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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, 11 Dec 2014 17:33:55 +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/2014/Dec/11/t14183194994dw1rffhqcndmdd.htm/, Retrieved Thu, 31 Oct 2024 23:06:14 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=266235, Retrieved Thu, 31 Oct 2024 23:06:14 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact96

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Pearson Correlation] [] [2014-12-11 17:33:55] [ff8f75f765a8f6d34a5ce09978012557] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
2,1
1,5
2
2
2,1
2
2,3
2,1
2,1
2,2
2,1
2,1
2,1
2
2,3
1,8
2
2,2
2
2,1
2
1,8
2,2
2,2
1,7
2,1
2,3
2,7
1,9
2
2
1,9
2
2
2
2,1
2
1,8
2
2,2
2,2
2,1
1,8
1,9
2,1
2
1,9
2,2
2
2
1,7
2
2,2
1,7
2
2,2
2
1,9
2
2
1,6
2,1
2,1
2
1,9
2,2
2,1
1,8
2,3
2,3
2,2
2,1
2,2
1,9
1,8
2,1
1,8
2
1,7
2,1
2,1
2,1
1,8
2
2,1
1,9
2,1
1
2,2
2,1
1,9
2
1,9
2
1,8
2
2
2
1,8
2
1,1
1,8
1,8
2
1,9
2,1
1,6
2,2
1,9
2
2,1
1,3
1,8
1,9
2,1
1,8
0,75
1,5
3
2,25
3
1,5
3
3
3
0,75
3
2,25
1,5
1,5
2,25
3
3
1,5
2,25
2,25
1,5
2,25
1,5
2,25
2,25
3
3
3
1,5
3
3
2,25
1,5
2,25
2,25
3
0,75
2,25
3
3
1,5
2,25
3
2,25
1,5
2,25
2,25
1,5
2,25
1,5
2,25
3
3
3
3
1,5
2,25
1,5
2,25
2,25
2,25
3
1,5
2,25
2,25
3
2,25
3
2,25
1,5
3
1,5
3
3
3
3
2,25
2,25
0,75
3
0,75
1,5
1,5
3
1,5
2,25
3
3
1,5
3
3
1,5
1,5
2,25
1,5
1,5
2,25
1,5
2,25
3
3
0,75
1,5
1,5
2,25
2,25
1,5
2,25
0,75
2,25
0,75
2,25
3
0,75
0,75
3
3
3
3
1,5
3
3
3
3
1,5
2,25
0,75
0,75
2,25
3
2,25
3
2,25
3
1,5
3
3
0,75
1,5
3
3
3
2,25
2,25
3
1,5
2,25
2,25
2,25
0,75
2,25
1,5
2,25
1,5
0,75
1,5
1,5
2,25
1,5
1,5
3
2,25
1,5
0,75
2,25
3
3
1,5
1,5
2,25
0,75
Dataseries Y:
Download CSV
Histogram 
1,5
1,8
2,1
2,1
1,9
1,6
2,1
2,1
2,2
1,5
1,9
2,2
1,6
1,5
1,9
0,1
2,2
1,8
1,6
2,2
2,1
1,9
1,6
1,9
2,2
1,8
2,4
2,4
2,5
1,9
2,1
1,9
2,1
1,9
1,5
1,9
2,1
1,5
2,1
2,1
1,8
2,4
2,1
1,9
2,1
1,9
2,4
2,1
2,2
2,2
1,8
2,1
2,4
2,2
2,1
1,5
1,9
1,8
1,8
1,6
1,2
1,8
1,5
2,1
2,4
2,4
1,5
1,8
2,1
2,2
2,1
1,9
2,1
1,9
1,6
2,4
1,9
1,9
1,9
2,1
1,8
2,1
2,4
2,1
2,2
2,1
2,2
1,6
2,4
2,1
1,9
2,4
2,1
1,8
2,1
1,8
1,9
1,9
2,4
1,8
1,8
2,1
2,1
2,4
1,9
1,8
1,8
2,2
2,4
1,8
2,4
1,8
1,9
2,4
2,1
1,9
2,1
2,7
2,1
2,1
2,1
2,1
2,1
2,1
2,1
2,1
2,4
1,95
2,1
2,1
1,95
2,1
2,4
2,1
2,25
2,4
2,25
2,55
1,95
2,4
2,1
2,1
2,4
2,1
2,1
2,25
2,25
2,4
2,1
2,1
2,4
2,1
1,95
2,1
2,25
2,25
2,4
2,25
2,25
2,1
2,1
2,1
2,7
2,1
2,1
2,25
2,7
2,4
2,1
2,1
2,4
1,95
2,7
2,1
2,25
2,1
2,7
2,1
2,1
1,65
1,65
2,1
2,1
2,1
2,1
2,1
2,4
2,4
2,1
2,25
2,4
2,1
2,1
2,4
2,4
2,1
2,1
2,4
2,1
2,7
2,1
2,1
2,25
2,1
2,4
2,25
2,25
2,1
2,1
2,4
2,25
2,1
2,1
1,65
1,65
2,7
2,1
1,95
2,25
2,4
1,95
2,1
2,4
2,1
2,1
2,4
2,4
2,4
2,25
2,4
2,1
2,1
1,8
2,7
2,1
2,1
2,4
2,55
2,55
2,1
2,1
2,1
2,25
2,25
2,1
2,1
1,95
2,4
2,1
2,4
2,4
2,4
2,25
1,95
2,1
2,1
2,55
2,1
2,1
2,1
1,95
2,25
2,4
1,95
2,1
2,1
1,95
2,1
2,1
1,95
2,1
1,95
2,4
2,4
2,4
1,95
2,7
2,1
1,95
2,1
1,95
2,1
2,25
2,7
2,1
2,4
1,35

