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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 computationWed, 10 Dec 2014 14:10:23 +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/10/t1418220650meaoz4fv1uz5nda.htm/, Retrieved Sun, 19 May 2024 15:41:02 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=265235, Retrieved Sun, 19 May 2024 15:41:02 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact57

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Pearson Correlation] [] [2014-12-10 14:10:23] [37e054ac358b2aa7c2a1d0b751dfa890] [Current]
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Dataset

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

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=265235&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=265235&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=265235&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
Mean3.1441441441441419.8558558558559
Biased Variance0.97021345669994313.3305738170603
Biased Standard Deviation0.9849941404393953.6511058348205
Covariance0.384602784602785
Correlation0.105980035743702
Determination0.0112317679762364
T-Test1.1127306693111
p-value (2 sided)0.26827213344649
p-value (1 sided)0.134136066723245
Degrees of Freedom109
Number of Observations111

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 3.14414414414414 & 19.8558558558559 \tabularnewline
Biased Variance & 0.970213456699943 & 13.3305738170603 \tabularnewline
Biased Standard Deviation & 0.984994140439395 & 3.6511058348205 \tabularnewline
Covariance & 0.384602784602785 \tabularnewline
Correlation & 0.105980035743702 \tabularnewline
Determination & 0.0112317679762364 \tabularnewline
T-Test & 1.1127306693111 \tabularnewline
p-value (2 sided) & 0.26827213344649 \tabularnewline
p-value (1 sided) & 0.134136066723245 \tabularnewline
Degrees of Freedom & 109 \tabularnewline
Number of Observations & 111 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=265235&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]3.14414414414414[/C][C]19.8558558558559[/C][/ROW]
[ROW][C]Biased Variance[/C][C]0.970213456699943[/C][C]13.3305738170603[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]0.984994140439395[/C][C]3.6511058348205[/C][/ROW]
[ROW][C]Covariance[/C][C]0.384602784602785[/C][/ROW]
[ROW][C]Correlation[/C][C]0.105980035743702[/C][/ROW]
[ROW][C]Determination[/C][C]0.0112317679762364[/C][/ROW]
[ROW][C]T-Test[/C][C]1.1127306693111[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0.26827213344649[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0.134136066723245[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]109[/C][/ROW]
[ROW][C]Number of Observations[/C][C]111[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=265235&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=265235&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
Mean3.1441441441441419.8558558558559
Biased Variance0.97021345669994313.3305738170603
Biased Standard Deviation0.9849941404393953.6511058348205
Covariance0.384602784602785
Correlation0.105980035743702
Determination0.0112317679762364
T-Test1.1127306693111
p-value (2 sided)0.26827213344649
p-value (1 sided)0.134136066723245
Degrees of Freedom109
Number of Observations111






Normality Tests
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 5.7165, p-value = 0.05737
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 0.5366, p-value = 0.7647
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 7.3745, p-value < 2.2e-16

> ad.y
	Anderson-Darling normality test
data:  y
A = 0.661, p-value = 0.08228


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

> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 5.7165, p-value = 0.05737
alternative hypothesis: greater

 \tabularnewline

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 0.5366, p-value = 0.7647
alternative hypothesis: greater

 \tabularnewline

> ad.x
	Anderson-Darling normality test
data:  x
A = 7.3745, p-value < 2.2e-16

 \tabularnewline

> ad.y
	Anderson-Darling normality test
data:  y
A = 0.661, p-value = 0.08228

 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=265235&T=2

[TABLE]
[ROW][C]Normality Tests[/C][/ROW]
[ROW][C]
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 5.7165, p-value = 0.05737
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 0.5366, p-value = 0.7647
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> ad.x
	Anderson-Darling normality test
data:  x
A = 7.3745, p-value < 2.2e-16

[/C][/ROW]
[ROW][C]
> ad.y
	Anderson-Darling normality test
data:  y
A = 0.661, p-value = 0.08228

[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=265235&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=265235&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 = 5.7165, p-value = 0.05737
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 0.5366, p-value = 0.7647
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 7.3745, p-value < 2.2e-16

> ad.y
	Anderson-Darling normality test
data:  y
A = 0.661, p-value = 0.08228


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()