A = 1.1025, p-value = 0.006092

[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=319487&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=319487&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 = 2.5282, p-value = 0.2825
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 3.4735, p-value = 0.1761
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 1.0098, p-value = 0.01041

> ad.y
	Anderson-Darling normality test
data:  y
A = 1.1025, p-value = 0.006092


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('
',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()