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Author*The author of this computation has been verified*
R Software Modulerwasp_correlation.wasp
Title produced by softwarePearson Correlation
Date of computationSun, 13 Dec 2015 23:27:13 +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/13/t1450049251z0voxu2rzeq4woy.htm/, Retrieved Thu, 16 May 2024 20:14:41 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=286250, Retrieved Thu, 16 May 2024 20:14:41 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact62
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Pearson Correlation] [hahah] [2015-12-13 23:27:13] [b11eaa2e13e6bae1ff447872cd0e766a] [Current]
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Dataseries X:
9.100000381
8.699999809
7.199999809
8.899999619
8.300000191
10.89999962
10
9.100000381
8.699999809
7.599999905
10.80000019
9.5
8.800000191
9.5
8.699999809
11.19999981
9.699999809
9.600000381
9.100000381
9.199999809
8.300000191
8.399999619
9.399999619
9.800000191
10.39999962
9.899999619
9.199999809
10.30000019
8.899999619
9.600000381
10.30000019
10.39999962
9.699999809
9.600000381
10.69999981
10.30000019
10.69999981
9.600000381
10.5
7.699999809
10.19999981
9.899999619
8.399999619
10.39999962
9.199999809
13
8.800000191
9.199999809
7.800000191
8.199999809
7.400000095
10.39999962
8.899999619
Dataseries Y:
8
9.300000191
7.5
8.899999619
10.19999981
8.300000191
8.800000191
8.800000191
10.69999981
11.69999981
8.5
8.300000191
8.199999809
7.900000095
10.30000019
7.400000095
9.600000381
9.300000191
10.60000038
9.699999809
11.60000038
8.100000381
9.800000191
7.400000095
9.399999619
11.19999981
9.100000381
10.5
11.89999962
8.399999619
5
9.800000191
9.800000191
10.80000019
10.10000038
10.89999962
9.199999809
8.300000191
7.300000191
9.399999619
9.399999619
9.800000191
3.599999905
8.399999619
10.80000019
10.10000038
9
10
11.30000019
11.30000019
12.80000019
10
6.699999809




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 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 & 4 seconds \tabularnewline
R Server & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=286250&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]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=286250&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=286250&T=0

As an alternative you can also use a 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'Sir Maurice George Kendall' @ kendall.wessa.net







Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean9.43584899194349.30566040971698
Biased Variance1.134752552840872.71185481065624
Biased Standard Deviation1.065247648596731.64677102556981
Covariance-0.3075144776493
Correlation-0.17199239325176
Determination0.029581383336468
T-Test-1.24685160303953
p-value (2 sided)0.218148006095737
p-value (1 sided)0.109074003047868
95% CI of Correlation[-0.422638389095727, 0.103094107014073]
Degrees of Freedom51
Number of Observations53

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 9.4358489919434 & 9.30566040971698 \tabularnewline
Biased Variance & 1.13475255284087 & 2.71185481065624 \tabularnewline
Biased Standard Deviation & 1.06524764859673 & 1.64677102556981 \tabularnewline
Covariance & -0.3075144776493 \tabularnewline
Correlation & -0.17199239325176 \tabularnewline
Determination & 0.029581383336468 \tabularnewline
T-Test & -1.24685160303953 \tabularnewline
p-value (2 sided) & 0.218148006095737 \tabularnewline
p-value (1 sided) & 0.109074003047868 \tabularnewline
95% CI of Correlation & [-0.422638389095727, 0.103094107014073] \tabularnewline
Degrees of Freedom & 51 \tabularnewline
Number of Observations & 53 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=286250&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]9.4358489919434[/C][C]9.30566040971698[/C][/ROW]
[ROW][C]Biased Variance[/C][C]1.13475255284087[/C][C]2.71185481065624[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]1.06524764859673[/C][C]1.64677102556981[/C][/ROW]
[ROW][C]Covariance[/C][C]-0.3075144776493[/C][/ROW]
[ROW][C]Correlation[/C][C]-0.17199239325176[/C][/ROW]
[ROW][C]Determination[/C][C]0.029581383336468[/C][/ROW]
[ROW][C]T-Test[/C][C]-1.24685160303953[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0.218148006095737[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0.109074003047868[/C][/ROW]
[ROW][C]95% CI of Correlation[/C][C][-0.422638389095727, 0.103094107014073][/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]51[/C][/ROW]
[ROW][C]Number of Observations[/C][C]53[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=286250&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=286250&T=1

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean9.43584899194349.30566040971698
Biased Variance1.134752552840872.71185481065624
Biased Standard Deviation1.065247648596731.64677102556981
Covariance-0.3075144776493
Correlation-0.17199239325176
Determination0.029581383336468
T-Test-1.24685160303953
p-value (2 sided)0.218148006095737
p-value (1 sided)0.109074003047868
95% CI of Correlation[-0.422638389095727, 0.103094107014073]
Degrees of Freedom51
Number of Observations53







Normality Tests
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 3.22, p-value = 0.1999
alternative hypothesis: greater
> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 12.633, p-value = 0.001806
alternative hypothesis: greater
> ad.x
	Anderson-Darling normality test
data:  x
A = 0.26787, p-value = 0.6715
> ad.y
	Anderson-Darling normality test
data:  y
A = 0.44143, p-value = 0.279

\begin{tabular}{lllllllll}
\hline
Normality Tests \tabularnewline
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 3.22, p-value = 0.1999
alternative hypothesis: greater
\tabularnewline
> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 12.633, p-value = 0.001806
alternative hypothesis: greater
\tabularnewline
> ad.x
	Anderson-Darling normality test
data:  x
A = 0.26787, p-value = 0.6715
\tabularnewline
> ad.y
	Anderson-Darling normality test
data:  y
A = 0.44143, p-value = 0.279
\tabularnewline \hline \end{tabular} %Source: https://freestatistics.org/blog/index.php?pk=286250&T=2

[TABLE]
[ROW][C]Normality Tests[/C][/ROW]
[ROW][C]
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 3.22, p-value = 0.1999
alternative hypothesis: greater
[/C][/ROW] [ROW][C]
> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 12.633, p-value = 0.001806
alternative hypothesis: greater
[/C][/ROW] [ROW][C]
> ad.x
	Anderson-Darling normality test
data:  x
A = 0.26787, p-value = 0.6715
[/C][/ROW] [ROW][C]
> ad.y
	Anderson-Darling normality test
data:  y
A = 0.44143, p-value = 0.279
[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=286250&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=286250&T=2

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Normality Tests
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 3.22, p-value = 0.1999
alternative hypothesis: greater
> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 12.633, p-value = 0.001806
alternative hypothesis: greater
> ad.x
	Anderson-Darling normality test
data:  x
A = 0.26787, p-value = 0.6715
> ad.y
	Anderson-Darling normality test
data:  y
A = 0.44143, p-value = 0.279



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()