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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, 07 Dec 2015 15:35:06 +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/07/t1449503830e6s8jw5y040vkkx.htm/, Retrieved Thu, 16 May 2024 15:17:48 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=285416, Retrieved Thu, 16 May 2024 15:17:48 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact72

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Pearson Correlation] [] [2015-12-07 15:35:06] [cb7d5475d24805dc0b5071f8f45ad385] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
2188
2274
2318
2377
2480
2553
2574
2624
2738
2802
2906
2989
3058
3103
Dataseries Y:
Download CSV
Histogram 
8351
9239
9519
9368
9557
9759
9201
9468
11314
10442
8807
8219
7885
7357

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'George Udny Yule' @ yule.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 & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=285416&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=285416&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=285416&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'George Udny Yule' @ yule.wessa.net






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean2641.714285714299177.57142857143
Biased Variance83310.7755102041972233.102040816
Biased Standard Deviation288.636060654597986.01881424282
Covariance-102192.824175824
Correlation-0.333426357186818
Determination0.111173135666871
T-Test-1.22512940690997
p-value (2 sided)0.244030379029961
p-value (1 sided)0.122015189514981
95% CI of Correlation[-0.734131287708761, 0.239527817713605]
Degrees of Freedom12
Number of Observations14

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 2641.71428571429 & 9177.57142857143 \tabularnewline
Biased Variance & 83310.7755102041 & 972233.102040816 \tabularnewline
Biased Standard Deviation & 288.636060654597 & 986.01881424282 \tabularnewline
Covariance & -102192.824175824 \tabularnewline
Correlation & -0.333426357186818 \tabularnewline
Determination & 0.111173135666871 \tabularnewline
T-Test & -1.22512940690997 \tabularnewline
p-value (2 sided) & 0.244030379029961 \tabularnewline
p-value (1 sided) & 0.122015189514981 \tabularnewline
95% CI of Correlation & [-0.734131287708761, 0.239527817713605] \tabularnewline
Degrees of Freedom & 12 \tabularnewline
Number of Observations & 14 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=285416&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]2641.71428571429[/C][C]9177.57142857143[/C][/ROW]
[ROW][C]Biased Variance[/C][C]83310.7755102041[/C][C]972233.102040816[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]288.636060654597[/C][C]986.01881424282[/C][/ROW]
[ROW][C]Covariance[/C][C]-102192.824175824[/C][/ROW]
[ROW][C]Correlation[/C][C]-0.333426357186818[/C][/ROW]
[ROW][C]Determination[/C][C]0.111173135666871[/C][/ROW]
[ROW][C]T-Test[/C][C]-1.22512940690997[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0.244030379029961[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0.122015189514981[/C][/ROW]
[ROW][C]95% CI of Correlation[/C][C][-0.734131287708761, 0.239527817713605][/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]12[/C][/ROW]
[ROW][C]Number of Observations[/C][C]14[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=285416&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=285416&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
Mean2641.714285714299177.57142857143
Biased Variance83310.7755102041972233.102040816
Biased Standard Deviation288.636060654597986.01881424282
Covariance-102192.824175824
Correlation-0.333426357186818
Determination0.111173135666871
T-Test-1.22512940690997
p-value (2 sided)0.244030379029961
p-value (1 sided)0.122015189514981
95% CI of Correlation[-0.734131287708761, 0.239527817713605]
Degrees of Freedom12
Number of Observations14






Normality Tests
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 0.89561, p-value = 0.639
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 0.078596, p-value = 0.9615
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 0.21355, p-value = 0.8145

> ad.y
	Anderson-Darling normality test
data:  y
A = 0.2846, p-value = 0.5738


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

> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 0.89561, p-value = 0.639
alternative hypothesis: greater

 \tabularnewline

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 0.078596, p-value = 0.9615
alternative hypothesis: greater

 \tabularnewline

> ad.x
	Anderson-Darling normality test
data:  x
A = 0.21355, p-value = 0.8145

 \tabularnewline

> ad.y
	Anderson-Darling normality test
data:  y
A = 0.2846, p-value = 0.5738

 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=285416&T=2

[TABLE]
[ROW][C]Normality Tests[/C][/ROW]
[ROW][C]
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 0.89561, p-value = 0.639
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 0.078596, p-value = 0.9615
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> ad.x
	Anderson-Darling normality test
data:  x
A = 0.21355, p-value = 0.8145

[/C][/ROW]
[ROW][C]
> ad.y
	Anderson-Darling normality test
data:  y
A = 0.2846, p-value = 0.5738

[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=285416&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=285416&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 = 0.89561, p-value = 0.639
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 0.078596, p-value = 0.9615
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 0.21355, p-value = 0.8145

> ad.y
	Anderson-Darling normality test
data:  y
A = 0.2846, p-value = 0.5738


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()