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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, 14 Dec 2014 18:12:12 +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/2014/Dec/14/t1418580747bfc16yv5e9v3y42.htm/, Retrieved Thu, 16 May 2024 10:21:31 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=267792, Retrieved Thu, 16 May 2024 10:21:31 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact94

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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 
112,9
12,2
12,8
7,4
6,7
12,6
14,8
13,3
11,1
8,2
11,4
6,4
10,6
12
6,3
11,3
11,9
9,3
9,6
10
6,4
13,8
10,8
13,8
11,7
10,9
16,1
13,4
9,9
11,5
8,3
11,7
6,1
9
9,7
10,8
10,3
10,4
12,7
9,3
11,8
5,9
11,4
13
10,8
12,3
11,3
11,8
7,9
12,7
12,3
11,6
6,7
10,9
12,1
13,3
10,1
5,7
14,3
8
13,3
9,3
12,5
7,6
15,9
9,2
9,1
11,1
13
14,5
12,2
12,3
11,4
8,8
14,6
7,3
12,6
NA
13
12,6
13,2
9,9
7,7
10,5
13,4
10,9
4,3
10,3
11,8
11,2
11,4
8,6
13,2
12,6
5,6
9,9
8,8
7,7
9
7,3
11,4
13,6
7,9
10,7
10,3
8,3
9,6
14,2
8,5
13,5
4,9
6,4
9,6
11,6
11,1
4,35
12,7
18,1
17,85
16,6
12,6
17,1
19,1
16,1
13,35
18,4
14,7
10,6
12,6
16,2
13,6
18,9
14,1
14,5
16,15
14,75
14,8
12,45
12,65
17,35
8,6
18,4
16,1
11,6
17,75
15,25
17,65
15,6
16,35
17,65
13,6
11,7
14,35
14,75
18,25
9,9
16
18,25
16,85
14,6
13,85
18,95
15,6
14,85
11,75
18,45
15,9
17,1
16,1
19,9
10,95
18,45
15,1
15
11,35
15,95
18,1
14,6
15,4
15,4
17,6
13,35
19,1
15,35
7,6
13,4
13,9
19,1
15,25
12,9
16,1
17,35
13,15
12,15
12,6
10,35
15,4
9,6
18,2
13,6
14,85
14,75
14,1
14,9
16,25
19,25
13,6
13,6
15,65
12,75
14,6
9,85
12,65
11,9
19,2
16,6
11,2
15,25
11,9
13,2
16,35
12,4
15,85
14,35
18,15
11,15
15,65
17,75
7,65
12,35
15,6
19,3
15,2
17,1
15,6
18,4
19,05
18,55
19,1
13,1
12,85
9,5
4,5
11,85
13,6
11,7
12,4
13,35
11,4
14,9
19,9
17,75
11,2
14,6
17,6
14,05
16,1
13,35
11,85
11,95
14,75
15,15
13,2
16,85
7,85
7,7
12,6
7,85
10,95
12,35
9,95
14,9
16,65
13,4
13,95
15,7
16,85
10,95
15,35
12,2
15,1
17,75
15,2
14,6
16,65
8,1
Dataseries Y:
Download CSV
Histogram 
9
10,5
11
11,5
10,5
13,5
10,5
12
14,5
11
10,5
11
11
13,5
9,5
10
12,5
11
11,5
9,5
10,5
17,5
10,5
11,5
11,5
11
17,5
9,5
9,5
9,5
9,5
10,5
8
10
16
11,5
12,5
9
12
14
11,5
10
12,5
11,5
9
9,5
13
10
13
8
11
10,5
9
9
9,5
12
9,5
10
10,5
8,5
9,5
10,5
12
9
11,5
10,5
10
14
10
13,5
10,5
14,5
10
9
13
12,5
10,5
11,5
11,5
11
10
11
10,5
10,5
9,5
10
8,5
11
11
11,5
12
10,5
9,5
8,5
9
7,5
9,5
9,5
8,5
9,5
9,5
9
12
9
9,5
9
10,5
9,5
11
10
8,5
8,5
9
9,5
9
5
5
20
20
15
10
20
20
20
10
20
5
15
15
20
15
20
15
15
20
15
15
10
10
15
5
20
15
10
20
20
20
20
20
20
15
20
15
20
20
20
15
20
20
10
10
20
15
15
10
15
10
20
5
20
5
20
15
15
10
15
15
20
20
20
15
15
20
20
5
10
15
20
15
20
15
15
15
15
5
5
15
10
15
10
10
20
10
10
15
20
10
20
15
20
10
5
5
5
20
15
5
20
15
10
20
15
15
20
20
5
15
20
5
15
20
20
5
20
10
15
20
20
20
10
20
10
5
5
20
10
10
15
10
15
20
20
10
15
20
15
20
20
20
10
10
10
20
15
10
10
15
15
5
10
10
15
15
10
10
15
15
5
15
10
10
15
15
15
15
5

