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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

Sat, 10 Dec 2016 13:51:20 +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/10/t1481374337pb5795j1h6xx0hm.htm/, Retrieved Fri, 01 Nov 2024 03:29:36 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=298671, Retrieved Fri, 01 Nov 2024 03:29:36 +0000

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

-       [Pearson Correlation] [] [2016-12-10 12:51:20] [94ac3c9a028ddd47e8862e80eac9f626] [Current]

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Dataseries X:

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Dataseries Y:

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Histogram

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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=298671&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=298671&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298671&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	12.6796116504854	15.4757281553398
Biased Variance	1.75172023753417	3.47271184843058
Biased Standard Deviation	1.32352568450112	1.86352135711684
Covariance	2.34999048162955
Correlation	0.943544314767181
Determination	0.890275873929469
T-Test	28.6267419941372
p-value (2 sided)	2.87528922161775e-50
p-value (1 sided)	1.43764461080888e-50
95% CI of Correlation	[0.917566456600598, 0.961499955666173]
Degrees of Freedom	101
Number of Observations	103

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 12.6796116504854 & 15.4757281553398 \tabularnewline
Biased Variance & 1.75172023753417 & 3.47271184843058 \tabularnewline
Biased Standard Deviation & 1.32352568450112 & 1.86352135711684 \tabularnewline
Covariance & 2.34999048162955 \tabularnewline
Correlation & 0.943544314767181 \tabularnewline
Determination & 0.890275873929469 \tabularnewline
T-Test & 28.6267419941372 \tabularnewline
p-value (2 sided) & 2.87528922161775e-50 \tabularnewline
p-value (1 sided) & 1.43764461080888e-50 \tabularnewline
95% CI of Correlation & [0.917566456600598, 0.961499955666173] \tabularnewline
Degrees of Freedom & 101 \tabularnewline
Number of Observations & 103 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298671&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]12.6796116504854[/C][C]15.4757281553398[/C][/ROW]
[ROW][C]Biased Variance[/C][C]1.75172023753417[/C][C]3.47271184843058[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]1.32352568450112[/C][C]1.86352135711684[/C][/ROW]
[ROW][C]Covariance[/C][C]2.34999048162955[/C][/ROW]
[ROW][C]Correlation[/C][C]0.943544314767181[/C][/ROW]
[ROW][C]Determination[/C][C]0.890275873929469[/C][/ROW]
[ROW][C]T-Test[/C][C]28.6267419941372[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]2.87528922161775e-50[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]1.43764461080888e-50[/C][/ROW]
[ROW][C]95% CI of Correlation[/C][C][0.917566456600598, 0.961499955666173][/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]101[/C][/ROW]
[ROW][C]Number of Observations[/C][C]103[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298671&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298671&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	12.6796116504854	15.4757281553398
Biased Variance	1.75172023753417	3.47271184843058
Biased Standard Deviation	1.32352568450112	1.86352135711684
Covariance	2.34999048162955
Correlation	0.943544314767181
Determination	0.890275873929469
T-Test	28.6267419941372
p-value (2 sided)	2.87528922161775e-50
p-value (1 sided)	1.43764461080888e-50
95% CI of Correlation	[0.917566456600598, 0.961499955666173]
Degrees of Freedom	101
Number of Observations	103

Normality Tests
> jarque.x Jarque-Bera Normality Test data: x JB = 53.125, p-value = 2.911e-12 alternative hypothesis: greater
> jarque.y Jarque-Bera Normality Test data: y JB = 4.8025, p-value = 0.0906 alternative hypothesis: greater
> ad.x Anderson-Darling normality test data: x A = 5.405, p-value = 1.995e-13
> ad.y Anderson-Darling normality test data: y A = 1.9626, p-value = 4.908e-05

\begin{tabular}{lllllllll}
\hline
Normality Tests \tabularnewline
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 53.125, p-value = 2.911e-12
alternative hypothesis: greater
 \tabularnewline
> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 4.8025, p-value = 0.0906
alternative hypothesis: greater
 \tabularnewline
> ad.x
	Anderson-Darling normality test
data:  x
A = 5.405, p-value = 1.995e-13
 \tabularnewline
> ad.y
	Anderson-Darling normality test
data:  y
A = 1.9626, p-value = 4.908e-05
 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298671&T=2

[TABLE]
[ROW][C]Normality Tests[/C][/ROW]
[ROW][C]> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 53.125, p-value = 2.911e-12
alternative hypothesis: greater
[/C][/ROW]
[ROW][C]> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 4.8025, p-value = 0.0906
alternative hypothesis: greater
[/C][/ROW]
[ROW][C]> ad.x
	Anderson-Darling normality test
data:  x
A = 5.405, p-value = 1.995e-13
[/C][/ROW]
[ROW][C]> ad.y
	Anderson-Darling normality test
data:  y
A = 1.9626, p-value = 4.908e-05
[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298671&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298671&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 = 53.125, p-value = 2.911e-12 alternative hypothesis: greater
> jarque.y Jarque-Bera Normality Test data: y JB = 4.8025, p-value = 0.0906 alternative hypothesis: greater
> ad.x Anderson-Darling normality test data: x A = 5.405, p-value = 1.995e-13
> ad.y Anderson-Darling normality test data: y A = 1.9626, p-value = 4.908e-05

Figure 1

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Postscript link

PDF link

Figure 2

PNG link

Postscript link

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Figure 3

PNG link

Postscript link

PDF link

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()

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code