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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_correlation.wasp
Title produced by softwarePearson Correlation
Date of computationSun, 29 Nov 2015 15:35:01 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/Nov/29/t1448811484o0le94f9d8ae38n.htm/, Retrieved Wed, 15 May 2024 09:43:55 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=284485, Retrieved Wed, 15 May 2024 09:43:55 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact110

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Pearson Correlation] [] [2015-09-24 13:12:15] [32b17a345b130fdf5cc88718ed94a974]
- R  D    [Pearson Correlation] [Verband Temperatu...] [2015-11-29 15:35:01] [b74db8f86f66c6a92c3e0b31073ff4c2] [Current]
- RMPD      [Multiple Regression] [Orkanen] [2015-12-13 19:45:12] [74be16979710d4c4e7c6647856088456]
- R PD        [Multiple Regression] [Orkanen] [2015-12-17 08:40:36] [74be16979710d4c4e7c6647856088456]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
14.15
13.95
13.96
13.99
14.08
14.03
13.93
13.95
13.94
14.01
13.98
13.84
14.16
13.92
13.97
14
14
13.87
13.94
13.98
13.95
14.01
13.96
13.88
13.76
13.79
13.97
13.84
13.94
13.97
13.92
13.87
13.9
13.85
13.7
13.87
13.74
13.64
13.83
13.88
14.01
13.98
14.02
14.1
14.11
14.14
14.04
14.19
14.17
14.14
13.94
14.09
14.06
14.07
14.07
14.07
14.05
13.99
13.85
13.95
14.13
14.2
14.2
14.18
14.13
14.07
14.06
14.07
14.1
14.1
14
14.16
13.85
13.97
13.91
13.9
13.83
13.9
13.79
13.88
13.94
13.95
14.08
13.87
14.16
13.9
13.74
13.82
13.82
13.88
13.9
14.04
13.92
13.96
13.8
13.74
13.84
13.71
13.78
13.78
13.76
13.81
13.87
13.76
13.82
13.82
13.83
13.91
13.92
14
13.99
14.01
14.09
14.13
14.03
14.1
14.05
14.02
14.11
14.21
14.38
14.23
14.1
14.04
14.12
14
14.11
14.03
14.03
14.04
14.06
14.1
14.11
14.12
14.24
14.17
14.08
14.07
14.09
14.02
14.01
13.98
13.92
14.03
14.01
14.19
13.73
13.92
13.94
14.03
14.04
14.03
14.07
14.04
13.93
14.17
14.06
14.2
14.16
14.11
14.16
14.13
14.01
14.05
14.04
14.1
14.05
14.02
14.11
14.21
14.38
14.23
14.1
14.04
14.12
14
14.11
14.03
14.03
14.04
14.06
14.1
14.11
14.12
14.24
14.17
14.08
14.07
14.09
14.02
14.01
13.98
13.92
14.03
14.01
14.19
13.73
13.92
13.94
14.03
14.04
14.03
14.07
14.04
13.93
14.17
14.06
14.2
14.16
14.11
14.16
14.13
14.01
14.05
14.04
14.03
14.04
13.9
14.09
14.16
14.09
14.08
13.95
14.01
14
13.99
14
14.02
14.06
14.02
13.97
14.19
13.97
13.98
14.03
14.04
14.13
14.22
14.21
14.15
14.17
14.03
14.02
13.91
13.81
13.78
13.83
13.96
13.9
14.1
13.99
13.9
13.88
13.89
14.03
14.19
14.16
14.1
14.03
14.06
14.07
14.11
14.17
14.23
14.11
14.25
14.03
14.07
13.99
14.01
13.98
13.93
14.06
13.98
14
13.86
13.98
13.8
13.8
13.89
13.88
13.78
13.89
13.93
13.95
13.92
13.96
13.91
13.76
13.79
13.99
13.99
13.99
14.04
14.01
14.13
14.01
14.07
14.04
14.18
14.26
14.31
14.26
14.2
14.18
14.14
14.08
14
14.04
14.08
14
13.94
13.83
13.75
13.92
13.91
13.91
13.9
13.95
14.02
13.89
13.89
13.89
13.87
14.03
13.96
14.06
