FreeStatistics.org

Free Statistics

of Irreproducible Research!

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 computationWed, 14 Dec 2016 18:56:42 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Dec/14/t1481738233r1h3w4i15j5nu0o.htm/, Retrieved Fri, 01 Nov 2024 03:36:46 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=299668, Retrieved Fri, 01 Nov 2024 03:36:46 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsPearson Correlation
Estimated Impact114

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Pearson Correlation] [Pearson Correlat...] [2016-12-14 17:56:42] [7a1d1ad32a278442444f0033012c5937] [Current]
Feedback Forum

Post a new message

Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
13
16
17
11
12
16
13
12
13
17
17
15
16
14
16
17
12
0
11
13
16
11
16
11
13
11
16
15
16
16
13
15
17
11
13
17
11
14
14
18
11
17
13
16
15
15
12
15
13
3
17
13
13
11
14
13
11
17
16
11
17
16
16
16
15
12
17
14
14
16
11
11
10
10
13
15
16
14
15
17
12
10
12
17
13
20
17
18
11
17
14
11
17
12
17
11
16
18
18
16
4
13
15
13
11
13
12
12
11
16
12
10
11
12
14
16
16
13
16
14
15
14
12
15
13
15
16
12
11
11
11
12
18
10
11
8
18
3
15
19
17
10
14
12
13
17
14
19
14
12
9
16
16
15
12
11
17
10
11
18
15
18
15
11
12
10
16
10
16
Dataseries Y:
Download CSV
Histogram 
14
19
17
17
15
20
15
19
15
15
19
12
20
18
15
14
20
0
16
16
16
10
19
19
16
15
18
17
19
17
10
19
20
5
19
16
15
16
18
16
15
17
10
20
19
7
13
16
16
4
18
18
16
17
19
16
19
13
16
13
12
17
17
17
16
16
14
16
13
16
14
20
12
13
18
14
19
18
14
18
19
15
14
17
19
13
19
18
20
15
15
15
20
15
19
18
18
15
20
17
12
18
19
20
10
17
15
16
18
18
14
15
12
17
14
18
17
17
20
16
14
15
18
20
17
17
17
17
15
17
18
17
20
15
16
15
18
11
15
18
20
19
14
16
15
17
18
20
17
18
15
16
11
15
18
17
16
12
19
18
15
17
19
18
19
16
16
16
14

Tables (Output of Computation)





Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R ServerBig 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=299668&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=299668&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299668&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 Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R ServerBig Analytics Cloud Computing Center






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean13.704142011834316.1360946745562
Biased Variance9.332586394033829.26550190819649
Biased Standard Deviation3.054928214219413.04392869630622
Covariance4.12383770076078
Correlation0.440847779253601
Determination0.194346764472831
T-Test6.3470630892728
p-value (2 sided)1.99039779778105e-09
p-value (1 sided)9.95198898890526e-10
95% CI of Correlation[0.310555329764503, 0.554880305470016]
Degrees of Freedom167
Number of Observations169

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 13.7041420118343 & 16.1360946745562 \tabularnewline
Biased Variance & 9.33258639403382 & 9.26550190819649 \tabularnewline
Biased Standard Deviation & 3.05492821421941 & 3.04392869630622 \tabularnewline
Covariance & 4.12383770076078 \tabularnewline
Correlation & 0.440847779253601 \tabularnewline
Determination & 0.194346764472831 \tabularnewline
T-Test & 6.3470630892728 \tabularnewline
p-value (2 sided) & 1.99039779778105e-09 \tabularnewline
p-value (1 sided) & 9.95198898890526e-10 \tabularnewline
95% CI of Correlation & [0.310555329764503, 0.554880305470016] \tabularnewline
Degrees of Freedom & 167 \tabularnewline
Number of Observations & 169 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299668&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]13.7041420118343[/C][C]16.1360946745562[/C][/ROW]
[ROW][C]Biased Variance[/C][C]9.33258639403382[/C][C]9.26550190819649[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]3.05492821421941[/C][C]3.04392869630622[/C][/ROW]
[ROW][C]Covariance[/C][C]4.12383770076078[/C][/ROW]
[ROW][C]Correlation[/C][C]0.440847779253601[/C][/ROW]
[ROW][C]Determination[/C][C]0.194346764472831[/C][/ROW]
[ROW][C]T-Test[/C][C]6.3470630892728[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]1.99039779778105e-09[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]9.95198898890526e-10[/C][/ROW]
[ROW][C]95% CI of Correlation[/C][C][0.310555329764503, 0.554880305470016][/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]167[/C][/ROW]
[ROW][C]Number of Observations[/C][C]169[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299668&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299668&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
Mean13.704142011834316.1360946745562
Biased Variance9.332586394033829.26550190819649
Biased Standard Deviation3.054928214219413.04392869630622
Covariance4.12383770076078
Correlation0.440847779253601
Determination0.194346764472831
T-Test6.3470630892728
p-value (2 sided)1.99039779778105e-09
p-value (1 sided)9.95198898890526e-10
95% CI of Correlation[0.310555329764503, 0.554880305470016]
Degrees of Freedom167
Number of Observations169






Normality Tests
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 83.002, p-value < 2.2e-16
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 321.63, p-value < 2.2e-16
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 2.735, p-value = 6.473e-07

> ad.y
	Anderson-Darling normality test
data:  y
A = 4.2383, p-value = 1.42e-10


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

> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 83.002, p-value < 2.2e-16
alternative hypothesis: greater

 \tabularnewline

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 321.63, p-value < 2.2e-16
alternative hypothesis: greater

 \tabularnewline

> ad.x
	Anderson-Darling normality test
data:  x
A = 2.735, p-value = 6.473e-07

 \tabularnewline

> ad.y
	Anderson-Darling normality test
data:  y
A = 4.2383, p-value = 1.42e-10

 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299668&T=2

[TABLE]
[ROW][C]Normality Tests[/C][/ROW]
[ROW][C]
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 83.002, p-value < 2.2e-16
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 321.63, p-value < 2.2e-16
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> ad.x
	Anderson-Darling normality test
data:  x
A = 2.735, p-value = 6.473e-07

[/C][/ROW]
[ROW][C]
> ad.y
	Anderson-Darling normality test
data:  y
A = 4.2383, p-value = 1.42e-10

[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299668&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299668&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 = 83.002, p-value < 2.2e-16
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 321.63, p-value < 2.2e-16
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 2.735, p-value = 6.473e-07

> ad.y
	Anderson-Darling normality test
data:  y
A = 4.2383, p-value = 1.42e-10


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = grey ; par2 = no ;
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()