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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 computationMon, 14 Dec 2015 13:13:19 +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/14/t1450098816ud8hf81vfw5qs1p.htm/, Retrieved Thu, 16 May 2024 13:15:08 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=286296, Retrieved Thu, 16 May 2024 13:15:08 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact99

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Pearson Correlation] [1] [2015-12-14 13:13:19] [d72fa962b0284db92b9d0a7bd6cc1894] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
258236
265787
275062
282633
298705
311488
326673
344709
354057
348781
365101
379106
387419
392699
400643
Dataseries Y:
Download CSV
Histogram 
474427
469740
491481
538141
576612
596397
588261
532459
504865
554529
567192
546473
560367
584302
597774

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 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 & 3 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=286296&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]3 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=286296&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=286296&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 time3 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean332739.933333333545534.666666667
Biased Variance2184371207.662221732238648.48889
Biased Standard Deviation46737.257168796541620.1711732291
Covariance1286475627.04762
Correlation0.617264435966206
Determination0.381015383908678
T-Test2.8288049546888
p-value (2 sided)0.0142231171446086
p-value (1 sided)0.00711155857230428
95% CI of Correlation[0.153556366137253, 0.858171916442216]
Degrees of Freedom13
Number of Observations15

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 332739.933333333 & 545534.666666667 \tabularnewline
Biased Variance & 2184371207.66222 & 1732238648.48889 \tabularnewline
Biased Standard Deviation & 46737.2571687965 & 41620.1711732291 \tabularnewline
Covariance & 1286475627.04762 \tabularnewline
Correlation & 0.617264435966206 \tabularnewline
Determination & 0.381015383908678 \tabularnewline
T-Test & 2.8288049546888 \tabularnewline
p-value (2 sided) & 0.0142231171446086 \tabularnewline
p-value (1 sided) & 0.00711155857230428 \tabularnewline
95% CI of Correlation & [0.153556366137253, 0.858171916442216] \tabularnewline
Degrees of Freedom & 13 \tabularnewline
Number of Observations & 15 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=286296&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]332739.933333333[/C][C]545534.666666667[/C][/ROW]
[ROW][C]Biased Variance[/C][C]2184371207.66222[/C][C]1732238648.48889[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]46737.2571687965[/C][C]41620.1711732291[/C][/ROW]
[ROW][C]Covariance[/C][C]1286475627.04762[/C][/ROW]
[ROW][C]Correlation[/C][C]0.617264435966206[/C][/ROW]
[ROW][C]Determination[/C][C]0.381015383908678[/C][/ROW]
[ROW][C]T-Test[/C][C]2.8288049546888[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0.0142231171446086[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0.00711155857230428[/C][/ROW]
[ROW][C]95% CI of Correlation[/C][C][0.153556366137253, 0.858171916442216][/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=286296&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=286296&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
Mean332739.933333333545534.666666667
Biased Variance2184371207.662221732238648.48889
Biased Standard Deviation46737.257168796541620.1711732291
Covariance1286475627.04762
Correlation0.617264435966206
Determination0.381015383908678
T-Test2.8288049546888
p-value (2 sided)0.0142231171446086
p-value (1 sided)0.00711155857230428
95% CI of Correlation[0.153556366137253, 0.858171916442216]
Degrees of Freedom13
Number of Observations15






Normality Tests
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 1.1798, p-value = 0.5544
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 1.2934, p-value = 0.5238
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 0.32102, p-value = 0.4975

> ad.y
	Anderson-Darling normality test
data:  y
A = 0.41556, p-value = 0.2909


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

> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 1.1798, p-value = 0.5544
alternative hypothesis: greater

 \tabularnewline

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 1.2934, p-value = 0.5238
alternative hypothesis: greater

 \tabularnewline

> ad.x
	Anderson-Darling normality test
data:  x
A = 0.32102, p-value = 0.4975

 \tabularnewline

> ad.y
	Anderson-Darling normality test
data:  y
A = 0.41556, p-value = 0.2909

 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=286296&T=2

[TABLE]
[ROW][C]Normality Tests[/C][/ROW]
[ROW][C]
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 1.1798, p-value = 0.5544
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 1.2934, p-value = 0.5238
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> ad.x
	Anderson-Darling normality test
data:  x
A = 0.32102, p-value = 0.4975

[/C][/ROW]
[ROW][C]
> ad.y
	Anderson-Darling normality test
data:  y
A = 0.41556, p-value = 0.2909

[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=286296&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=286296&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 = 1.1798, p-value = 0.5544
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 1.2934, p-value = 0.5238
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 0.32102, p-value = 0.4975

> ad.y
	Anderson-Darling normality test
data:  y
A = 0.41556, p-value = 0.2909


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()