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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_correlation.wasp
Title produced by softwarePearson Correlation
Date of computationWed, 20 Jul 2016 19:44:27 +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/Jul/20/t1469048146oc3pepyze1iq85s.htm/, Retrieved Sat, 04 May 2024 04:21:04 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=295904, Retrieved Sat, 04 May 2024 04:21:04 +0000
QR Codes:

Original text written by user:PIB en millones según la estimación para el año 2016 del Fondo Monetario Internacional
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact132

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Pearson Correlation] [Correlación núm v...] [2016-07-20 18:44:27] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
7
14
3
15
5
4
1
3
49
4
1
1
20
2
13
21
4
13
14
8
1
1
1
7
4
3
3
12
1
6
1
2
2
2
191
1
Dataseries Y:
Download CSV
Histogram 
404293
1138085
494121
3101247
1631943
482347
422422
332477
3934664
258702
149692
1092634
1615074
224999
2703378
2756748
8642758
2170909
4901102
1848518
17793
815646
1091700
832623
356209
168187
1005449
3684643
1720027
473413
160998
1665332
1099030
339481
18558129
552298

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 4 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=295904&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=295904&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295904&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 Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.wessa.net






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean12.22222222222221967974.19444444
Biased Variance994.22839506172810710207418589
Biased Standard Deviation31.53138745855833272645.32428875
Covariance94069225.6126984
Correlation0.886280288607309
Determination0.785492749973856
T-Test11.1580823248466
p-value (2 sided)6.55710951792256e-13
p-value (1 sided)3.27855475896128e-13
95% CI of Correlation[0.786857620534014, 0.940861047531719]
Degrees of Freedom34
Number of Observations36

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 12.2222222222222 & 1967974.19444444 \tabularnewline
Biased Variance & 994.228395061728 & 10710207418589 \tabularnewline
Biased Standard Deviation & 31.5313874585583 & 3272645.32428875 \tabularnewline
Covariance & 94069225.6126984 \tabularnewline
Correlation & 0.886280288607309 \tabularnewline
Determination & 0.785492749973856 \tabularnewline
T-Test & 11.1580823248466 \tabularnewline
p-value (2 sided) & 6.55710951792256e-13 \tabularnewline
p-value (1 sided) & 3.27855475896128e-13 \tabularnewline
95% CI of Correlation & [0.786857620534014, 0.940861047531719] \tabularnewline
Degrees of Freedom & 34 \tabularnewline
Number of Observations & 36 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=295904&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]12.2222222222222[/C][C]1967974.19444444[/C][/ROW]
[ROW][C]Biased Variance[/C][C]994.228395061728[/C][C]10710207418589[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]31.5313874585583[/C][C]3272645.32428875[/C][/ROW]
[ROW][C]Covariance[/C][C]94069225.6126984[/C][/ROW]
[ROW][C]Correlation[/C][C]0.886280288607309[/C][/ROW]
[ROW][C]Determination[/C][C]0.785492749973856[/C][/ROW]
[ROW][C]T-Test[/C][C]11.1580823248466[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]6.55710951792256e-13[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]3.27855475896128e-13[/C][/ROW]
[ROW][C]95% CI of Correlation[/C][C][0.786857620534014, 0.940861047531719][/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]34[/C][/ROW]
[ROW][C]Number of Observations[/C][C]36[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=295904&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295904&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
Mean12.22222222222221967974.19444444
Biased Variance994.22839506172810710207418589
Biased Standard Deviation31.53138745855833272645.32428875
Covariance94069225.6126984
Correlation0.886280288607309
Determination0.785492749973856
T-Test11.1580823248466
p-value (2 sided)6.55710951792256e-13
p-value (1 sided)3.27855475896128e-13
95% CI of Correlation[0.786857620534014, 0.940861047531719]
Degrees of Freedom34
Number of Observations36






Normality Tests
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 1151, p-value < 2.2e-16
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 466.07, p-value < 2.2e-16
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 8.2547, p-value < 2.2e-16

> ad.y
	Anderson-Darling normality test
data:  y
A = 5.1603, p-value = 5.054e-13


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

> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 1151, p-value < 2.2e-16
alternative hypothesis: greater

 \tabularnewline

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 466.07, p-value < 2.2e-16
alternative hypothesis: greater

 \tabularnewline

> ad.x
	Anderson-Darling normality test
data:  x
A = 8.2547, p-value < 2.2e-16

 \tabularnewline

> ad.y
	Anderson-Darling normality test
data:  y
A = 5.1603, p-value = 5.054e-13

 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=295904&T=2

[TABLE]
[ROW][C]Normality Tests[/C][/ROW]
[ROW][C]
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 1151, p-value < 2.2e-16
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 466.07, p-value < 2.2e-16
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> ad.x
	Anderson-Darling normality test
data:  x
A = 8.2547, p-value < 2.2e-16

[/C][/ROW]
[ROW][C]
> ad.y
	Anderson-Darling normality test
data:  y
A = 5.1603, p-value = 5.054e-13

[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=295904&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295904&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 = 1151, p-value < 2.2e-16
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 466.07, p-value < 2.2e-16
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 8.2547, p-value < 2.2e-16

> ad.y
	Anderson-Darling normality test
data:  y
A = 5.1603, p-value = 5.054e-13


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$estimate)[1,1]
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Pearson Product Moment Correlation - Ungrouped Data',3,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Statistic',1,TRUE)
a<-table.element(a,'Variable X',1,TRUE)
a<-table.element(a,'Variable Y',1,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('arithmetic_mean.htm','Mean',''),header=TRUE)
a<-table.element(a,mean(x))
a<-table.element(a,mean(y))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('biased.htm','Biased Variance',''),header=TRUE)
a<-table.element(a,varx)
a<-table.element(a,vary)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('biased1.htm','Biased Standard Deviation',''),header=TRUE)
a<-table.element(a,sqrt(varx))
a<-table.element(a,sqrt(vary))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('covariance.htm','Covariance',''),header=TRUE)
a<-table.element(a,cov(x,y),2)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('pearson_correlation.htm','Correlation',''),header=TRUE)
a<-table.element(a,cxy,2)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('coeff_of_determination.htm','Determination',''),header=TRUE)
a<-table.element(a,cxy*cxy,2)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('ttest_statistic.htm','T-Test',''),header=TRUE)
a<-table.element(a,as.matrix(corxy$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')
qq.plot(x,main='QQplot of variable x')
dev.off()
bitmap(file='test3.png')
qq.plot(y,main='QQplot of variable y')
dev.off()