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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 computationSun, 28 Aug 2016 09:39:05 +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/Aug/28/t1472373611gammq0rwq1cygr7.htm/, Retrieved Sat, 04 May 2024 21:05:22 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Sat, 04 May 2024 21:05:22 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0

Tree of Dependent Computations

Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
6.8
6.3
6.4
6.2
6.9
6.4
6.3
6.8
6.9
6.7
6.9
6.9
6.3
6.1
6.2
6.8
6.5
7.6
6.3
7.1
6.8
7.3
6.4
6.8
7.2
6.4
6.6
6.8
6.1
6.5
6.4
6
6
7.3
6.1
6.7
6.4
5.8
6.9
7
7.3
5.9
6.2
6.8
7
5.9
6.1
5.7
7.1
5.8
7.4
6.8
6.8
7
Dataseries Y:
Download CSV
Histogram 
0.442
0.435
0.456
0.416
0.449
0.431
0.487
0.469
0.435
0.48
0.516
0.493
0.374
0.424
0.441
0.503
0.503
0.425
0.371
0.504
0.4
0.482
0.475
0.428
0.559
0.441
0.492
0.402
0.415
0.492
0.484
0.387
0.436
0.482
0.34
0.516
0.475
0.412
0.411
0.407
0.445
0.291
0.449
0.546
0.48
0.359
0.528
0.352
0.414
0.425
0.599
0.482
0.457
0.435

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time5 seconds
R Server'Herman Ole Andreas Wold' @ wold.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 & 5 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]5 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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 time5 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean6.587037037037040.449111111111111
Biased Variance0.2066838134430730.00313883950617284
Biased Standard Deviation0.4546249151147270.0560253469973443
Covariance0.0128599580712788
Correlation0.495545885281671
Determination0.245565724419595
T-Test4.11409997056712
p-value (2 sided)0.000138972330496433
p-value (1 sided)6.94861652482167e-05
95% CI of Correlation[0.262633558805795, 0.673889615845366]
Degrees of Freedom52
Number of Observations54

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 6.58703703703704 & 0.449111111111111 \tabularnewline
Biased Variance & 0.206683813443073 & 0.00313883950617284 \tabularnewline
Biased Standard Deviation & 0.454624915114727 & 0.0560253469973443 \tabularnewline
Covariance & 0.0128599580712788 \tabularnewline
Correlation & 0.495545885281671 \tabularnewline
Determination & 0.245565724419595 \tabularnewline
T-Test & 4.11409997056712 \tabularnewline
p-value (2 sided) & 0.000138972330496433 \tabularnewline
p-value (1 sided) & 6.94861652482167e-05 \tabularnewline
95% CI of Correlation & [0.262633558805795, 0.673889615845366] \tabularnewline
Degrees of Freedom & 52 \tabularnewline
Number of Observations & 54 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]6.58703703703704[/C][C]0.449111111111111[/C][/ROW]
[ROW][C]Biased Variance[/C][C]0.206683813443073[/C][C]0.00313883950617284[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]0.454624915114727[/C][C]0.0560253469973443[/C][/ROW]
[ROW][C]Covariance[/C][C]0.0128599580712788[/C][/ROW]
[ROW][C]Correlation[/C][C]0.495545885281671[/C][/ROW]
[ROW][C]Determination[/C][C]0.245565724419595[/C][/ROW]
[ROW][C]T-Test[/C][C]4.11409997056712[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0.000138972330496433[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]6.94861652482167e-05[/C][/ROW]
[ROW][C]95% CI of Correlation[/C][C][0.262633558805795, 0.673889615845366][/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]52[/C][/ROW]
[ROW][C]Number of Observations[/C][C]54[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
Mean6.587037037037040.449111111111111
Biased Variance0.2066838134430730.00313883950617284
Biased Standard Deviation0.4546249151147270.0560253469973443
Covariance0.0128599580712788
Correlation0.495545885281671
Determination0.245565724419595
T-Test4.11409997056712
p-value (2 sided)0.000138972330496433
p-value (1 sided)6.94861652482167e-05
95% CI of Correlation[0.262633558805795, 0.673889615845366]
Degrees of Freedom52
Number of Observations54






Normality Tests
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 1.4138, p-value = 0.4932
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 0.78335, p-value = 0.6759
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 0.5451, p-value = 0.154

> ad.y
	Anderson-Darling normality test
data:  y
A = 0.2924, p-value = 0.5922


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

> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 1.4138, p-value = 0.4932
alternative hypothesis: greater

 \tabularnewline

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 0.78335, p-value = 0.6759
alternative hypothesis: greater

 \tabularnewline

> ad.x
	Anderson-Darling normality test
data:  x
A = 0.5451, p-value = 0.154

 \tabularnewline

> ad.y
	Anderson-Darling normality test
data:  y
A = 0.2924, p-value = 0.5922

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

[TABLE]
[ROW][C]Normality Tests[/C][/ROW]
[ROW][C]
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 1.4138, p-value = 0.4932
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 0.78335, p-value = 0.6759
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> ad.x
	Anderson-Darling normality test
data:  x
A = 0.5451, p-value = 0.154

[/C][/ROW]
[ROW][C]
> ad.y
	Anderson-Darling normality test
data:  y
A = 0.2924, p-value = 0.5922

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

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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 = 1.4138, p-value = 0.4932
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 0.78335, p-value = 0.6759
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 0.5451, p-value = 0.154

> ad.y
	Anderson-Darling normality test
data:  y
A = 0.2924, p-value = 0.5922


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$estimate)[1,1]
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Pearson Product Moment Correlation - Ungrouped Data',3,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Statistic',1,TRUE)
a<-table.element(a,'Variable X',1,TRUE)
a<-table.element(a,'Variable Y',1,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('arithmetic_mean.htm','Mean',''),header=TRUE)
a<-table.element(a,mean(x))
a<-table.element(a,mean(y))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('biased.htm','Biased Variance',''),header=TRUE)
a<-table.element(a,varx)
a<-table.element(a,vary)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('biased1.htm','Biased Standard Deviation',''),header=TRUE)
a<-table.element(a,sqrt(varx))
a<-table.element(a,sqrt(vary))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('covariance.htm','Covariance',''),header=TRUE)
a<-table.element(a,cov(x,y),2)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('pearson_correlation.htm','Correlation',''),header=TRUE)
a<-table.element(a,cxy,2)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('coeff_of_determination.htm','Determination',''),header=TRUE)
a<-table.element(a,cxy*cxy,2)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('ttest_statistic.htm','T-Test',''),header=TRUE)
a<-table.element(a,as.matrix(corxy$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,'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')
qq.plot(x,main='QQplot of variable x')
dev.off()
bitmap(file='test3.png')
qq.plot(y,main='QQplot of variable y')
dev.off()