Repository of Reproducible Computations

Free Statistics

of Irreproducible Research!

Author's title

Author

*The author of this computation has been verified*

R Software Module

rwasp_correlation.wasp

Title produced by software

Pearson Correlation

Date of computation

Tue, 13 Dec 2016 15:22:27 +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/13/t1481638955hjgbk8dcr3sxoqe.htm/, Retrieved Fri, 01 Nov 2024 03:26:46 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=299120, Retrieved Fri, 01 Nov 2024 03:26:46 +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

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

-       [Pearson Correlation] [] [2016-12-13 14:22:27] [94ac3c9a028ddd47e8862e80eac9f626] [Current]

Feedback Forum

Post a new message

Dataseries X:

Download CSV

Histogram

Boxplots

Dataseries Y:

Download CSV

Histogram

10
11
11
11
12
12
12
13
13
13
13
13
13
13
13
14
14
14
14
14
14
14
14
14
14
14
14
14
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
17
17
17
17
17
17
17
17
17
17
17
17
17
17
17
17
17
17
17
17
18
18
18
18
18
18
18
18
19
19
20
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA

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=299120&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=299120&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299120&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	13.5922330097087	15.4757281553398
Biased Variance	2.55217268357055	3.47271184843058
Biased Standard Deviation	1.59755209103508	1.86352135711684
Covariance	2.91157433847325
Correlation	0.968504019916408
Determination	0.938000036594242
T-Test	39.0900654843186
p-value (2 sided)	8.47407082383922e-63
p-value (1 sided)	4.23703541191961e-63
95% CI of Correlation	[0.953737890833525, 0.978608639168302]
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 & 13.5922330097087 & 15.4757281553398 \tabularnewline
Biased Variance & 2.55217268357055 & 3.47271184843058 \tabularnewline
Biased Standard Deviation & 1.59755209103508 & 1.86352135711684 \tabularnewline
Covariance & 2.91157433847325 \tabularnewline
Correlation & 0.968504019916408 \tabularnewline
Determination & 0.938000036594242 \tabularnewline
T-Test & 39.0900654843186 \tabularnewline
p-value (2 sided) & 8.47407082383922e-63 \tabularnewline
p-value (1 sided) & 4.23703541191961e-63 \tabularnewline
95% CI of Correlation & [0.953737890833525, 0.978608639168302] \tabularnewline
Degrees of Freedom & 101 \tabularnewline
Number of Observations & 103 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299120&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]13.5922330097087[/C][C]15.4757281553398[/C][/ROW]
[ROW][C]Biased Variance[/C][C]2.55217268357055[/C][C]3.47271184843058[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]1.59755209103508[/C][C]1.86352135711684[/C][/ROW]
[ROW][C]Covariance[/C][C]2.91157433847325[/C][/ROW]
[ROW][C]Correlation[/C][C]0.968504019916408[/C][/ROW]
[ROW][C]Determination[/C][C]0.938000036594242[/C][/ROW]
[ROW][C]T-Test[/C][C]39.0900654843186[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]8.47407082383922e-63[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]4.23703541191961e-63[/C][/ROW]
[ROW][C]95% CI of Correlation[/C][C][0.953737890833525, 0.978608639168302][/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=299120&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299120&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	13.5922330097087	15.4757281553398
Biased Variance	2.55217268357055	3.47271184843058
Biased Standard Deviation	1.59755209103508	1.86352135711684
Covariance	2.91157433847325
Correlation	0.968504019916408
Determination	0.938000036594242
T-Test	39.0900654843186
p-value (2 sided)	8.47407082383922e-63
p-value (1 sided)	4.23703541191961e-63
95% CI of Correlation	[0.953737890833525, 0.978608639168302]
Degrees of Freedom	101
Number of Observations	103

Normality Tests
> jarque.x Jarque-Bera Normality Test data: x JB = 13.531, p-value = 0.001153 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 = 2.4679, p-value = 2.799e-06
> 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 = 13.531, p-value = 0.001153
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 = 2.4679, p-value = 2.799e-06
 \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=299120&T=2

[TABLE]
[ROW][C]Normality Tests[/C][/ROW]
[ROW][C]> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 13.531, p-value = 0.001153
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 = 2.4679, p-value = 2.799e-06
[/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=299120&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299120&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 = 13.531, p-value = 0.001153 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 = 2.4679, p-value = 2.799e-06
> ad.y Anderson-Darling normality test data: y A = 1.9626, p-value = 4.908e-05

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