13.98
14.08
13.95
13.95
13.84
13.94
13.88
13.83
13.8
13.92
13.9
13.73
13.87
13.76
13.86
13.9
13.85
13.9
13.75
13.87
13.97
13.97
14.14
14.18
14.17
14.2
14.17
14.15
14.1
14.04
14.01
14.15
14.03
14.04
14.05
14.12
14.09
13.98
13.94
14.04
13.86
14.03
13.99
14.08
14.01
14.04
13.9
14.09
14.04
13.97
14.08
13.99
14.11
14.16
14.18
14.18
14.38
14.18
14.22
14.13
14.2
14.25
14.14
14.15
14.13
14.1
14.09
14.23
14.11
14.4
14.3
14.37
14.24
14.14
14.17
14.19
14.24
14.11
14.07
14.15
14.28
14.03
14.06
13.94
14.05
14.12
14
14.12
13.99
14.04
14.05
14.06
14.33
14.45
14.39
14.39
14.23
14.25
14.15
14.12
14.26
14.28
14.12
14.29
14.12
14.22
14.09
14.17
14.01
14.22
13.98
14.12
14.09
14.11
14.05
13.96
13.81
14.09
13.87
14.1
14.08
14.09
14.08
13.95
14.08
14
14.05
13.98
14.04
14.24
14.28
14.23
14.16
14.11
14.07
14.07
14.08
14.02
14.08
14.01
14.08
14.23
14.39
14.13
14.21
14.21
14.26
14.36
14.18
14.34
14.26
14.22
14.46
14.51
14.32
14.44
14.35
14.3
14.32
14.24
14.27
14.26
14.26
14.05
14.22
14.11
14.25
14.26
14.16
14.07
14.06
14.22
14.24
14.25
14.23
14.14
14.29
14.33
14.34
14.65
14.43
14.32
14.31
14.34
14.28
14.23
14.4
14.45
14.39
14.35
14.43
14.29
14.41
14.31
14.42
14.43
14.3
14.36
14.22
14.16
14.2
14.38
14.37
14.34
14.19
14.22
14.15
14
14.01
13.94
14
13.93
14.13
14.28
14.26
14.3
14.18
14.18
14.1
14.09
14.03
14.02
14.16
14
14.14
14.28
13.94
14.25
14.26
14.22
14.29
14.2
14.19
14.25
14.38
14.37
14.29
14.44
14.7
14.44
14.34
14.11
14.33
14.46
14.37
14.24
14.42
14.37
14.26
14.23
14.43
14.25
14.2
14.21
14.18
14.3
14.32
14.16
14.15
14.28
14.31
14.27
14.31
14.46
14.33
14.31
14.43
14.28
14.36
14.45
14.5
14.55
14.53
14.55
14.83
14.56
14.58
14.59
14.59
14.67
14.6
14.43
14.42
14.4
14.51
14.45
14.64
14.27
14.28
14.23
14.28
14.26
14.27
14.25
14.3
14.32
14.37
14.21
14.49
14.46
14.5
14.3
14.31
14.28
14.37
14.29
14.21
14.21
14.19
14.38
14.4
14.56
14.42
14.47
14.45
14.46
14.45
14.45
14.43
14.68
14.47
14.74
14.75
14.81
14.54
14.51
14.43
14.53
14.43
14.46
14.48
14.51
14.33
Dataseries Y:
Download CSV
Histogram 
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Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Gertrude Mary Cox' @ cox.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 & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284485&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284485&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284485&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 Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean14.11628787878790.843939393939394
Biased Variance0.03845303833792472.04685720844812
Biased Standard Deviation0.1960944627926161.43068417494852
Covariance-0.000352577366993229
Correlation-0.00125483552530066
Determination1.57461219555658e-06
T-Test-0.0321884522170039
p-value (2 sided)0.974331526249113
p-value (1 sided)0.487165763124557
95% CI of Correlation[-0.0775642026196977, 0.0750691485058719]
Degrees of Freedom658
Number of Observations660

