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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 computationThu, 01 Feb 2018 10:12:30 +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/2018/Feb/01/t15174763930765z951c4xlnv1.htm/, Retrieved Sun, 28 Apr 2024 21:50:05 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=313922, Retrieved Sun, 28 Apr 2024 21:50:05 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact84

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [Tijdreeks 1 - Stap 2] [2012-07-27 09:10:44] [226376a35b8869827dc57271384c00a4]
- RMPD    [Pearson Correlation] [] [2018-02-01 09:12:30] [f8fa2047a2fda95724f8ed0c0d56b790] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
88.6
71.6
93.3
84.3
80.6
75.2
69.7
82
69.4
83.3
79.6
82.6
80.6
83.5
76.3
Dataseries Y:
Download CSV
Histogram 
20
16
19.8
18.4
17.1
15.5
14.7
17.1
15.4
16.2
15
17.2
16
17
14.4

Tables (Output of Computation)





Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time6 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 time6 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=313922&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]6 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=313922&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=313922&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 time6 seconds
R ServerBig Analytics Cloud Computing Center






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean80.0416.6533333333333
Biased Variance41.98906666666662.70382222222222
Biased Standard Deviation6.479897118524851.64433032637065
Covariance9.53414285714286
Correlation0.835143786782374
Determination0.697465144601204
T-Test5.47450960243449
p-value (2 sided)0.000106671855974303
p-value (1 sided)5.33359279871513e-05
95% CI of Correlation[0.56429282201005, 0.94368555742217]
Degrees of Freedom13
Number of Observations15

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 80.04 & 16.6533333333333 \tabularnewline
Biased Variance & 41.9890666666666 & 2.70382222222222 \tabularnewline
Biased Standard Deviation & 6.47989711852485 & 1.64433032637065 \tabularnewline
Covariance & 9.53414285714286 \tabularnewline
Correlation & 0.835143786782374 \tabularnewline
Determination & 0.697465144601204 \tabularnewline
T-Test & 5.47450960243449 \tabularnewline
p-value (2 sided) & 0.000106671855974303 \tabularnewline
p-value (1 sided) & 5.33359279871513e-05 \tabularnewline
95% CI of Correlation & [0.56429282201005, 0.94368555742217] \tabularnewline
Degrees of Freedom & 13 \tabularnewline
Number of Observations & 15 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=313922&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]80.04[/C][C]16.6533333333333[/C][/ROW]
[ROW][C]Biased Variance[/C][C]41.9890666666666[/C][C]2.70382222222222[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]6.47989711852485[/C][C]1.64433032637065[/C][/ROW]
[ROW][C]Covariance[/C][C]9.53414285714286[/C][/ROW]
[ROW][C]Correlation[/C][C]0.835143786782374[/C][/ROW]
[ROW][C]Determination[/C][C]0.697465144601204[/C][/ROW]
[ROW][C]T-Test[/C][C]5.47450960243449[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0.000106671855974303[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]5.33359279871513e-05[/C][/ROW]
[ROW][C]95% CI of Correlation[/C][C][0.56429282201005, 0.94368555742217][/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]13[/C][/ROW]
[ROW][C]Number of Observations[/C][C]15[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=313922&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=313922&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
Mean80.0416.6533333333333
Biased Variance41.98906666666662.70382222222222
Biased Standard Deviation6.479897118524851.64433032637065
Covariance9.53414285714286
Correlation0.835143786782374
Determination0.697465144601204
T-Test5.47450960243449
p-value (2 sided)0.000106671855974303
p-value (1 sided)5.33359279871513e-05
95% CI of Correlation[0.56429282201005, 0.94368555742217]
Degrees of Freedom13
Number of Observations15






Normality Tests
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 0.13672, p-value = 0.9339
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 1.3289, p-value = 0.5146
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 0.30834, p-value = 0.5197

> ad.y
	Anderson-Darling normality test
data:  y
A = 0.44083, p-value = 0.2508


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

> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 0.13672, p-value = 0.9339
alternative hypothesis: greater

 \tabularnewline

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 1.3289, p-value = 0.5146
alternative hypothesis: greater

 \tabularnewline

> ad.x
	Anderson-Darling normality test
data:  x
A = 0.30834, p-value = 0.5197

 \tabularnewline

> ad.y
	Anderson-Darling normality test
data:  y
A = 0.44083, p-value = 0.2508

 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=313922&T=2

[TABLE]
[ROW][C]Normality Tests[/C][/ROW]
[ROW][C]
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 0.13672, p-value = 0.9339
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 1.3289, p-value = 0.5146
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> ad.x
	Anderson-Darling normality test
data:  x
A = 0.30834, p-value = 0.5197

[/C][/ROW]
[ROW][C]
> ad.y
	Anderson-Darling normality test
data:  y
A = 0.44083, p-value = 0.2508

[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=313922&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=313922&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 = 0.13672, p-value = 0.9339
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 1.3289, p-value = 0.5146
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 0.30834, p-value = 0.5197

> ad.y
	Anderson-Darling normality test
data:  y
A = 0.44083, p-value = 0.2508


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 0 ;
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()