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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 18:56:07 +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/t1481738651eksqenmhro0i1ug.htm/, Retrieved Fri, 01 Nov 2024 03:35:55 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=299670, Retrieved Fri, 01 Nov 2024 03:35:55 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact78

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Pearson Correlation] [] [2016-12-14 17:56:07] [462f83e9ca944f1b841aaa868aea0854] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
15
13
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13
12
17
12
13
13
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NA
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NA
14
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NA
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NA
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10
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11
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15
8
13
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15
14
13
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12
19
15
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15
13
15
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11
17
13
9
12
13
17
14
13
16
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10
12
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18
14
14
13
13
16
NA
13
14
8
13
13
16
14
13
14
12
16
18
16
15
18
15
14
14
15
9
17
11
15
NA
15
13
NA
15
15
14
13
Dataseries Y:
Download CSV
Histogram 
25
23
23
NA
NA
29
NA
NA
NA
27
20
22
21
28
25
20
NA
NA
NA
NA
26
NA
21
NA
NA
NA
23
25
27
27
27
21
21
NA
21
24
NA
29
23
25
NA
23
25
33
23
21
NA
1
24
NA
25
NA
NA
19
20
17
NA
23
23
NA
25
21
25
27
20
29
26
9
22
28
NA
NA
NA
NA
NA
23
19
20
24
19
NA
20
NA
21
NA
20
25
21
NA
18
20
NA
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NA
19
NA
24
25
14
21
NA
NA
25
21
NA
NA
NA
NA
NA
23
NA
NA
NA
23
NA
29
21
NA
19
21
29
23
NA
27
NA
23
24
NA
NA
NA
23
NA
24
NA
22
NA
28
NA
22
23
14
NA
22
NA
23
22
23
20
27
NA
NA
26
31
25
23
NA
25
NA
NA
19
25
7
25
NA
NA
NA
25
NA
21

Tables (Output of Computation)





Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time5 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 time5 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299670&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]5 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=299670&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299670&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 time5 seconds
R ServerBig Analytics Cloud Computing Center






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean13.8423.2
Biased Variance3.494411.02
Biased Standard Deviation1.869331431287673.31963853453957
Covariance6.15353535353535
Correlation0.981709037463807
Determination0.963752634238115
T-Test51.045516414691
p-value (2 sided)2.07787408599658e-72
p-value (1 sided)1.03893704299829e-72
95% CI of Correlation[0.972888591778665, 0.987677756027037]
Degrees of Freedom98
Number of Observations100

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 13.84 & 23.2 \tabularnewline
Biased Variance & 3.4944 & 11.02 \tabularnewline
Biased Standard Deviation & 1.86933143128767 & 3.31963853453957 \tabularnewline
Covariance & 6.15353535353535 \tabularnewline
Correlation & 0.981709037463807 \tabularnewline
Determination & 0.963752634238115 \tabularnewline
T-Test & 51.045516414691 \tabularnewline
p-value (2 sided) & 2.07787408599658e-72 \tabularnewline
p-value (1 sided) & 1.03893704299829e-72 \tabularnewline
95% CI of Correlation & [0.972888591778665, 0.987677756027037] \tabularnewline
Degrees of Freedom & 98 \tabularnewline
Number of Observations & 100 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299670&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]13.84[/C][C]23.2[/C][/ROW]
[ROW][C]Biased Variance[/C][C]3.4944[/C][C]11.02[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]1.86933143128767[/C][C]3.31963853453957[/C][/ROW]
[ROW][C]Covariance[/C][C]6.15353535353535[/C][/ROW]
[ROW][C]Correlation[/C][C]0.981709037463807[/C][/ROW]
[ROW][C]Determination[/C][C]0.963752634238115[/C][/ROW]
[ROW][C]T-Test[/C][C]51.045516414691[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]2.07787408599658e-72[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]1.03893704299829e-72[/C][/ROW]
[ROW][C]95% CI of Correlation[/C][C][0.972888591778665, 0.987677756027037][/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]98[/C][/ROW]
[ROW][C]Number of Observations[/C][C]100[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299670&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299670&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
Mean13.8423.2
Biased Variance3.494411.02
Biased Standard Deviation1.869331431287673.31963853453957
Covariance6.15353535353535
Correlation0.981709037463807
Determination0.963752634238115
T-Test51.045516414691
p-value (2 sided)2.07787408599658e-72
p-value (1 sided)1.03893704299829e-72
95% CI of Correlation[0.972888591778665, 0.987677756027037]
Degrees of Freedom98
Number of Observations100






Normality Tests
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 4.741, p-value = 0.09343
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 1.0339, p-value = 0.5963
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 1.4199, p-value = 0.001074

> ad.y
	Anderson-Darling normality test
data:  y
A = 0.84561, p-value = 0.02851


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

> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 4.741, p-value = 0.09343
alternative hypothesis: greater

 \tabularnewline

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 1.0339, p-value = 0.5963
alternative hypothesis: greater

 \tabularnewline

> ad.x
	Anderson-Darling normality test
data:  x
A = 1.4199, p-value = 0.001074

 \tabularnewline

> ad.y
	Anderson-Darling normality test
data:  y
A = 0.84561, p-value = 0.02851

 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299670&T=2

[TABLE]
[ROW][C]Normality Tests[/C][/ROW]
[ROW][C]
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 4.741, p-value = 0.09343
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 1.0339, p-value = 0.5963
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> ad.x
	Anderson-Darling normality test
data:  x
A = 1.4199, p-value = 0.001074

[/C][/ROW]
[ROW][C]
> ad.y
	Anderson-Darling normality test
data:  y
A = 0.84561, p-value = 0.02851

[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299670&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299670&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 = 4.741, p-value = 0.09343
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 1.0339, p-value = 0.5963
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 1.4199, p-value = 0.001074

> ad.y
	Anderson-Darling normality test
data:  y
A = 0.84561, p-value = 0.02851


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()