Repository of Reproducible Computations

Free Statistics

of Irreproducible Research!

Author's title

Author

*Unverified author*

R Software Module

rwasp_correlation.wasp

Title produced by software

Pearson Correlation

Date of computation

Tue, 22 Jan 2019 18:26:01 +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/2019/Jan/22/t1548186195r2pcqc5bk03n7ri.htm/, Retrieved Mon, 29 Apr 2024 06:45:20 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=316960, Retrieved Mon, 29 Apr 2024 06:45:20 +0000

QR Codes:

Paste this QR Code to cite your computation.

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

126

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

-       [Pearson Correlation] [] [2019-01-22 17:26:01] [d41d8cd98f00b204e9800998ecf8427e] [Current]

Feedback Forum

Post a new message

Dataseries X:

Download CSV

Histogram

Boxplots

3.1
3.2
3.8
4.5
3.9
3.1
4.2
4.1
4.2
3.3
5.3
3.2
4.3
1.2
1.7
4.0
3.0
2.9
1.5

Dataseries Y:

Download CSV

Histogram

11.08
7.46
6.7
5.2
4.3
13.16
10.91
3.18
8.5
6.3
9.9
14.03
9.4
18.01
5.85
2.7
11.4
12.3
20.05

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	4 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 time4 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=316960&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=316960&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=316960&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	4 seconds
R Server	Big Analytics Cloud Computing Center

Pearson Product Moment Correlation - Ungrouped Data
Statistic	Variable X	Variable Y
Mean	3.39473684210526	9.49631578947368
Biased Variance	1.06260387811634	21.1589390581717
Biased Standard Deviation	1.03082679346064	4.59988467879052
Covariance	-2.91268713450292
Correlation	-0.581942532262186
Determination	0.338657110855725
T-Test	-2.95047008759593
p-value (2 sided)	0.00895046317220369
p-value (1 sided)	0.00447523158610184
95% CI of Correlation	[-0.819530486356243, -0.173626969176024]
Degrees of Freedom	17
Number of Observations	19

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 3.39473684210526 & 9.49631578947368 \tabularnewline
Biased Variance & 1.06260387811634 & 21.1589390581717 \tabularnewline
Biased Standard Deviation & 1.03082679346064 & 4.59988467879052 \tabularnewline
Covariance & -2.91268713450292 \tabularnewline
Correlation & -0.581942532262186 \tabularnewline
Determination & 0.338657110855725 \tabularnewline
T-Test & -2.95047008759593 \tabularnewline
p-value (2 sided) & 0.00895046317220369 \tabularnewline
p-value (1 sided) & 0.00447523158610184 \tabularnewline
95% CI of Correlation & [-0.819530486356243, -0.173626969176024] \tabularnewline
Degrees of Freedom & 17 \tabularnewline
Number of Observations & 19 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=316960&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]3.39473684210526[/C][C]9.49631578947368[/C][/ROW]
[ROW][C]Biased Variance[/C][C]1.06260387811634[/C][C]21.1589390581717[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]1.03082679346064[/C][C]4.59988467879052[/C][/ROW]
[ROW][C]Covariance[/C][C]-2.91268713450292[/C][/ROW]
[ROW][C]Correlation[/C][C]-0.581942532262186[/C][/ROW]
[ROW][C]Determination[/C][C]0.338657110855725[/C][/ROW]
[ROW][C]T-Test[/C][C]-2.95047008759593[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0.00895046317220369[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0.00447523158610184[/C][/ROW]
[ROW][C]95% CI of Correlation[/C][C][-0.819530486356243, -0.173626969176024][/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]17[/C][/ROW]
[ROW][C]Number of Observations[/C][C]19[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=316960&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=316960&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	3.39473684210526	9.49631578947368
Biased Variance	1.06260387811634	21.1589390581717
Biased Standard Deviation	1.03082679346064	4.59988467879052
Covariance	-2.91268713450292
Correlation	-0.581942532262186
Determination	0.338657110855725
T-Test	-2.95047008759593
p-value (2 sided)	0.00895046317220369
p-value (1 sided)	0.00447523158610184
95% CI of Correlation	[-0.819530486356243, -0.173626969176024]
Degrees of Freedom	17
Number of Observations	19

Normality Tests
> jarque.x Jarque-Bera Normality Test data: x JB = 1.014, p-value = 0.6023 alternative hypothesis: greater
> jarque.y Jarque-Bera Normality Test data: y JB = 1.1102, p-value = 0.574 alternative hypothesis: greater
> ad.x Anderson-Darling normality test data: x A = 0.5709, p-value = 0.119
> ad.y Anderson-Darling normality test data: y A = 0.23987, p-value = 0.7419

\begin{tabular}{lllllllll}
\hline
Normality Tests \tabularnewline
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 1.014, p-value = 0.6023
alternative hypothesis: greater
 \tabularnewline
> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 1.1102, p-value = 0.574
alternative hypothesis: greater
 \tabularnewline
> ad.x
	Anderson-Darling normality test
data:  x
A = 0.5709, p-value = 0.119
 \tabularnewline
> ad.y
	Anderson-Darling normality test
data:  y
A = 0.23987, p-value = 0.7419
 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=316960&T=2

[TABLE]
[ROW][C]Normality Tests[/C][/ROW]
[ROW][C]> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 1.014, p-value = 0.6023
alternative hypothesis: greater
[/C][/ROW]
[ROW][C]> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 1.1102, p-value = 0.574
alternative hypothesis: greater
[/C][/ROW]
[ROW][C]> ad.x
	Anderson-Darling normality test
data:  x
A = 0.5709, p-value = 0.119
[/C][/ROW]
[ROW][C]> ad.y
	Anderson-Darling normality test
data:  y
A = 0.23987, p-value = 0.7419
[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=316960&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=316960&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 = 1.014, p-value = 0.6023 alternative hypothesis: greater
> jarque.y Jarque-Bera Normality Test data: y JB = 1.1102, p-value = 0.574 alternative hypothesis: greater
> ad.x Anderson-Darling normality test data: x A = 0.5709, p-value = 0.119
> ad.y Anderson-Darling normality test data: y A = 0.23987, p-value = 0.7419

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):

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