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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 computationFri, 12 Dec 2014 13:17:47 +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/12/t1418390294hniivey5fu4ule8.htm/, Retrieved Thu, 16 May 2024 16:24:45 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=266652, Retrieved Thu, 16 May 2024 16:24:45 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact72

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Pearson Correlation] [] [2014-12-12 13:17:47] [d33b7eb92cfcc384850e3711242e8bfe] [Current]
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Dataset

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

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'Gwilym Jenkins' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=266652&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=266652&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=266652&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'Gwilym Jenkins' @ jenkins.wessa.net






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean10.896969696969720.2848484848485
Biased Variance4.7833241505968830.6885583103765
Biased Standard Deviation2.187081194331135.53972547247393
Covariance0.310014781966001
Correlation0.0254325060431515
Determination0.000646812363634938
T-Test0.324805561999284
p-value (2 sided)0.745744721491582
p-value (1 sided)0.372872360745791
Degrees of Freedom163
Number of Observations165

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 10.8969696969697 & 20.2848484848485 \tabularnewline
Biased Variance & 4.78332415059688 & 30.6885583103765 \tabularnewline
Biased Standard Deviation & 2.18708119433113 & 5.53972547247393 \tabularnewline
Covariance & 0.310014781966001 \tabularnewline
Correlation & 0.0254325060431515 \tabularnewline
Determination & 0.000646812363634938 \tabularnewline
T-Test & 0.324805561999284 \tabularnewline
p-value (2 sided) & 0.745744721491582 \tabularnewline
p-value (1 sided) & 0.372872360745791 \tabularnewline
Degrees of Freedom & 163 \tabularnewline
Number of Observations & 165 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=266652&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]10.8969696969697[/C][C]20.2848484848485[/C][/ROW]
[ROW][C]Biased Variance[/C][C]4.78332415059688[/C][C]30.6885583103765[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]2.18708119433113[/C][C]5.53972547247393[/C][/ROW]
[ROW][C]Covariance[/C][C]0.310014781966001[/C][/ROW]
[ROW][C]Correlation[/C][C]0.0254325060431515[/C][/ROW]
[ROW][C]Determination[/C][C]0.000646812363634938[/C][/ROW]
[ROW][C]T-Test[/C][C]0.324805561999284[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0.745744721491582[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0.372872360745791[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]163[/C][/ROW]
[ROW][C]Number of Observations[/C][C]165[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=266652&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=266652&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
Mean10.896969696969720.2848484848485
Biased Variance4.7833241505968830.6885583103765
Biased Standard Deviation2.187081194331135.53972547247393
Covariance0.310014781966001
Correlation0.0254325060431515
Determination0.000646812363634938
T-Test0.324805561999284
p-value (2 sided)0.745744721491582
p-value (1 sided)0.372872360745791
Degrees of Freedom163
Number of Observations165






Normality Tests
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 9.4737, p-value = 0.008766
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 81.5075, p-value < 2.2e-16
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 3.4676, p-value = 1.054e-08

> ad.y
	Anderson-Darling normality test
data:  y
A = 3.5566, p-value = 6.395e-09


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

> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 9.4737, p-value = 0.008766
alternative hypothesis: greater

 \tabularnewline

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 81.5075, p-value < 2.2e-16
alternative hypothesis: greater

 \tabularnewline

> ad.x
	Anderson-Darling normality test
data:  x
A = 3.4676, p-value = 1.054e-08

 \tabularnewline

> ad.y
	Anderson-Darling normality test
data:  y
A = 3.5566, p-value = 6.395e-09

 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=266652&T=2

[TABLE]
[ROW][C]Normality Tests[/C][/ROW]
[ROW][C]
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 9.4737, p-value = 0.008766
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 81.5075, p-value < 2.2e-16
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> ad.x
	Anderson-Darling normality test
data:  x
A = 3.4676, p-value = 1.054e-08

[/C][/ROW]
[ROW][C]
> ad.y
	Anderson-Darling normality test
data:  y
A = 3.5566, p-value = 6.395e-09

[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=266652&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=266652&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 = 9.4737, p-value = 0.008766
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 81.5075, p-value < 2.2e-16
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 3.4676, p-value = 1.054e-08

> ad.y
	Anderson-Darling normality test
data:  y
A = 3.5566, p-value = 6.395e-09


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()