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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 computationFri, 18 Dec 2015 12:18:31 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/Dec/18/t1450441428rxodxkvv2x3pumq.htm/, Retrieved Thu, 16 May 2024 12:09:23 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=286879, Retrieved Thu, 16 May 2024 12:09:23 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact98

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
0
1
1
1
1
1
1
1
0
0
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
0
1
1
0
1
0
0
0
1
0
1
1
0
1
0
0
1
1
1
1
1
0
1
1
1
0
1
1
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
1
0
0
0
0
1
1
0
1
1
0
1
0
0
1
0
1
1
1
0
1
0
1
1
1
1
0
1
1
1
0
1
1
0
1
0
0
0
0
0
1
1
1
1
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
Dataseries Y:
Download CSV
Histogram 
7.5
6
6.5
1
1
5.5
8.5
6.5
4.5
2
5
0.5
5
5
2.5
5
5.5
3.5
3
4
0.5
6.5
4.5
7.5
5.5
4
7.5
7
4
5.5
2.5
5.5
3.5
2.5
4.5
4.5
4.5
6
2.5
5
0
5
6.5
5
6
4.5
5.5
1
7.5
6
5
1
5
6.5
7
4.5
0
8.5
3.5
7.5
3.5
6
1.5
9
3.5
3.5
4
6.5
7.5
6
5
5.5
3.5
7.5
6.5
6.5
6.5
7
3.5
1.5
4
7.5
4.5
0
3.5
5.5
5
4.5
2.5
7.5
7
0
4.5
3
1.5
3.5
2.5
5.5
8
1
5
4.5
3
3
8
2.5
7
0
1
3.5
5.5
5.5
0.5
7.5
9
9.5
8.5
7
8
10
7
8.5
9
9.5
4
6
8
5.5
9.5
7.5
7
7.5
8
7
7
6
10
2.5
9
8
6
8.5
6
9
8
9
5.5
7
5.5
9
2
8.5
9
8.5
9
7.5
10
9
7.5
6
10.5
8.5
8
10
10.5
6.5
9.5
8.5
7.5
5
8
10
7
7.5
7.5
9.5
6
10
7
3
6
7
10
7
3.5
8
10
5.5
6
6.5
6.5
8.5
4
9.5
8
8.5
5.5
7
9
8
10
8
6
8
5
9
4.5
8.5
9.5
8.5
7.5
7.5
5
7
8
5.5
8.5
9.5
7
8
8.5
3.5
6.5
6.5
10.5
8.5
8
10
10
9.5
9
10
7.5
4.5
4.5
0.5
6.5
4.5
5.5
5
6
4
8
10.5
6.5
8
8.5
5.5
7
5
3.5
5
9
8.5
5
9.5
3
1.5
6
0.5
6.5
7.5
4.5
8
9
7.5
8.5
7
9.5
6.5
9.5
6
8
9.5
8
8
9
5

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Gwilym Jenkins' @ jenkins.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 & 4 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=286879&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]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=286879&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=286879&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 time4 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean0.5107913669064756.18345323741007
Biased Variance0.249883546400296.39620102479168
Biased Standard Deviation0.4998835328356892.52907117827705
Covariance-0.054333428564008
Correlation-0.0428225180648915
Determination0.00183376805341796
T-Test-0.7120742899852
p-value (2 sided)0.477020247720301
p-value (1 sided)0.23851012386015
95% CI of Correlation[-0.159661183798389, 0.075199320773574]
Degrees of Freedom276
Number of Observations278

