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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 computationTue, 21 Oct 2014 20:59:04 +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/Oct/21/t141392160992yp7618qif1pop.htm/, Retrieved Mon, 13 May 2024 02:58:46 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=244746, Retrieved Mon, 13 May 2024 02:58:46 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact68

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Pearson Correlation] [Top marginal inco...] [2014-10-21 19:59:04] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
86.45
82.13
82.13
91
91
92
92
91
91
91
91
91
91
91
91
91
91
77
70
70
70
75.25
77
71.75
70
70
70
70
70
70
70
70
70
70
69.13
50
50
50
50
50
38.5
28
28
28
31
31
39.6
39.6
39.6
39.6
39.6
39.6
39.6
39.6
39.1
38.6
35
35
35
35
35
35
35
35
35
39.5
39.5
Dataseries Y:
Download CSV
Histogram 
56.6
55.3
56.6
57.1
57.4
56.8
55.5
57.2
57.6
57.0
55.4
56.0
56.4
55.0
55.7
55.5
55.7
56.2
57.1
57.4
57.5
58.1
57.0
56.6
57.0
57.9
57.7
56.1
56.9
58.1
59.5
60.0
58.9
58.7
57.6
58.4
59.7
60.3
60.8
61.6
62.4
62.8
62.5
61.6
61.4
61.7
62.7
62.9
63.4
63.9
64.2
64.2
64.2
63.5
63.0
62.0
62.3
62.8
63.1
62.9
61.9
58.7
58.5
58.4
58.6
58.6
59.0

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 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 & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=244746&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 Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=244746&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=244746&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 Ronald Aylmer Fisher' @ fisher.wessa.net






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean60.146865671641859.210447761194
Biased Variance507.3942245043447.76332368010693
Biased Standard Deviation22.52541285979782.78627415738418
Covariance-53.7644061510629
Correlation-0.843854128349525
Determination0.712089789932536
T-Test-12.6793072082486
p-value (2 sided)3.09611236796287e-19
p-value (1 sided)1.54805618398144e-19
Degrees of Freedom65
Number of Observations67

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 60.1468656716418 & 59.210447761194 \tabularnewline
Biased Variance & 507.394224504344 & 7.76332368010693 \tabularnewline
Biased Standard Deviation & 22.5254128597978 & 2.78627415738418 \tabularnewline
Covariance & -53.7644061510629 \tabularnewline
Correlation & -0.843854128349525 \tabularnewline
Determination & 0.712089789932536 \tabularnewline
T-Test & -12.6793072082486 \tabularnewline
p-value (2 sided) & 3.09611236796287e-19 \tabularnewline
p-value (1 sided) & 1.54805618398144e-19 \tabularnewline
Degrees of Freedom & 65 \tabularnewline
Number of Observations & 67 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=244746&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]60.1468656716418[/C][C]59.210447761194[/C][/ROW]
[ROW][C]Biased Variance[/C][C]507.394224504344[/C][C]7.76332368010693[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]22.5254128597978[/C][C]2.78627415738418[/C][/ROW]
[ROW][C]Covariance[/C][C]-53.7644061510629[/C][/ROW]
[ROW][C]Correlation[/C][C]-0.843854128349525[/C][/ROW]
[ROW][C]Determination[/C][C]0.712089789932536[/C][/ROW]
[ROW][C]T-Test[/C][C]-12.6793072082486[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]3.09611236796287e-19[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]1.54805618398144e-19[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]65[/C][/ROW]
[ROW][C]Number of Observations[/C][C]67[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=244746&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=244746&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
Mean60.146865671641859.210447761194
Biased Variance507.3942245043447.76332368010693
Biased Standard Deviation22.52541285979782.78627415738418
Covariance-53.7644061510629
Correlation-0.843854128349525
Determination0.712089789932536
T-Test-12.6793072082486
p-value (2 sided)3.09611236796287e-19
p-value (1 sided)1.54805618398144e-19
Degrees of Freedom65
Number of Observations67






Normality Tests
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 6.8273, p-value = 0.03292
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 5.8426, p-value = 0.05386
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 3.4689, p-value = 9.122e-09

> ad.y
	Anderson-Darling normality test
data:  y
A = 2.017, p-value = 3.436e-05


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

> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 6.8273, p-value = 0.03292
alternative hypothesis: greater

 \tabularnewline

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 5.8426, p-value = 0.05386
alternative hypothesis: greater

 \tabularnewline

> ad.x
	Anderson-Darling normality test
data:  x
A = 3.4689, p-value = 9.122e-09

 \tabularnewline

> ad.y
	Anderson-Darling normality test
data:  y
A = 2.017, p-value = 3.436e-05

 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=244746&T=2

[TABLE]
[ROW][C]Normality Tests[/C][/ROW]
[ROW][C]
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 6.8273, p-value = 0.03292
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 5.8426, p-value = 0.05386
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> ad.x
	Anderson-Darling normality test
data:  x
A = 3.4689, p-value = 9.122e-09

[/C][/ROW]
[ROW][C]
> ad.y
	Anderson-Darling normality test
data:  y
A = 2.017, p-value = 3.436e-05

[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=244746&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=244746&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 = 6.8273, p-value = 0.03292
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 5.8426, p-value = 0.05386
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 3.4689, p-value = 9.122e-09

> ad.y
	Anderson-Darling normality test
data:  y
A = 2.017, p-value = 3.436e-05


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()