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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 11:31:07 +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/t1418556875x4cjuxa4ye77geq.htm/, Retrieved Thu, 16 May 2024 12:57:02 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=267455, Retrieved Thu, 16 May 2024 12:57:02 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact83

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-       [Pearson Correlation] [] [2014-12-14 11:31:07] [6e98989d1e11d52934121e5a163a7817] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
7,5
2,5
6,0
6,5
1,0
1,0
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6,5
4,5
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5,0
2,5
5,0
5,5
3,5
3,0
4,0
0,5
6,5
4,5
7,5
5,5
4,0
7,5
7,0
4,0
5,5
2,5
5,5
0,5
3,5
2,5
4,5
4,5
4,5
6,0
2,5
5,0
0,0
5,0
6,5
5,0
6,0
4,5
5,5
1,0
7,5
6,0
5,0
1,0
5,0
6,5
7,0
4,5
0,0
8,5
3,5
7,5
3,5
6,0
1,5
9,0
3,5
3,5
4,0
6,5
7,5
6,0
5,0
5,5
3,5
7,5
1,0
6,5
NA
6,5
6,5
7,0
3,5
1,5
4,0
7,5
4,5
0,0
3,5
5,5
5,0
4,5
2,5
7,5
7,0
0,0
4,5
3,0
1,5
3,5
2,5
5,5
8,0
1,0
5,0
4,5
3,0
3,0
8,0
2,5
7,0
0,0
1,0
3,5
5,5
5,5
0,5
7,5
9
9,5
8,5
7
8
10
7
8,5
9
9,5
4
6
8
5,5
9,5
7,5
7
7,5
8
7
7
6
10
2,5
9
8
6
8,5
6
9
8
8
9
5,5
5
7
5,5
9
2
8,5
9
8,5
9
7,5
10
9
7,5
6
10,5
8,5
8
10
10,5
6,5
9,5
8,5
7,5
5
8
10
7
7,5
7,5
9,5
6
10
7
3
6
7
10
7
3,5
8
10
5,5
6
6,5
6,5
8,5
4
9,5
8
8,5
5,5
7
9
8
10
8
6
8
5
9
4,5
8,5
7
9,5
8,5
7,5
7,5
5
7
8
5,5
8,5
7,5
9,5
7
8
8,5
3,5
6,5
6,5
10,5
8,5
8
10
10
9,5
9
10
7,5
4,5
4,5
0,5
6,5
4,5
5,5
5
6
4
8
10,5
8,5
6,5
8
8,5
5,5
7
5
3,5
5
9
8,5
5
9,5
3
1,5
6
0,5
6,5
7,5
4,5
8
9
7,5
8,5
7
9,5
6,5
9,5
6
8
9,5
8
8
9
5
Dataseries Y:
Download CSV
Histogram 
21
26
22
22
18
23
12
20
22
21
19
22
15
20
19
18
15
20
21
21
15
16
23
21
18
25
9
30
20
23
16
16
19
25
25
18
23
21
10
14
22
26
23
23
24
24
18
23
15
19
16
25
23
17
19
21
18
27
21
13
8
29
28
23
21
19
19
20
18
19
17
19
25
19
22
23
26
14
28
16
24
20
12
24
22
12
22
20
10
23
17
22
24
18
21
20
20
22
19
20
26
23
24
21
21
19
8
17
20
11
8
15
18
18
19
19
23
22
21
25
30
17
27
23
23
18
18
23
19
15
20
16
24
25
25
19
19
16
19
19
23
21
22
19
20
20
3
23
14
23
20
15
13
16
7
24
17
24
24
19
25
20
28
23
27
18
28
21
19
23
27
22
28
25
21
22
28
20
29
25
25
20
20
16
20
20
23
18
25
18
19
25
25
25
24
19
26
10
17
13
17
30
25
4
16
21
23
22
17
20
20
22
16
23
16
0
18
25
23
12
18
24
11
18
14
23
24
29
18
15
29
16
19
22
16
23
23
19
4
20
24
20
4
24
22
16
3
15
24
17
20
27
23
26
23
17
20
22
19
24
19
23
15
27
26
22
22
18
15
22
27
10
20
17
23
19
13
27
23
16
25
2
26
20
23
22
24

