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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 computationSun, 13 Jul 2014 18:12:04 +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/2014/Jul/13/t1405271617b2vtmktshk5a0tn.htm/, Retrieved Tue, 14 May 2024 01:24:27 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=235300, Retrieved Tue, 14 May 2024 01:24:27 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact186

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Pearson Correlation] [Spending?GDP : Un...] [2014-07-13 17:12:04] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
21.13
20.49
20
19.78
19.26
18.6
18.18
17.61
17.39
17.53
18.31
18.76
18.68
18.88
19.16
18.84
20.26
24.4
23.11
23.19
21.77
20.57
21.06
Dataseries Y:
Download CSV
Histogram 
5.8
5.3
4.4
4.1
3.8
3.3
2.8
2.4
2.7
3.0
4.6
4.9
4.1
3.9
3.5
3.5
4.3
8.1
8.1
8.3
7.2
6.3
5.0

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gertrude Mary Cox' @ cox.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 & 1 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235300&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235300&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235300&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 time1 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean19.86782608695654.75652173913043
Biased Variance3.430764839319473.02506616257089
Biased Standard Deviation1.852232393442971.73927173339041
Covariance3.15540118577075
Correlation0.936885494773502
Determination0.87775443031699
T-Test12.2794693115641
p-value (2 sided)4.75695038915092e-11
p-value (1 sided)2.37847519457546e-11
Degrees of Freedom21
Number of Observations23

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 19.8678260869565 & 4.75652173913043 \tabularnewline
Biased Variance & 3.43076483931947 & 3.02506616257089 \tabularnewline
Biased Standard Deviation & 1.85223239344297 & 1.73927173339041 \tabularnewline
Covariance & 3.15540118577075 \tabularnewline
Correlation & 0.936885494773502 \tabularnewline
Determination & 0.87775443031699 \tabularnewline
T-Test & 12.2794693115641 \tabularnewline
p-value (2 sided) & 4.75695038915092e-11 \tabularnewline
p-value (1 sided) & 2.37847519457546e-11 \tabularnewline
Degrees of Freedom & 21 \tabularnewline
Number of Observations & 23 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235300&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]19.8678260869565[/C][C]4.75652173913043[/C][/ROW]
[ROW][C]Biased Variance[/C][C]3.43076483931947[/C][C]3.02506616257089[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]1.85223239344297[/C][C]1.73927173339041[/C][/ROW]
[ROW][C]Covariance[/C][C]3.15540118577075[/C][/ROW]
[ROW][C]Correlation[/C][C]0.936885494773502[/C][/ROW]
[ROW][C]Determination[/C][C]0.87775443031699[/C][/ROW]
[ROW][C]T-Test[/C][C]12.2794693115641[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]4.75695038915092e-11[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]2.37847519457546e-11[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]21[/C][/ROW]
[ROW][C]Number of Observations[/C][C]23[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235300&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235300&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
Mean19.86782608695654.75652173913043
Biased Variance3.430764839319473.02506616257089
Biased Standard Deviation1.852232393442971.73927173339041
Covariance3.15540118577075
Correlation0.936885494773502
Determination0.87775443031699
T-Test12.2794693115641
p-value (2 sided)4.75695038915092e-11
p-value (1 sided)2.37847519457546e-11
Degrees of Freedom21
Number of Observations23






Normality Tests
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 2.5608, p-value = 0.2779
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 2.5593, p-value = 0.2781
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 0.5618, p-value = 0.1296

> ad.y
	Anderson-Darling normality test
data:  y
A = 0.7735, p-value = 0.03788


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

> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 2.5608, p-value = 0.2779
alternative hypothesis: greater

 \tabularnewline

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 2.5593, p-value = 0.2781
alternative hypothesis: greater

 \tabularnewline

> ad.x
	Anderson-Darling normality test
data:  x
A = 0.5618, p-value = 0.1296

 \tabularnewline

> ad.y
	Anderson-Darling normality test
data:  y
A = 0.7735, p-value = 0.03788

 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235300&T=2

[TABLE]
[ROW][C]Normality Tests[/C][/ROW]
[ROW][C]
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 2.5608, p-value = 0.2779
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 2.5593, p-value = 0.2781
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> ad.x
	Anderson-Darling normality test
data:  x
A = 0.5618, p-value = 0.1296

[/C][/ROW]
[ROW][C]
> ad.y
	Anderson-Darling normality test
data:  y
A = 0.7735, p-value = 0.03788

[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235300&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235300&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 = 2.5608, p-value = 0.2779
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 2.5593, p-value = 0.2781
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 0.5618, p-value = 0.1296

> ad.y
	Anderson-Darling normality test
data:  y
A = 0.7735, p-value = 0.03788


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()