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 14.1162878787879 & 0.843939393939394 \tabularnewline
Biased Variance & 0.0384530383379247 & 2.04685720844812 \tabularnewline
Biased Standard Deviation & 0.196094462792616 & 1.43068417494852 \tabularnewline
Covariance & -0.000352577366993229 \tabularnewline
Correlation & -0.00125483552530066 \tabularnewline
Determination & 1.57461219555658e-06 \tabularnewline
T-Test & -0.0321884522170039 \tabularnewline
p-value (2 sided) & 0.974331526249113 \tabularnewline
p-value (1 sided) & 0.487165763124557 \tabularnewline
95% CI of Correlation & [-0.0775642026196977, 0.0750691485058719] \tabularnewline
Degrees of Freedom & 658 \tabularnewline
Number of Observations & 660 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284485&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]14.1162878787879[/C][C]0.843939393939394[/C][/ROW]
[ROW][C]Biased Variance[/C][C]0.0384530383379247[/C][C]2.04685720844812[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]0.196094462792616[/C][C]1.43068417494852[/C][/ROW]
[ROW][C]Covariance[/C][C]-0.000352577366993229[/C][/ROW]
[ROW][C]Correlation[/C][C]-0.00125483552530066[/C][/ROW]
[ROW][C]Determination[/C][C]1.57461219555658e-06[/C][/ROW]
[ROW][C]T-Test[/C][C]-0.0321884522170039[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0.974331526249113[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0.487165763124557[/C][/ROW]
[ROW][C]95% CI of Correlation[/C][C][-0.0775642026196977, 0.0750691485058719][/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]658[/C][/ROW]
[ROW][C]Number of Observations[/C][C]660[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284485&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284485&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
Mean14.11628787878790.843939393939394
Biased Variance0.03845303833792472.04685720844812
Biased Standard Deviation0.1960944627926161.43068417494852
Covariance-0.000352577366993229
Correlation-0.00125483552530066
Determination1.57461219555658e-06
T-Test-0.0321884522170039
p-value (2 sided)0.974331526249113
p-value (1 sided)0.487165763124557
95% CI of Correlation[-0.0775642026196977, 0.0750691485058719]
Degrees of Freedom658
Number of Observations660






Normality Tests
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 36.978, p-value = 9.341e-09
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 911.21, p-value < 2.2e-16
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 3.4519, p-value = 1.23e-08

> ad.y
	Anderson-Darling normality test
data:  y
A = 90.718, p-value < 2.2e-16


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

> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 36.978, p-value = 9.341e-09
alternative hypothesis: greater

 \tabularnewline

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 911.21, p-value < 2.2e-16
alternative hypothesis: greater

 \tabularnewline

> ad.x
	Anderson-Darling normality test
data:  x
A = 3.4519, p-value = 1.23e-08

 \tabularnewline

> ad.y
	Anderson-Darling normality test
data:  y
A = 90.718, p-value < 2.2e-16

 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284485&T=2

[TABLE]
[ROW][C]Normality Tests[/C][/ROW]
[ROW][C]
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 36.978, p-value = 9.341e-09
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 911.21, p-value < 2.2e-16
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> ad.x
	Anderson-Darling normality test
data:  x
A = 3.4519, p-value = 1.23e-08

[/C][/ROW]
[ROW][C]
> ad.y
	Anderson-Darling normality test
data:  y
A = 90.718, p-value < 2.2e-16

[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284485&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284485&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 = 36.978, p-value = 9.341e-09
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 911.21, p-value < 2.2e-16
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 3.4519, p-value = 1.23e-08

> ad.y
	Anderson-Darling normality test
data:  y
A = 90.718, p-value < 2.2e-16


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