FreeStatistics.org

Free Statistics

of Irreproducible Research!

Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_correlation.wasp
Title produced by softwarePearson Correlation
Date of computationWed, 05 Aug 2020 19:35:03 +0200
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2020/Aug/05/t1596649252n28z9dm8zjv14cl.htm/, Retrieved Wed, 24 Apr 2024 01:35:38 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Wed, 24 Apr 2024 01:35:38 +0200
QR Codes:

Original text written by user:
IsPrivate?This computation is private
User-defined keywordsX ray severity score, SpO2
Estimated Impact0

Tree of Dependent Computations

Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
85
99
98
99
97
99
99
99
99
99
99
99
98
95
98
98
99
96
88
94
88
98
98
96
98
98
98
96
94
100
98
99
97
97
99
99
98
98
99
98
98
99
98
98
98
99
98
99
85
95
98
98
98
99
99
98
99
99
92
99
98
99
98
98
98
99
99
98
98
98
98
98
98
98
99
97
98
96
99
99
98
98
98
99
99
99
99
99
99
99
99
99
99
99
99
98
98
99
99
98
98
88
98
98
98
84
99
96
99
99
100
85
60
96
99
94
98
99
96
97
97
97
98
98
99
99
97
96
98
99
99
99
98
99
98
98
98
98
98
98
99
99
92
99
99
96
98
98
96
98
96
98
99
98
98
98
98
97
98
96
97
85
92
70
98
99
99
96
99
99
99
98
99
98
99
98
99
99
98
97
98
91
99
99
99
99
97
98
98
98
96
88
95
98
96
92
98
98
97
98
97
96
98
98
97
98
98
98
98
98
98
98
99
97
98
98
99
98
98
98
99
99
98
98
99
99
98
82
98
98
98
99
99
98
98
98
98
98
93
99
98
99
98
98
98
80
99
98
98
97
98
100
98
98
99
98
100
98
96
86
97
98
94
88
97
96
99
98
98
98
98
97
99
99
96
97
98
99
98
99
98
99
98
99
99
99
98
98
99
96
97
98
99
98
99
99
99
99
99
98
98
99
99
98
99
98
97
99
98
98
98
97
99
98
99
66
99
98
99
99
99
98
99
99
98
98
99
99
99
98
100
98
97
98
99
93
98
99
98
99
96
99
98
99
93
99
98
99
99
97
99
98
99
99
98
96
98
99
98
99
99
98
99
96
97
99
98
96
99
90
98
97
98
97
99
98
99
99
98
94
98
99
98
97
98
96
98
99
85
96
98
96
92
98
99
98
100
97
100
98
96
99
99
98
98
98
100
98
100
97
96
90
98
97
97
Dataseries Y:
Download CSV
Histogram 
28
0
0
0
4
0
0
0
0
0
0
0
0
12
10
0
0
4
20
10
18
0
0
12
0
0
0
0
0
0
0
0
0
0
0
0
0
22
0
0
0
0
0
0
0
0
0
0
32
12
0
0
0
0
0
0
0
0
18
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
20
0
0
0
0
0
28
30
10
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
12
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
12
0
16
16
24
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
14
0
0
0
0
0
0
0
0
26
40
0
0
0
12
0
0
0
0
0
0
0
0
0
0
12
0
12
24
0
0
0
0
0
0
0
0
0
19
12
28
0
0
0
0
0
31
0
0
0
0
0
0
0
12
0
0
12
0
0
0
0
0
0
20
0
0
0
0
2
27
0
0
0
0
0
0
12
24
0
0
28
35
6
12
24
7
0
0
1
12
20
19
25
12
9
24
0
0
18
19
18
0
12
8
12
21
14
4
9
0
0
0
20
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
26
12
12
0
0
22
0
0
5
0
0
0
0
14
2
12
0
0
0
0
32
3
28
20
0
35
29
0
26
26
0
0
0
29
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
12
0
12
0
0
32
0
0
0
0
12
0
22
4
12
12
12
0
24
0
0
26
34
0
0
7
0
0
0
0
0
0
0
0
0
12
0
0
0
3
12
0
12
28
21
0
15
12

Tables (Output of Computation)





Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 time2 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]2 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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 time2 seconds
R ServerBig Analytics Cloud Computing Center






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean97.26506024096394.27228915662651
Biased Variance14.835767165045774.0005574103644
Biased Standard Deviation3.851722623066958.60235766580095
Covariance-17.1689657179442
Correlation-0.516920645428577
Determination0.267206953670297
T-Test-12.271799017667
p-value (2 sided)9.91061600650595e-30
p-value (1 sided)4.95530800325298e-30
95% CI of Correlation[-0.584116756134733, -0.442687055342169]
Degrees of Freedom413
Number of Observations415

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 97.2650602409639 & 4.27228915662651 \tabularnewline
Biased Variance & 14.8357671650457 & 74.0005574103644 \tabularnewline
Biased Standard Deviation & 3.85172262306695 & 8.60235766580095 \tabularnewline
Covariance & -17.1689657179442 \tabularnewline
Correlation & -0.516920645428577 \tabularnewline
Determination & 0.267206953670297 \tabularnewline
T-Test & -12.271799017667 \tabularnewline
p-value (2 sided) & 9.91061600650595e-30 \tabularnewline
p-value (1 sided) & 4.95530800325298e-30 \tabularnewline
95% CI of Correlation & [-0.584116756134733, -0.442687055342169] \tabularnewline
Degrees of Freedom & 413 \tabularnewline
Number of Observations & 415 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]97.2650602409639[/C][C]4.27228915662651[/C][/ROW]
[ROW][C]Biased Variance[/C][C]14.8357671650457[/C][C]74.0005574103644[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]3.85172262306695[/C][C]8.60235766580095[/C][/ROW]
[ROW][C]Covariance[/C][C]-17.1689657179442[/C][/ROW]
[ROW][C]Correlation[/C][C]-0.516920645428577[/C][/ROW]
[ROW][C]Determination[/C][C]0.267206953670297[/C][/ROW]
[ROW][C]T-Test[/C][C]-12.271799017667[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]9.91061600650595e-30[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]4.95530800325298e-30[/C][/ROW]
[ROW][C]95% CI of Correlation[/C][C][-0.584116756134733, -0.442687055342169][/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]413[/C][/ROW]
[ROW][C]Number of Observations[/C][C]415[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
Mean97.26506024096394.27228915662651
Biased Variance14.835767165045774.0005574103644
Biased Standard Deviation3.851722623066958.60235766580095
Covariance-17.1689657179442
Correlation-0.516920645428577
Determination0.267206953670297
T-Test-12.271799017667
p-value (2 sided)9.91061600650595e-30
p-value (1 sided)4.95530800325298e-30
95% CI of Correlation[-0.584116756134733, -0.442687055342169]
Degrees of Freedom413
Number of Observations415






Normality Tests
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 27702, p-value < 2.2e-16
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 420.16, p-value < 2.2e-16
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 72.033, p-value < 2.2e-16

> ad.y
	Anderson-Darling normality test
data:  y
A = 84.213, p-value < 2.2e-16


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

> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 27702, p-value < 2.2e-16
alternative hypothesis: greater

 \tabularnewline

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 420.16, p-value < 2.2e-16
alternative hypothesis: greater

 \tabularnewline

> ad.x
	Anderson-Darling normality test
data:  x
A = 72.033, p-value < 2.2e-16

 \tabularnewline

> ad.y
	Anderson-Darling normality test
data:  y
A = 84.213, p-value < 2.2e-16

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

[TABLE]
[ROW][C]Normality Tests[/C][/ROW]
[ROW][C]
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 27702, p-value < 2.2e-16
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 420.16, p-value < 2.2e-16
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> ad.x
	Anderson-Darling normality test
data:  x
A = 72.033, p-value < 2.2e-16

[/C][/ROW]
[ROW][C]
> ad.y
	Anderson-Darling normality test
data:  y
A = 84.213, p-value < 2.2e-16

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

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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 = 27702, p-value < 2.2e-16
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 420.16, p-value < 2.2e-16
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 72.033, p-value < 2.2e-16

> ad.y
	Anderson-Darling normality test
data:  y
A = 84.213, p-value < 2.2e-16


Figures (Output of Computation)

Input Parameters & R Code

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()