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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 computationThu, 15 Dec 2016 20:51:38 +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/15/t1481831562jl1d4ljd9fyr5nd.htm/, Retrieved Fri, 03 May 2024 12:49:25 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=299985, Retrieved Fri, 03 May 2024 12:49:25 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact70

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Pearson Correlation] [pearson correlati...] [2016-12-15 19:51:38] [74a1aee5dc3270c40ddc0c460955e440] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
7
7
11
11
10
9
9
11
NA
11
6
8
13
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10
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5
NA
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NA
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13
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NA
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8
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4
9
10
9
NA
12
14
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12
9
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7
10
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11
10
10
7
11
13
11
11
9
9
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9
10
13
11
13
14
8
10
10
10
9
9
8
9
NA
12
10
11
10
10
13
12
10
10
12
5
11
7
11
10
11
11
14
11
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13
10
7
11
9
8
9
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9
12
9
10
12
10
9
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13
10
NA
10
9
13
12
NA
11
12
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NA
10
10
7
9
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11
11
12
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14
12
9
13
10
8
10
10
NA
10
9
12
10
9
10
9
11
8
10
9
10
Dataseries Y:
Download CSV
Histogram 
10
13
14
NA
NA
13
13
NA
NA
14
14
12
12
11
12
14
NA
NA
11
NA
13
NA
13
NA
NA
NA
12
12
13
13
10
12
13
NA
10
14
NA
10
10
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NA
14
10
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12
12
NA
12
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NA
14
NA
NA
8
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10
NA
14
12
NA
14
13
13
13
12
10
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11
10
13
NA
NA
NA
NA
NA
12
13
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10
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NA
7
NA
13
NA
15
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NA
13
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NA
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NA
14
NA
12
13
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13
NA
NA
12
10
NA
NA
NA
NA
NA
12
NA
NA
NA
9
14
12
13
NA
13
11
12
11
NA
12
NA
12
13
NA
NA
NA
8
12
13
NA
8
NA
13
NA
12
15
14
NA
11
12
10
14
10
15
11
NA
NA
12
13
12
9
NA
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NA
NA
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NA
NA
NA
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NA
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=299985&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=299985&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299985&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
Mean10.259615384615412.0961538461538
Biased Variance4.134522928994082.79844674556213
Biased Standard Deviation2.033352632721161.67285586514862
Covariance-0.432972367438387
Correlation-0.126064509964879
Determination0.0158922606726851
T-Test-1.28342827293975
p-value (2 sided)0.202250269114047
p-value (1 sided)0.101125134557023
95% CI of Correlation[-0.311099688721072, 0.0681790017309968]
Degrees of Freedom102
Number of Observations104

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 10.2596153846154 & 12.0961538461538 \tabularnewline
Biased Variance & 4.13452292899408 & 2.79844674556213 \tabularnewline
Biased Standard Deviation & 2.03335263272116 & 1.67285586514862 \tabularnewline
Covariance & -0.432972367438387 \tabularnewline
Correlation & -0.126064509964879 \tabularnewline
Determination & 0.0158922606726851 \tabularnewline
T-Test & -1.28342827293975 \tabularnewline
p-value (2 sided) & 0.202250269114047 \tabularnewline
p-value (1 sided) & 0.101125134557023 \tabularnewline
95% CI of Correlation & [-0.311099688721072, 0.0681790017309968] \tabularnewline
Degrees of Freedom & 102 \tabularnewline
Number of Observations & 104 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299985&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]10.2596153846154[/C][C]12.0961538461538[/C][/ROW]
[ROW][C]Biased Variance[/C][C]4.13452292899408[/C][C]2.79844674556213[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]2.03335263272116[/C][C]1.67285586514862[/C][/ROW]
[ROW][C]Covariance[/C][C]-0.432972367438387[/C][/ROW]
[ROW][C]Correlation[/C][C]-0.126064509964879[/C][/ROW]
[ROW][C]Determination[/C][C]0.0158922606726851[/C][/ROW]
[ROW][C]T-Test[/C][C]-1.28342827293975[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0.202250269114047[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0.101125134557023[/C][/ROW]
[ROW][C]95% CI of Correlation[/C][C][-0.311099688721072, 0.0681790017309968][/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]102[/C][/ROW]
[ROW][C]Number of Observations[/C][C]104[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299985&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299985&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
Mean10.259615384615412.0961538461538
Biased Variance4.134522928994082.79844674556213
Biased Standard Deviation2.033352632721161.67285586514862
Covariance-0.432972367438387
Correlation-0.126064509964879
Determination0.0158922606726851
T-Test-1.28342827293975
p-value (2 sided)0.202250269114047
p-value (1 sided)0.101125134557023
95% CI of Correlation[-0.311099688721072, 0.0681790017309968]
Degrees of Freedom102
Number of Observations104






Normality Tests
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 2.2151, p-value = 0.3304
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 6.7181, p-value = 0.03477
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 1.4136, p-value = 0.001115

> ad.y
	Anderson-Darling normality test
data:  y
A = 2.3965, p-value = 4.199e-06


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

> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 2.2151, p-value = 0.3304
alternative hypothesis: greater

 \tabularnewline

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 6.7181, p-value = 0.03477
alternative hypothesis: greater

 \tabularnewline

> ad.x
	Anderson-Darling normality test
data:  x
A = 1.4136, p-value = 0.001115

 \tabularnewline

> ad.y
	Anderson-Darling normality test
data:  y
A = 2.3965, p-value = 4.199e-06

 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299985&T=2

[TABLE]
[ROW][C]Normality Tests[/C][/ROW]
[ROW][C]
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 2.2151, p-value = 0.3304
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 6.7181, p-value = 0.03477
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> ad.x
	Anderson-Darling normality test
data:  x
A = 1.4136, p-value = 0.001115

[/C][/ROW]
[ROW][C]
> ad.y
	Anderson-Darling normality test
data:  y
A = 2.3965, p-value = 4.199e-06

[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299985&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299985&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 = 2.2151, p-value = 0.3304
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 6.7181, p-value = 0.03477
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 1.4136, p-value = 0.001115

> ad.y
	Anderson-Darling normality test
data:  y
A = 2.3965, p-value = 4.199e-06


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()