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 0.510791366906475 & 6.18345323741007 \tabularnewline
Biased Variance & 0.24988354640029 & 6.39620102479168 \tabularnewline
Biased Standard Deviation & 0.499883532835689 & 2.52907117827705 \tabularnewline
Covariance & -0.054333428564008 \tabularnewline
Correlation & -0.0428225180648915 \tabularnewline
Determination & 0.00183376805341796 \tabularnewline
T-Test & -0.7120742899852 \tabularnewline
p-value (2 sided) & 0.477020247720301 \tabularnewline
p-value (1 sided) & 0.23851012386015 \tabularnewline
95% CI of Correlation & [-0.159661183798389, 0.075199320773574] \tabularnewline
Degrees of Freedom & 276 \tabularnewline
Number of Observations & 278 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=286879&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]0.510791366906475[/C][C]6.18345323741007[/C][/ROW]
[ROW][C]Biased Variance[/C][C]0.24988354640029[/C][C]6.39620102479168[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]0.499883532835689[/C][C]2.52907117827705[/C][/ROW]
[ROW][C]Covariance[/C][C]-0.054333428564008[/C][/ROW]
[ROW][C]Correlation[/C][C]-0.0428225180648915[/C][/ROW]
[ROW][C]Determination[/C][C]0.00183376805341796[/C][/ROW]
[ROW][C]T-Test[/C][C]-0.7120742899852[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0.477020247720301[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0.23851012386015[/C][/ROW]
[ROW][C]95% CI of Correlation[/C][C][-0.159661183798389, 0.075199320773574][/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]276[/C][/ROW]
[ROW][C]Number of Observations[/C][C]278[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=286879&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=286879&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
Mean0.5107913669064756.18345323741007
Biased Variance0.249883546400296.39620102479168
Biased Standard Deviation0.4998835328356892.52907117827705
Covariance-0.054333428564008
Correlation-0.0428225180648915
Determination0.00183376805341796
T-Test-0.7120742899852
p-value (2 sided)0.477020247720301
p-value (1 sided)0.23851012386015
95% CI of Correlation[-0.159661183798389, 0.075199320773574]
Degrees of Freedom276
Number of Observations278






Normality Tests
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 46.333, p-value = 8.686e-11
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 13.672, p-value = 0.001074
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 49.806, p-value < 2.2e-16

> ad.y
	Anderson-Darling normality test
data:  y
A = 2.417, p-value = 3.984e-06


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

> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 46.333, p-value = 8.686e-11
alternative hypothesis: greater

 \tabularnewline

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 13.672, p-value = 0.001074
alternative hypothesis: greater

 \tabularnewline

> ad.x
	Anderson-Darling normality test
data:  x
A = 49.806, p-value < 2.2e-16

 \tabularnewline

> ad.y
	Anderson-Darling normality test
data:  y
A = 2.417, p-value = 3.984e-06

 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=286879&T=2

[TABLE]
[ROW][C]Normality Tests[/C][/ROW]
[ROW][C]
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 46.333, p-value = 8.686e-11
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 13.672, p-value = 0.001074
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> ad.x
	Anderson-Darling normality test
data:  x
A = 49.806, p-value < 2.2e-16

[/C][/ROW]
[ROW][C]
> ad.y
	Anderson-Darling normality test
data:  y
A = 2.417, p-value = 3.984e-06

[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=286879&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=286879&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 = 46.333, p-value = 8.686e-11
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 13.672, p-value = 0.001074
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 49.806, p-value < 2.2e-16

> ad.y
	Anderson-Darling normality test
data:  y
A = 2.417, p-value = 3.984e-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$estimate)[1,1]
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Pearson Product Moment Correlation - Ungrouped Data',3,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Statistic',1,TRUE)
a<-table.element(a,'Variable X',1,TRUE)
a<-table.element(a,'Variable Y',1,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('arithmetic_mean.htm','Mean',''),header=TRUE)
a<-table.element(a,mean(x))
a<-table.element(a,mean(y))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('biased.htm','Biased Variance',''),header=TRUE)
a<-table.element(a,varx)
a<-table.element(a,vary)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('biased1.htm','Biased Standard Deviation',''),header=TRUE)
a<-table.element(a,sqrt(varx))
a<-table.element(a,sqrt(vary))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('covariance.htm','Covariance',''),header=TRUE)
a<-table.element(a,cov(x,y),2)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('pearson_correlation.htm','Correlation',''),header=TRUE)
a<-table.element(a,cxy,2)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('coeff_of_determination.htm','Determination',''),header=TRUE)
a<-table.element(a,cxy*cxy,2)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('ttest_statistic.htm','T-Test',''),header=TRUE)
a<-table.element(a,as.matrix(corxy$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()