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.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 & 1 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=267792&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=267792&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=267792&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 time1 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.wessa.net






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean13.304385964912312.9017543859649
Biased Variance46.52427023699620.0640320098492
Biased Standard Deviation6.820870196462914.47928923043033
Covariance8.75201692611811
Correlation0.285451768565266
Determination0.081482712177038
T-Test5.01051409844447
p-value (2 sided)9.57719837657578e-07
p-value (1 sided)4.78859918828789e-07
Degrees of Freedom283
Number of Observations285

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 13.3043859649123 & 12.9017543859649 \tabularnewline
Biased Variance & 46.524270236996 & 20.0640320098492 \tabularnewline
Biased Standard Deviation & 6.82087019646291 & 4.47928923043033 \tabularnewline
Covariance & 8.75201692611811 \tabularnewline
Correlation & 0.285451768565266 \tabularnewline
Determination & 0.081482712177038 \tabularnewline
T-Test & 5.01051409844447 \tabularnewline
p-value (2 sided) & 9.57719837657578e-07 \tabularnewline
p-value (1 sided) & 4.78859918828789e-07 \tabularnewline
Degrees of Freedom & 283 \tabularnewline
Number of Observations & 285 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=267792&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]13.3043859649123[/C][C]12.9017543859649[/C][/ROW]
[ROW][C]Biased Variance[/C][C]46.524270236996[/C][C]20.0640320098492[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]6.82087019646291[/C][C]4.47928923043033[/C][/ROW]
[ROW][C]Covariance[/C][C]8.75201692611811[/C][/ROW]
[ROW][C]Correlation[/C][C]0.285451768565266[/C][/ROW]
[ROW][C]Determination[/C][C]0.081482712177038[/C][/ROW]
[ROW][C]T-Test[/C][C]5.01051409844447[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]9.57719837657578e-07[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]4.78859918828789e-07[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]283[/C][/ROW]
[ROW][C]Number of Observations[/C][C]285[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=267792&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=267792&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
Mean13.304385964912312.9017543859649
Biased Variance46.52427023699620.0640320098492
Biased Standard Deviation6.820870196462914.47928923043033
Covariance8.75201692611811
Correlation0.285451768565266
Determination0.081482712177038
T-Test5.01051409844447
p-value (2 sided)9.57719837657578e-07
p-value (1 sided)4.78859918828789e-07
Degrees of Freedom283
Number of Observations285






Normality Tests
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 297071.6, p-value < 2.2e-16
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 12.5781, p-value = 0.001857
alternative hypothesis: greater

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

> ad.y
	Anderson-Darling normality test
data:  y
A = 10.5849, p-value < 2.2e-16


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

> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 297071.6, p-value < 2.2e-16
alternative hypothesis: greater

 \tabularnewline

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 12.5781, p-value = 0.001857
alternative hypothesis: greater

 \tabularnewline

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

 \tabularnewline

> ad.y
	Anderson-Darling normality test
data:  y
A = 10.5849, p-value < 2.2e-16

 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=267792&T=2

[TABLE]
[ROW][C]Normality Tests[/C][/ROW]
[ROW][C]
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 297071.6, p-value < 2.2e-16
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 12.5781, p-value = 0.001857
alternative hypothesis: greater

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

[/C][/ROW]
[ROW][C]
> ad.y
	Anderson-Darling normality test
data:  y
A = 10.5849, p-value < 2.2e-16

[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=267792&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=267792&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 = 297071.6, p-value < 2.2e-16
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 12.5781, p-value = 0.001857
alternative hypothesis: greater

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

> ad.y
	Anderson-Darling normality test
data:  y
A = 10.5849, 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):
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,'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()