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Maurice George Kendall' @ kendall.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 & 2 seconds \tabularnewline
R Server & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=267455&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=267455&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=267455&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 time2 seconds
R Server'Sir Maurice George Kendall' @ kendall.wessa.net






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean6.1503496503496519.986013986014
Biased Variance6.5141082693530226.223580615189
Biased Standard Deviation2.552275116313495.12089646597049
Covariance1.80211017053122
Correlation0.137399984236765
Determination0.0188787556682632
T-Test2.33767704945088
p-value (2 sided)0.0200985243412819
p-value (1 sided)0.0100492621706409
Degrees of Freedom284
Number of Observations286

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 6.15034965034965 & 19.986013986014 \tabularnewline
Biased Variance & 6.51410826935302 & 26.223580615189 \tabularnewline
Biased Standard Deviation & 2.55227511631349 & 5.12089646597049 \tabularnewline
Covariance & 1.80211017053122 \tabularnewline
Correlation & 0.137399984236765 \tabularnewline
Determination & 0.0188787556682632 \tabularnewline
T-Test & 2.33767704945088 \tabularnewline
p-value (2 sided) & 0.0200985243412819 \tabularnewline
p-value (1 sided) & 0.0100492621706409 \tabularnewline
Degrees of Freedom & 284 \tabularnewline
Number of Observations & 286 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=267455&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]6.15034965034965[/C][C]19.986013986014[/C][/ROW]
[ROW][C]Biased Variance[/C][C]6.51410826935302[/C][C]26.223580615189[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]2.55227511631349[/C][C]5.12089646597049[/C][/ROW]
[ROW][C]Covariance[/C][C]1.80211017053122[/C][/ROW]
[ROW][C]Correlation[/C][C]0.137399984236765[/C][/ROW]
[ROW][C]Determination[/C][C]0.0188787556682632[/C][/ROW]
[ROW][C]T-Test[/C][C]2.33767704945088[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0.0200985243412819[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0.0100492621706409[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]284[/C][/ROW]
[ROW][C]Number of Observations[/C][C]286[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=267455&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=267455&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
Mean6.1503496503496519.986013986014
Biased Variance6.5141082693530226.223580615189
Biased Standard Deviation2.552275116313495.12089646597049
Covariance1.80211017053122
Correlation0.137399984236765
Determination0.0188787556682632
T-Test2.33767704945088
p-value (2 sided)0.0200985243412819
p-value (1 sided)0.0100492621706409
Degrees of Freedom284
Number of Observations286






Normality Tests
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 14.7045, p-value = 0.0006411
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 91.0602, p-value < 2.2e-16
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 2.7094, p-value = 7.692e-07

> ad.y
	Anderson-Darling normality test
data:  y
A = 3.9472, p-value = 7.513e-10


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

> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 14.7045, p-value = 0.0006411
alternative hypothesis: greater

 \tabularnewline

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 91.0602, p-value < 2.2e-16
alternative hypothesis: greater

 \tabularnewline

> ad.x
	Anderson-Darling normality test
data:  x
A = 2.7094, p-value = 7.692e-07

 \tabularnewline

> ad.y
	Anderson-Darling normality test
data:  y
A = 3.9472, p-value = 7.513e-10

 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=267455&T=2

[TABLE]
[ROW][C]Normality Tests[/C][/ROW]
[ROW][C]
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 14.7045, p-value = 0.0006411
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 91.0602, p-value < 2.2e-16
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> ad.x
	Anderson-Darling normality test
data:  x
A = 2.7094, p-value = 7.692e-07

[/C][/ROW]
[ROW][C]
> ad.y
	Anderson-Darling normality test
data:  y
A = 3.9472, p-value = 7.513e-10

[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=267455&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=267455&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 = 14.7045, p-value = 0.0006411
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 91.0602, p-value < 2.2e-16
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 2.7094, p-value = 7.692e-07

> ad.y
	Anderson-Darling normality test
data:  y
A = 3.9472, p-value = 7.513e-10


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()