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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, 21 Dec 2016 15:34:24 +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/21/t1482330883xgtez12vwj98sub.htm/, Retrieved Mon, 06 May 2024 10:45:36 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=302331, Retrieved Mon, 06 May 2024 10:45:36 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact51

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Pearson Correlation] [] [2016-12-21 14:34:24] [cedc5386ad7644fa02c81dc221bdf6b7] [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
2
3
1
2
3
2
2
3
5
2
5
2
2
4
1
2
2
3
2
3
2
3
4
4
3
2
2
1
4
4
3
2
2
2
2
3
2
2
3
3
2
2
4
4
3
4
4
4
4
5
3
4
4
2
2
3
4
2
5
1
3
3
2
2
1
2
1
2
2
2
2
3
2
1
1
3
2
3
1
2
2
3
2
2
3
1
4
3
2
3
3
3
4
3
2
3
2
1
1
2
4
3
2
2
3
3
3
2
2
2
3
4
2
2
1
3
3
4
3
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
3
3
3
4
3
NA
3
4
3
3
3
4
3
4
3
4
NA
NA
4
3
3
3
3
4
3
4
3
3
3
3
3
4
2
3
3
3
4
4
4
3
3
3
3
3
3
3
3
3
NA
3
3
4
3
3
3
3
3
4
3
3
3
3
3
3
2
3
3
4
3
3
3
3
3
4
3
3
3
5
3
3
3
3
4
4
5
4
4
3
4
3
3
3
3
3
3
4
5
4
3
NA
4
3
3
3
4
4
3
3
4
4
3
3
3
NA
4
3
4
3
3
3
3
4
3
4
3
3
3
3
3
3
NA
5
3
3
NA
5
NA
3
4
3
3
3
NA
3
3
4
4
3
4
3
4
3
3
3
3
3
3
3
4
3
3
4
3
4
3
4
3
5

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=302331&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=302331&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302331&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
Mean2.591194968553463.32075471698113
Biased Variance0.9460859934338040.318500059333096
Biased Standard Deviation0.9726695191244580.564358094947788
Covariance-0.0642464771913064
Correlation-0.116302544514039
Determination0.01352628186044
T-Test-1.46722352972999
p-value (2 sided)0.144315603558597
p-value (1 sided)0.0721578017792985
95% CI of Correlation[-0.26711440425466, 0.040070018789842]
Degrees of Freedom157
Number of Observations159

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 2.59119496855346 & 3.32075471698113 \tabularnewline
Biased Variance & 0.946085993433804 & 0.318500059333096 \tabularnewline
Biased Standard Deviation & 0.972669519124458 & 0.564358094947788 \tabularnewline
Covariance & -0.0642464771913064 \tabularnewline
Correlation & -0.116302544514039 \tabularnewline
Determination & 0.01352628186044 \tabularnewline
T-Test & -1.46722352972999 \tabularnewline
p-value (2 sided) & 0.144315603558597 \tabularnewline
p-value (1 sided) & 0.0721578017792985 \tabularnewline
95% CI of Correlation & [-0.26711440425466, 0.040070018789842] \tabularnewline
Degrees of Freedom & 157 \tabularnewline
Number of Observations & 159 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302331&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]2.59119496855346[/C][C]3.32075471698113[/C][/ROW]
[ROW][C]Biased Variance[/C][C]0.946085993433804[/C][C]0.318500059333096[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]0.972669519124458[/C][C]0.564358094947788[/C][/ROW]
[ROW][C]Covariance[/C][C]-0.0642464771913064[/C][/ROW]
[ROW][C]Correlation[/C][C]-0.116302544514039[/C][/ROW]
[ROW][C]Determination[/C][C]0.01352628186044[/C][/ROW]
[ROW][C]T-Test[/C][C]-1.46722352972999[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0.144315603558597[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0.0721578017792985[/C][/ROW]
[ROW][C]95% CI of Correlation[/C][C][-0.26711440425466, 0.040070018789842][/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]157[/C][/ROW]
[ROW][C]Number of Observations[/C][C]159[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302331&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302331&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
Mean2.591194968553463.32075471698113
Biased Variance0.9460859934338040.318500059333096
Biased Standard Deviation0.9726695191244580.564358094947788
Covariance-0.0642464771913064
Correlation-0.116302544514039
Determination0.01352628186044
T-Test-1.46722352972999
p-value (2 sided)0.144315603558597
p-value (1 sided)0.0721578017792985
95% CI of Correlation[-0.26711440425466, 0.040070018789842]
Degrees of Freedom157
Number of Observations159






Normality Tests
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 4.8882, p-value = 0.0868
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 41.34, p-value = 1.055e-09
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 8.0499, p-value < 2.2e-16

> ad.y
	Anderson-Darling normality test
data:  y
A = 26.853, p-value < 2.2e-16


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

> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 4.8882, p-value = 0.0868
alternative hypothesis: greater

 \tabularnewline

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 41.34, p-value = 1.055e-09
alternative hypothesis: greater

 \tabularnewline

> ad.x
	Anderson-Darling normality test
data:  x
A = 8.0499, p-value < 2.2e-16

 \tabularnewline

> ad.y
	Anderson-Darling normality test
data:  y
A = 26.853, p-value < 2.2e-16

 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302331&T=2

[TABLE]
[ROW][C]Normality Tests[/C][/ROW]
[ROW][C]
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 4.8882, p-value = 0.0868
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 41.34, p-value = 1.055e-09
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> ad.x
	Anderson-Darling normality test
data:  x
A = 8.0499, p-value < 2.2e-16

[/C][/ROW]
[ROW][C]
> ad.y
	Anderson-Darling normality test
data:  y
A = 26.853, p-value < 2.2e-16

[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302331&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302331&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 = 4.8882, p-value = 0.0868
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 41.34, p-value = 1.055e-09
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 8.0499, p-value < 2.2e-16

> ad.y
	Anderson-Darling normality test
data:  y
A = 26.853, p-value < 2.2e-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()