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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 computationTue, 08 Dec 2015 21:27:11 +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/08/t1449610346fvwbgxyf23ftgrt.htm/, Retrieved Thu, 16 May 2024 07:56:21 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=285571, Retrieved Thu, 16 May 2024 07:56:21 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact113

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [One Sample Tests about the Mean] [] [2015-09-17 17:14:23] [32b17a345b130fdf5cc88718ed94a974]
- RMPD  [Bivariate Kernel Density Estimation] [Kernel Density Sp...] [2015-12-08 20:14:32] [08054cfd69be47a1043f60b064067192]
- RM D    [Tukey lambda PPCC Plot] [Verdeling cijfers...] [2015-12-08 20:39:14] [08054cfd69be47a1043f60b064067192]
- RM D        [Pearson Correlation] [Pearson Correlation] [2015-12-08 21:27:11] [0e991996cbbd17b3741fb533250e72dd] [Current]
- R             [Pearson Correlation] [Pearson Correlation] [2015-12-08 21:34:10] [08054cfd69be47a1043f60b064067192]
- RM D          [Notched Boxplots] [Notched Boxplot] [2015-12-08 21:46:09] [08054cfd69be47a1043f60b064067192]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
16.3
17.4
18.1
18.0
17.8
17.5
17.4
17.7
18.1
18.5
18.7
18.9
19.5
19.9
20.2
20.2
19.9
19.6
19.4
19.6
19.8
20.1
20.2
20.2
20.8
21.2
21.3
20.9
20.6
20.5
20.8
21.3
21.9
22.3
22.6
22.7
23.7
24.3
24.6
24.5
24.5
24.2
24.4
24.8
25.2
25.6
25.9
25.8
26.7
27.1
27.0
26.6
26.1
25.6
25.6
25.6
25.8
26.0
25.9
25.4
26.0
26.0
25.8
25.1
24.5
23.8
23.7
23.6
23.7
23.9
23.8
23.5
23.9
23.9
23.6
23.0
22.4
21.7
21.2
21.1
21.2
21.6
Dataseries Y:
Download CSV
Histogram 
9.8
10.0
10.2
10.3
10.3
10.4
10.6
11.1
11.3
11.4
11.3
11.5
11.5
11.8
11.8
11.9
11.8
11.9
11.9
12.2
12.2
12.1
12.3
12.4
12.5
12.6
12.7
12.4
12.3
11.9
12.0
12.6
13.2
13.6
14.1
14.7
14.7
15.0
15.3
15.5
15.1
15.0
15.2
15.9
16.2
16.8
17.1
17.6
17.9
17.8
17.6
17.1
16.7
16.1
16.2
15.8
15.7
15.7
15.5
15.4
15.3
15.3
15.0
14.6
14.1
13.8
13.7
13.3
13.3
13.6
13.6
13.9
14.1
13.9
13.4
12.9
12.1
11.9
11.8
12.1
12.4
12.5

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'Herman Ole Andreas Wold' @ wold.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 & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=285571&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=285571&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=285571&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'Herman Ole Andreas Wold' @ wold.wessa.net






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean22.412195121951213.5378048780488
Biased Variance8.100095181439624.26844883997621
Biased Standard Deviation2.846066615776872.0660224684103
Covariance5.66027401385125
Correlation0.950886148406473
Determination0.904184467231296
T-Test27.4761295348566
p-value (2 sided)0
p-value (1 sided)0
95% CI of Correlation[0.924687409643707, 0.968122165655794]
Degrees of Freedom80
Number of Observations82

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 22.4121951219512 & 13.5378048780488 \tabularnewline
Biased Variance & 8.10009518143962 & 4.26844883997621 \tabularnewline
Biased Standard Deviation & 2.84606661577687 & 2.0660224684103 \tabularnewline
Covariance & 5.66027401385125 \tabularnewline
Correlation & 0.950886148406473 \tabularnewline
Determination & 0.904184467231296 \tabularnewline
T-Test & 27.4761295348566 \tabularnewline
p-value (2 sided) & 0 \tabularnewline
p-value (1 sided) & 0 \tabularnewline
95% CI of Correlation & [0.924687409643707, 0.968122165655794] \tabularnewline
Degrees of Freedom & 80 \tabularnewline
Number of Observations & 82 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=285571&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]22.4121951219512[/C][C]13.5378048780488[/C][/ROW]
[ROW][C]Biased Variance[/C][C]8.10009518143962[/C][C]4.26844883997621[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]2.84606661577687[/C][C]2.0660224684103[/C][/ROW]
[ROW][C]Covariance[/C][C]5.66027401385125[/C][/ROW]
[ROW][C]Correlation[/C][C]0.950886148406473[/C][/ROW]
[ROW][C]Determination[/C][C]0.904184467231296[/C][/ROW]
[ROW][C]T-Test[/C][C]27.4761295348566[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0[/C][/ROW]
[ROW][C]95% CI of Correlation[/C][C][0.924687409643707, 0.968122165655794][/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]80[/C][/ROW]
[ROW][C]Number of Observations[/C][C]82[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=285571&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=285571&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
Mean22.412195121951213.5378048780488
Biased Variance8.100095181439624.26844883997621
Biased Standard Deviation2.846066615776872.0660224684103
Covariance5.66027401385125
Correlation0.950886148406473
Determination0.904184467231296
T-Test27.4761295348566
p-value (2 sided)0
p-value (1 sided)0
95% CI of Correlation[0.924687409643707, 0.968122165655794]
Degrees of Freedom80
Number of Observations82






Normality Tests
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 4.847, p-value = 0.08861
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 3.5923, p-value = 0.1659
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 1.2587, p-value = 0.002658

> ad.y
	Anderson-Darling normality test
data:  y
A = 1.0354, p-value = 0.00953


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

> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 4.847, p-value = 0.08861
alternative hypothesis: greater

 \tabularnewline

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 3.5923, p-value = 0.1659
alternative hypothesis: greater

 \tabularnewline

> ad.x
	Anderson-Darling normality test
data:  x
A = 1.2587, p-value = 0.002658

 \tabularnewline

> ad.y
	Anderson-Darling normality test
data:  y
A = 1.0354, p-value = 0.00953

 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=285571&T=2

[TABLE]
[ROW][C]Normality Tests[/C][/ROW]
[ROW][C]
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 4.847, p-value = 0.08861
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 3.5923, p-value = 0.1659
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> ad.x
	Anderson-Darling normality test
data:  x
A = 1.2587, p-value = 0.002658

[/C][/ROW]
[ROW][C]
> ad.y
	Anderson-Darling normality test
data:  y
A = 1.0354, p-value = 0.00953

[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=285571&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=285571&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 = 4.847, p-value = 0.08861
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 3.5923, p-value = 0.1659
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 1.2587, p-value = 0.002658

> ad.y
	Anderson-Darling normality test
data:  y
A = 1.0354, p-value = 0.00953


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = grey ;
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()