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Author

*The author of this computation has been verified*

R Software Module

rwasp_correlation.wasp

Title produced by software

Pearson Correlation

Date of computation

Mon, 12 Dec 2016 16:53:04 +0100

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Dec/12/t1481558133mp4omstpgwakb8n.htm/, Retrieved Fri, 01 Nov 2024 03:37:36 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=298927, Retrieved Fri, 01 Nov 2024 03:37:36 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

108

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

-       [Pearson Correlation] [] [2016-12-12 15:53:04] [c4ef4c70482680cab119953cba46aca4] [Current]

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Dataseries Y:

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Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	3 seconds
R Server	Big 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 time3 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298927&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]

3 seconds[/C][/ROW] [ROW]

R Server[/C]

Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=298927&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298927&T=0

As an alternative you can also use a 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 Output	view raw output of R engine
Computing time	3 seconds
R Server	Big Analytics Cloud Computing Center

Pearson Product Moment Correlation - Ungrouped Data
Statistic	Variable X	Variable Y
Mean	3.87878787878788	4.1969696969697
Biased Variance	0.216368227731864	0.318526170798898
Biased Standard Deviation	0.465153982818447	0.564381228248157
Covariance	0.0260320037105751
Correlation	0.0981587850547415
Determination	0.00963514708342295
T-Test	0.971443243024761
p-value (2 sided)	0.333743801327963
p-value (1 sided)	0.166871900663982
95% CI of Correlation	[-0.101214343261179, 0.289952007203174]
Degrees of Freedom	97
Number of Observations	99

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 3.87878787878788 & 4.1969696969697 \tabularnewline
Biased Variance & 0.216368227731864 & 0.318526170798898 \tabularnewline
Biased Standard Deviation & 0.465153982818447 & 0.564381228248157 \tabularnewline
Covariance & 0.0260320037105751 \tabularnewline
Correlation & 0.0981587850547415 \tabularnewline
Determination & 0.00963514708342295 \tabularnewline
T-Test & 0.971443243024761 \tabularnewline
p-value (2 sided) & 0.333743801327963 \tabularnewline
p-value (1 sided) & 0.166871900663982 \tabularnewline
95% CI of Correlation & [-0.101214343261179, 0.289952007203174] \tabularnewline
Degrees of Freedom & 97 \tabularnewline
Number of Observations & 99 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298927&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]3.87878787878788[/C][C]4.1969696969697[/C][/ROW]
[ROW][C]Biased Variance[/C][C]0.216368227731864[/C][C]0.318526170798898[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]0.465153982818447[/C][C]0.564381228248157[/C][/ROW]
[ROW][C]Covariance[/C][C]0.0260320037105751[/C][/ROW]
[ROW][C]Correlation[/C][C]0.0981587850547415[/C][/ROW]
[ROW][C]Determination[/C][C]0.00963514708342295[/C][/ROW]
[ROW][C]T-Test[/C][C]0.971443243024761[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0.333743801327963[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0.166871900663982[/C][/ROW]
[ROW][C]95% CI of Correlation[/C][C][-0.101214343261179, 0.289952007203174][/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]97[/C][/ROW]
[ROW][C]Number of Observations[/C][C]99[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298927&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298927&T=1

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Pearson Product Moment Correlation - Ungrouped Data
Statistic	Variable X	Variable Y
Mean	3.87878787878788	4.1969696969697
Biased Variance	0.216368227731864	0.318526170798898
Biased Standard Deviation	0.465153982818447	0.564381228248157
Covariance	0.0260320037105751
Correlation	0.0981587850547415
Determination	0.00963514708342295
T-Test	0.971443243024761
p-value (2 sided)	0.333743801327963
p-value (1 sided)	0.166871900663982
95% CI of Correlation	[-0.101214343261179, 0.289952007203174]
Degrees of Freedom	97
Number of Observations	99

Normality Tests
> jarque.x Jarque-Bera Normality Test data: x JB = 5.7623, p-value = 0.05607 alternative hypothesis: greater
> jarque.y Jarque-Bera Normality Test data: y JB = 37.15, p-value = 8.572e-09 alternative hypothesis: greater
> ad.x Anderson-Darling normality test data: x A = 1.9976, p-value = 4.01e-05
> ad.y Anderson-Darling normality test data: y A = 1.3757, p-value = 0.00138

\begin{tabular}{lllllllll}
\hline
Normality Tests \tabularnewline
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 5.7623, p-value = 0.05607
alternative hypothesis: greater
 \tabularnewline
> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 37.15, p-value = 8.572e-09
alternative hypothesis: greater
 \tabularnewline
> ad.x
	Anderson-Darling normality test
data:  x
A = 1.9976, p-value = 4.01e-05
 \tabularnewline
> ad.y
	Anderson-Darling normality test
data:  y
A = 1.3757, p-value = 0.00138
 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298927&T=2

[TABLE]
[ROW][C]Normality Tests[/C][/ROW]
[ROW][C]> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 5.7623, p-value = 0.05607
alternative hypothesis: greater
[/C][/ROW]
[ROW][C]> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 37.15, p-value = 8.572e-09
alternative hypothesis: greater
[/C][/ROW]
[ROW][C]> ad.x
	Anderson-Darling normality test
data:  x
A = 1.9976, p-value = 4.01e-05
[/C][/ROW]
[ROW][C]> ad.y
	Anderson-Darling normality test
data:  y
A = 1.3757, p-value = 0.00138
[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298927&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298927&T=2

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Normality Tests
> jarque.x Jarque-Bera Normality Test data: x JB = 5.7623, p-value = 0.05607 alternative hypothesis: greater
> jarque.y Jarque-Bera Normality Test data: y JB = 37.15, p-value = 8.572e-09 alternative hypothesis: greater
> ad.x Anderson-Darling normality test data: x A = 1.9976, p-value = 4.01e-05
> ad.y Anderson-Darling normality test data: y A = 1.3757, p-value = 0.00138

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 1 ; par2 = 2 ; par3 = FALSE ;

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()

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code