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Maurice George Kendall' @ kendall.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 & 2 seconds \tabularnewline
R Server & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=266235&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=266235&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=266235&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 time2 seconds
R Server'Sir Maurice George Kendall' @ kendall.wessa.net






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean2.09111498257842.10383275261324
Biased Variance0.3557834258033970.0819016863140259
Biased Standard Deviation0.5964758384070530.286184706638957
Covariance0.0341600472698034
Correlation0.199417524701524
Determination0.0397673491580831
T-Test3.43555983361915
p-value (2 sided)0.000679315107289913
p-value (1 sided)0.000339657553644956
Degrees of Freedom285
Number of Observations287

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 2.0911149825784 & 2.10383275261324 \tabularnewline
Biased Variance & 0.355783425803397 & 0.0819016863140259 \tabularnewline
Biased Standard Deviation & 0.596475838407053 & 0.286184706638957 \tabularnewline
Covariance & 0.0341600472698034 \tabularnewline
Correlation & 0.199417524701524 \tabularnewline
Determination & 0.0397673491580831 \tabularnewline
T-Test & 3.43555983361915 \tabularnewline
p-value (2 sided) & 0.000679315107289913 \tabularnewline
p-value (1 sided) & 0.000339657553644956 \tabularnewline
Degrees of Freedom & 285 \tabularnewline
Number of Observations & 287 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=266235&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]2.0911149825784[/C][C]2.10383275261324[/C][/ROW]
[ROW][C]Biased Variance[/C][C]0.355783425803397[/C][C]0.0819016863140259[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]0.596475838407053[/C][C]0.286184706638957[/C][/ROW]
[ROW][C]Covariance[/C][C]0.0341600472698034[/C][/ROW]
[ROW][C]Correlation[/C][C]0.199417524701524[/C][/ROW]
[ROW][C]Determination[/C][C]0.0397673491580831[/C][/ROW]
[ROW][C]T-Test[/C][C]3.43555983361915[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0.000679315107289913[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0.000339657553644956[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]285[/C][/ROW]
[ROW][C]Number of Observations[/C][C]287[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=266235&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=266235&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
Mean2.09111498257842.10383275261324
Biased Variance0.3557834258033970.0819016863140259
Biased Standard Deviation0.5964758384070530.286184706638957
Covariance0.0341600472698034
Correlation0.199417524701524
Determination0.0397673491580831
T-Test3.43555983361915
p-value (2 sided)0.000679315107289913
p-value (1 sided)0.000339657553644956
Degrees of Freedom285
Number of Observations287






Normality Tests
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 1.567, p-value = 0.4568
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 821.164, p-value < 2.2e-16
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 8.4333, p-value < 2.2e-16

> ad.y
	Anderson-Darling normality test
data:  y
A = 8.0629, p-value < 2.2e-16


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

> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 1.567, p-value = 0.4568
alternative hypothesis: greater

 \tabularnewline

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 821.164, p-value < 2.2e-16
alternative hypothesis: greater

 \tabularnewline

> ad.x
	Anderson-Darling normality test
data:  x
A = 8.4333, p-value < 2.2e-16

 \tabularnewline

> ad.y
	Anderson-Darling normality test
data:  y
A = 8.0629, p-value < 2.2e-16

 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=266235&T=2

[TABLE]
[ROW][C]Normality Tests[/C][/ROW]
[ROW][C]
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 1.567, p-value = 0.4568
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 821.164, p-value < 2.2e-16
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> ad.x
	Anderson-Darling normality test
data:  x
A = 8.4333, p-value < 2.2e-16

[/C][/ROW]
[ROW][C]
> ad.y
	Anderson-Darling normality test
data:  y
A = 8.0629, p-value < 2.2e-16

[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=266235&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=266235&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 = 1.567, p-value = 0.4568
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 821.164, p-value < 2.2e-16
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 8.4333, p-value < 2.2e-16

> ad.y
	Anderson-Darling normality test
data:  y
A = 8.0629, p-value < 2.2e-16


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
Parameters (R input):
R code (references can be found in the software module):
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,'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()