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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, 17 Dec 2016 13:25:04 +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/17/t1481977522unucnfy1mnw1em8.htm/, Retrieved Thu, 02 May 2024 07:00:50 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=300753, Retrieved Thu, 02 May 2024 07:00:50 +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] [] [2016-12-17 12:25:04] [85f5800284aab30c091766186b093bb4] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
10
13
14
8
8
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13
9
9
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3
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9
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12
11
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9
8
8
8
12
13
7
8
8
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3
12
15
14
7
11
12
10
14
10
15
11
8
6
12
13
12
9
8
14
7
8
14
12
15
11
8
8
7
12
7
11
Dataseries Y:
Download CSV
Histogram 
10
15
13
13
11
15
12
15
14
12
15
9
15
14
11
11
15
0
12
11
12
8
14
14
14
12
14
13
14
14
8
14
15
3
14
13
12
12
14
13
12
13
10
15
15
5
9
11
12
0
14
15
12
13
15
12
14
12
12
10
11
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13
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13
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10
12
10
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15
9
10
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10
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10
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14
15
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12
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12
15
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14
12
15
15
9
14
15
15
7
13
12
12
15
14
10
11
10
13
11
14
13
13
15
13
11
11
14
15
13
13
13
13
11
14
14
13
15
12
12
12
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7
12
14
15
15
12
13
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12
13
9
11
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10
15
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11

Tables (Output of Computation)





Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time4 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 time4 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300753&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]4 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=300753&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300753&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 time4 seconds
R ServerBig Analytics Cloud Computing Center






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean10.579881656804712.4792899408284
Biased Variance7.095689926823295.98921606386331
Biased Standard Deviation2.663773625296132.44728749105276
Covariance2.541842772612
Correlation0.387604629587807
Determination0.150237348877901
T-Test5.43373396678829
p-value (2 sided)1.92487000404115e-07
p-value (1 sided)9.62435002020573e-08
95% CI of Correlation[0.251351906037912, 0.508793710742476]
Degrees of Freedom167
Number of Observations169

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 10.5798816568047 & 12.4792899408284 \tabularnewline
Biased Variance & 7.09568992682329 & 5.98921606386331 \tabularnewline
Biased Standard Deviation & 2.66377362529613 & 2.44728749105276 \tabularnewline
Covariance & 2.541842772612 \tabularnewline
Correlation & 0.387604629587807 \tabularnewline
Determination & 0.150237348877901 \tabularnewline
T-Test & 5.43373396678829 \tabularnewline
p-value (2 sided) & 1.92487000404115e-07 \tabularnewline
p-value (1 sided) & 9.62435002020573e-08 \tabularnewline
95% CI of Correlation & [0.251351906037912, 0.508793710742476] \tabularnewline
Degrees of Freedom & 167 \tabularnewline
Number of Observations & 169 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300753&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]10.5798816568047[/C][C]12.4792899408284[/C][/ROW]
[ROW][C]Biased Variance[/C][C]7.09568992682329[/C][C]5.98921606386331[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]2.66377362529613[/C][C]2.44728749105276[/C][/ROW]
[ROW][C]Covariance[/C][C]2.541842772612[/C][/ROW]
[ROW][C]Correlation[/C][C]0.387604629587807[/C][/ROW]
[ROW][C]Determination[/C][C]0.150237348877901[/C][/ROW]
[ROW][C]T-Test[/C][C]5.43373396678829[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]1.92487000404115e-07[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]9.62435002020573e-08[/C][/ROW]
[ROW][C]95% CI of Correlation[/C][C][0.251351906037912, 0.508793710742476][/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]167[/C][/ROW]
[ROW][C]Number of Observations[/C][C]169[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300753&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300753&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
Mean10.579881656804712.4792899408284
Biased Variance7.095689926823295.98921606386331
Biased Standard Deviation2.663773625296132.44728749105276
Covariance2.541842772612
Correlation0.387604629587807
Determination0.150237348877901
T-Test5.43373396678829
p-value (2 sided)1.92487000404115e-07
p-value (1 sided)9.62435002020573e-08
95% CI of Correlation[0.251351906037912, 0.508793710742476]
Degrees of Freedom167
Number of Observations169






Normality Tests
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 11.405, p-value = 0.003338
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 557.78, p-value < 2.2e-16
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 3.5672, p-value = 6.041e-09

> ad.y
	Anderson-Darling normality test
data:  y
A = 6.6101, p-value = 2.851e-16


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

> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 11.405, p-value = 0.003338
alternative hypothesis: greater

 \tabularnewline

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 557.78, p-value < 2.2e-16
alternative hypothesis: greater

 \tabularnewline

> ad.x
	Anderson-Darling normality test
data:  x
A = 3.5672, p-value = 6.041e-09

 \tabularnewline

> ad.y
	Anderson-Darling normality test
data:  y
A = 6.6101, p-value = 2.851e-16

 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300753&T=2

[TABLE]
[ROW][C]Normality Tests[/C][/ROW]
[ROW][C]
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 11.405, p-value = 0.003338
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 557.78, p-value < 2.2e-16
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> ad.x
	Anderson-Darling normality test
data:  x
A = 3.5672, p-value = 6.041e-09

[/C][/ROW]
[ROW][C]
> ad.y
	Anderson-Darling normality test
data:  y
A = 6.6101, p-value = 2.851e-16

[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300753&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300753&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 = 11.405, p-value = 0.003338
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 557.78, p-value < 2.2e-16
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 3.5672, p-value = 6.041e-09

> ad.y
	Anderson-Darling normality test
data:  y
A = 6.6101, p-value = 2.851e-16


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
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()