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Description of Statistical Computation

Author's title

Comparison of Solomon Islands GDP growth rate during the RAMSI period (5 ye...

Author*Unverified author*
R Software Modulerwasp_correlation.wasp
Title produced by softwarePearson Correlation
Date of computationMon, 01 Apr 2019 09:18:47 +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/2019/Apr/01/t15541037649syjs6tnwpako5g.htm/, Retrieved Sat, 04 May 2024 13:08:34 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=318765, Retrieved Sat, 04 May 2024 13:08:34 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsRAMSI - SI GDP
Estimated Impact102

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Pearson Correlation] [Comparison of Sol...] [2019-04-01 07:18:47] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
2007
2008
2009
2010
2011
2012
2013
2014
2015
2016
2017
Dataseries Y:
Download CSV
Histogram 
7.10
7.54
7.75
8.51
9.14
9.35
9.62
9.79
10.04
10.39
10.77

Tables (Output of Computation)





Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 time1 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=318765&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]1 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=318765&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=318765&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 time1 seconds
R ServerBig Analytics Cloud Computing Center






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean20129.09090909090909
Biased Variance101.34095371900826
Biased Standard Deviation3.162277660168381.15799556087589
Covariance3.966
Correlation0.98458480749439
Determination0.969407243148764
T-Test16.8874889319433
p-value (2 sided)4.01394512701159e-08
p-value (1 sided)2.00697256350579e-08
95% CI of Correlation[0.939755599397927, 0.996122283543825]
Degrees of Freedom9
Number of Observations11

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 2012 & 9.09090909090909 \tabularnewline
Biased Variance & 10 & 1.34095371900826 \tabularnewline
Biased Standard Deviation & 3.16227766016838 & 1.15799556087589 \tabularnewline
Covariance & 3.966 \tabularnewline
Correlation & 0.98458480749439 \tabularnewline
Determination & 0.969407243148764 \tabularnewline
T-Test & 16.8874889319433 \tabularnewline
p-value (2 sided) & 4.01394512701159e-08 \tabularnewline
p-value (1 sided) & 2.00697256350579e-08 \tabularnewline
95% CI of Correlation & [0.939755599397927, 0.996122283543825] \tabularnewline
Degrees of Freedom & 9 \tabularnewline
Number of Observations & 11 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=318765&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]2012[/C][C]9.09090909090909[/C][/ROW]
[ROW][C]Biased Variance[/C][C]10[/C][C]1.34095371900826[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]3.16227766016838[/C][C]1.15799556087589[/C][/ROW]
[ROW][C]Covariance[/C][C]3.966[/C][/ROW]
[ROW][C]Correlation[/C][C]0.98458480749439[/C][/ROW]
[ROW][C]Determination[/C][C]0.969407243148764[/C][/ROW]
[ROW][C]T-Test[/C][C]16.8874889319433[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]4.01394512701159e-08[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]2.00697256350579e-08[/C][/ROW]
[ROW][C]95% CI of Correlation[/C][C][0.939755599397927, 0.996122283543825][/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]9[/C][/ROW]
[ROW][C]Number of Observations[/C][C]11[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=318765&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=318765&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
Mean20129.09090909090909
Biased Variance101.34095371900826
Biased Standard Deviation3.162277660168381.15799556087589
Covariance3.966
Correlation0.98458480749439
Determination0.969407243148764
T-Test16.8874889319433
p-value (2 sided)4.01394512701159e-08
p-value (1 sided)2.00697256350579e-08
95% CI of Correlation[0.939755599397927, 0.996122283543825]
Degrees of Freedom9
Number of Observations11






Normality Tests
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 0.68218, p-value = 0.711
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 0.81828, p-value = 0.6642
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 0.14662, p-value = 0.9502

> ad.y
	Anderson-Darling normality test
data:  y
A = 0.27763, p-value = 0.5777


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

> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 0.68218, p-value = 0.711
alternative hypothesis: greater

 \tabularnewline

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 0.81828, p-value = 0.6642
alternative hypothesis: greater

 \tabularnewline

> ad.x
	Anderson-Darling normality test
data:  x
A = 0.14662, p-value = 0.9502

 \tabularnewline

> ad.y
	Anderson-Darling normality test
data:  y
A = 0.27763, p-value = 0.5777

 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=318765&T=2

[TABLE]
[ROW][C]Normality Tests[/C][/ROW]
[ROW][C]
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 0.68218, p-value = 0.711
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 0.81828, p-value = 0.6642
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> ad.x
	Anderson-Darling normality test
data:  x
A = 0.14662, p-value = 0.9502

[/C][/ROW]
[ROW][C]
> ad.y
	Anderson-Darling normality test
data:  y
A = 0.27763, p-value = 0.5777

[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=318765&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=318765&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 = 0.68218, p-value = 0.711
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 0.81828, p-value = 0.6642
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 0.14662, p-value = 0.9502

> ad.y
	Anderson-Darling normality test
data:  y
A = 0.27763, p-value = 0.5777


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()