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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 computationSun, 13 Dec 2015 15:48:04 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/Dec/13/t1450021751ztdbifn4ns1e1e7.htm/, Retrieved Thu, 16 May 2024 23:46:54 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=286193, Retrieved Thu, 16 May 2024 23:46:54 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsPearson Correlation Rente Inflatie
Estimated Impact80

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Pearson Correlation] [Pearson Correlati...] [2015-12-13 15:48:04] [82e318bc05a6a6c8bd1d09ba9bfa1655] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
2.55
2.47
1.64
1.59
2.1
2.78
1.8
1.82
4.49
-0.05
2.19
3.53
2.84
1.11
0.34
Dataseries Y:
Download CSV
Histogram 
4.02
4.3
3.22
2.26
2
2.02
2.76
3.84
3.91
1.27
1
1.25
0.88
0.55
0.16

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'Herman Ole Andreas Wold' @ wold.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 & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=286193&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=286193&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=286193&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'Herman Ole Andreas Wold' @ wold.wessa.net






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean2.082.22933333333333
Biased Variance1.229921.77247288888889
Biased Standard Deviation1.109017583269081.331342513739
Covariance0.658742857142857
Correlation0.416413176463318
Determination0.173399933532271
T-Test1.65138532737342
p-value (2 sided)0.122596538877078
p-value (1 sided)0.0612982694385389
95% CI of Correlation[-0.12183964807826, 0.765405152591352]
Degrees of Freedom13
Number of Observations15

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 2.08 & 2.22933333333333 \tabularnewline
Biased Variance & 1.22992 & 1.77247288888889 \tabularnewline
Biased Standard Deviation & 1.10901758326908 & 1.331342513739 \tabularnewline
Covariance & 0.658742857142857 \tabularnewline
Correlation & 0.416413176463318 \tabularnewline
Determination & 0.173399933532271 \tabularnewline
T-Test & 1.65138532737342 \tabularnewline
p-value (2 sided) & 0.122596538877078 \tabularnewline
p-value (1 sided) & 0.0612982694385389 \tabularnewline
95% CI of Correlation & [-0.12183964807826, 0.765405152591352] \tabularnewline
Degrees of Freedom & 13 \tabularnewline
Number of Observations & 15 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=286193&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]2.08[/C][C]2.22933333333333[/C][/ROW]
[ROW][C]Biased Variance[/C][C]1.22992[/C][C]1.77247288888889[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]1.10901758326908[/C][C]1.331342513739[/C][/ROW]
[ROW][C]Covariance[/C][C]0.658742857142857[/C][/ROW]
[ROW][C]Correlation[/C][C]0.416413176463318[/C][/ROW]
[ROW][C]Determination[/C][C]0.173399933532271[/C][/ROW]
[ROW][C]T-Test[/C][C]1.65138532737342[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0.122596538877078[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0.0612982694385389[/C][/ROW]
[ROW][C]95% CI of Correlation[/C][C][-0.12183964807826, 0.765405152591352][/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=286193&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=286193&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
Mean2.082.22933333333333
Biased Variance1.229921.77247288888889
Biased Standard Deviation1.109017583269081.331342513739
Covariance0.658742857142857
Correlation0.416413176463318
Determination0.173399933532271
T-Test1.65138532737342
p-value (2 sided)0.122596538877078
p-value (1 sided)0.0612982694385389
95% CI of Correlation[-0.12183964807826, 0.765405152591352]
Degrees of Freedom13
Number of Observations15






Normality Tests
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 0.024316, p-value = 0.9879
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 1.1757, p-value = 0.5555
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 0.22243, p-value = 0.7898

> ad.y
	Anderson-Darling normality test
data:  y
A = 0.38345, p-value = 0.3501


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

> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 0.024316, p-value = 0.9879
alternative hypothesis: greater

 \tabularnewline

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 1.1757, p-value = 0.5555
alternative hypothesis: greater

 \tabularnewline

> ad.x
	Anderson-Darling normality test
data:  x
A = 0.22243, p-value = 0.7898

 \tabularnewline

> ad.y
	Anderson-Darling normality test
data:  y
A = 0.38345, p-value = 0.3501

 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=286193&T=2

[TABLE]
[ROW][C]Normality Tests[/C][/ROW]
[ROW][C]
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 0.024316, p-value = 0.9879
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 1.1757, p-value = 0.5555
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> ad.x
	Anderson-Darling normality test
data:  x
A = 0.22243, p-value = 0.7898

[/C][/ROW]
[ROW][C]
> ad.y
	Anderson-Darling normality test
data:  y
A = 0.38345, p-value = 0.3501

[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=286193&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=286193&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 = 0.024316, p-value = 0.9879
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 1.1757, p-value = 0.5555
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 0.22243, p-value = 0.7898

> ad.y
	Anderson-Darling normality test
data:  y
A = 0.38345, p-value = 0.3501


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()