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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 computationSat, 10 Dec 2016 15:49:38 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Dec/10/t1481381417bevistm92hb624d.htm/, Retrieved Mon, 06 May 2024 09:40:57 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=298696, Retrieved Mon, 06 May 2024 09:40:57 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact74

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Pearson Correlation] [Pearson3] [2016-12-10 14:49:38] [462f83e9ca944f1b841aaa868aea0854] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
4
2
3
2
2
3
3
2
2
4
2
2
3
2
3
2
2
NA
3
2
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1
2
3
2
2
3
5
2
5
2
2
4
1
2
2
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3
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3
4
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3
2
2
1
4
4
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2
4
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5
3
4
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2
2
3
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2
5
1
3
3
2
2
1
2
1
2
2
2
2
3
2
1
1
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3
1
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2
3
2
2
3
1
4
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3
3
3
4
3
2
3
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1
1
2
4
3
2
2
3
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3
2
2
2
3
4
2
2
1
3
3
4
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1
1
2
1
5
3
2
2
4
2
4
4
3
4
3
4
3
4
2
4
1
4
3
2
2
2
4
3
3
2
Dataseries Y:
Download CSV
Histogram 
3
4
5
4
4
5
5
5
5
5
5
4
4
4
4
5
4
NA
4
5
4
4
4
4
5
5
4
4
5
5
3
5
4
5
4
5
4
4
4
5
4
5
3
5
4
5
5
4
3
NA
5
5
4
3
4
4
4
4
4
4
5
4
4
4
4
4
5
4
4
4
4
4
3
4
4
4
5
4
4
5
5
3
5
4
5
5
5
5
4
4
2
4
5
5
5
4
4
4
5
4
NA
5
4
4
4
5
4
5
4
4
4
3
4
3
5
4
4
5
4
4
4
4
4
4
5
4
4
5
4
4
3
4
4
4
3
4
5
3
4
5
5
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4
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3
5
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5
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3
4
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3
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5
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3
4

Tables (Output of Computation)





Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R ServerBig Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time3 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298696&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]3 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=298696&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298696&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 Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R ServerBig Analytics Cloud Computing Center






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean2.626506024096394.19879518072289
Biased Variance0.9689359849034690.400239512265931
Biased Standard Deviation0.9843454601426620.632644854769191
Covariance-0.143483023001095
Correlation-0.229017595878147
Determination0.0524490592218064
T-Test-3.01293312220031
p-value (2 sided)0.00299804798335547
p-value (1 sided)0.00149902399167774
95% CI of Correlation[-0.368484765366524, -0.0794682875064415]
Degrees of Freedom164
Number of Observations166

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 2.62650602409639 & 4.19879518072289 \tabularnewline
Biased Variance & 0.968935984903469 & 0.400239512265931 \tabularnewline
Biased Standard Deviation & 0.984345460142662 & 0.632644854769191 \tabularnewline
Covariance & -0.143483023001095 \tabularnewline
Correlation & -0.229017595878147 \tabularnewline
Determination & 0.0524490592218064 \tabularnewline
T-Test & -3.01293312220031 \tabularnewline
p-value (2 sided) & 0.00299804798335547 \tabularnewline
p-value (1 sided) & 0.00149902399167774 \tabularnewline
95% CI of Correlation & [-0.368484765366524, -0.0794682875064415] \tabularnewline
Degrees of Freedom & 164 \tabularnewline
Number of Observations & 166 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298696&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]2.62650602409639[/C][C]4.19879518072289[/C][/ROW]
[ROW][C]Biased Variance[/C][C]0.968935984903469[/C][C]0.400239512265931[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]0.984345460142662[/C][C]0.632644854769191[/C][/ROW]
[ROW][C]Covariance[/C][C]-0.143483023001095[/C][/ROW]
[ROW][C]Correlation[/C][C]-0.229017595878147[/C][/ROW]
[ROW][C]Determination[/C][C]0.0524490592218064[/C][/ROW]
[ROW][C]T-Test[/C][C]-3.01293312220031[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0.00299804798335547[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0.00149902399167774[/C][/ROW]
[ROW][C]95% CI of Correlation[/C][C][-0.368484765366524, -0.0794682875064415][/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]164[/C][/ROW]
[ROW][C]Number of Observations[/C][C]166[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298696&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298696&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
Mean2.626506024096394.19879518072289
Biased Variance0.9689359849034690.400239512265931
Biased Standard Deviation0.9843454601426620.632644854769191
Covariance-0.143483023001095
Correlation-0.229017595878147
Determination0.0524490592218064
T-Test-3.01293312220031
p-value (2 sided)0.00299804798335547
p-value (1 sided)0.00149902399167774
95% CI of Correlation[-0.368484765366524, -0.0794682875064415]
Degrees of Freedom164
Number of Observations166






Normality Tests
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 4.9429, p-value = 0.08446
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 3.0385, p-value = 0.2189
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 8.116, p-value < 2.2e-16

> ad.y
	Anderson-Darling normality test
data:  y
A = 17.606, p-value < 2.2e-16


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

> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 4.9429, p-value = 0.08446
alternative hypothesis: greater

 \tabularnewline

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 3.0385, p-value = 0.2189
alternative hypothesis: greater

 \tabularnewline

> ad.x
	Anderson-Darling normality test
data:  x
A = 8.116, p-value < 2.2e-16

 \tabularnewline

> ad.y
	Anderson-Darling normality test
data:  y
A = 17.606, p-value < 2.2e-16

 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298696&T=2

[TABLE]
[ROW][C]Normality Tests[/C][/ROW]
[ROW][C]
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 4.9429, p-value = 0.08446
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 3.0385, p-value = 0.2189
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> ad.x
	Anderson-Darling normality test
data:  x
A = 8.116, p-value < 2.2e-16

[/C][/ROW]
[ROW][C]
> ad.y
	Anderson-Darling normality test
data:  y
A = 17.606, p-value < 2.2e-16

[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298696&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298696&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 = 4.9429, p-value = 0.08446
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 3.0385, p-value = 0.2189
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 8.116, p-value < 2.2e-16

> ad.y
	Anderson-Darling normality test
data:  y
A = 17.606, p-value < 2.2e-16


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 8 ; par2 = 0 ;
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$estimate)[1,1]
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Pearson Product Moment Correlation - Ungrouped Data',3,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Statistic',1,TRUE)
a<-table.element(a,'Variable X',1,TRUE)
a<-table.element(a,'Variable Y',1,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Mean',header=TRUE)
a<-table.element(a,mean(x))
a<-table.element(a,mean(y))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Biased Variance',header=TRUE)
a<-table.element(a,varx)
a<-table.element(a,vary)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Biased Standard Deviation',header=TRUE)
a<-table.element(a,sqrt(varx))
a<-table.element(a,sqrt(vary))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Covariance',header=TRUE)
a<-table.element(a,cov(x,y),2)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Correlation',header=TRUE)
a<-table.element(a,cxy,2)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Determination',header=TRUE)
a<-table.element(a,cxy*cxy,2)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'T-Test',header=TRUE)
a<-table.element(a,as.matrix(corxy$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')
qqPlot(x,main='QQplot of variable x')
dev.off()
bitmap(file='test3.png')
qqPlot(y,main='QQplot of variable y')
dev.off()