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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, 01 Dec 2015 13:34:15 +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/01/t1448977159qe7crvepeobhzhi.htm/, Retrieved Thu, 16 May 2024 08:02:42 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=284731, Retrieved Thu, 16 May 2024 08:02:42 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact62

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [ML Fitting and QQ Plot- Normal Distribution] [Paper - Histogram...] [2015-12-01 12:09:02] [e7b69f276c668efa4454b31fcaf26444]
- RMPD  [Pearson Correlation] [Paper - Pearson C...] [2015-12-01 12:39:37] [e7b69f276c668efa4454b31fcaf26444]
-    D      [Pearson Correlation] [Paper - Pearson C...] [2015-12-01 13:34:15] [024df7c298481a95aca593c6dd9022cb] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
18
23
22
22
19
25
28
16
28
21
22
24
24
26
28
24
20
26
21
28
27
23
24
24
22
21
25
20
21
26
23
21
27
25
23
25
23
19
22
24
19
21
27
25
25
23
17
28
25
20
25
21
24
28
20
19
24
21
24
23
18
27
25
20
21
23
27
24
27
24
23
24
21
23
27
25
19
24
25
23
23
25
26
26
16
23
26
25
23
26
22
20
27
20
22
24
21
24
26
24
24
27
25
27
19
22
22
25
23
24
24
23
22
24
19
25
26
18
24
28
23
19
19
27
24
26
21
25
28
19
20
26
27
23
18
23
21
23
22
21
14
24
26
24
22
20
20
18
18
25
28
23
20
22
27
24
23
20
22
21
24
26
24
18
17
23
21
21
24
22
24
24
24
23
21
24
19
19
23
25
24
21
18
23
20
23
23
23
23
27
19
25
25
21
25
17
22
23
27
27
5
19
24
23
28
25
27
16
25
26
24
23
24
27
25
19
19
24
20
21
28
26
19
23
23
21
26
25
25
24
23
22
27
26
23
22
26
22
17
25
22
28
22
21
24
26
26
24
27
22
23
22
23
15
20
22
25
27
24
21
17
26
20
22
24
23
22
28
21
24
28
25
24
24
21
20
26
16
Dataseries Y:
Download CSV
Histogram 
12.9
12.2
12.8
7.4
6.7
12.6
14.8
13.3
11.1
8.2
11.4
6.4
10.6
12
6.3
11.3
11.9
9.3
9.6
10
6.4
13.8
10.8
13.8
11.7
10.9
16.1
13.4
9.9
11.5
8.3
11.7
9
9.7
10.8
10.3
10.4
12.7
9.3
11.8
5.9
11.4
13
10.8
12.3
11.3
11.8
7.9
12.7
12.3
11.6
6.7
10.9
12.1
13.3
10.1
5.7
14.3
8
13.3
9.3
12.5
7.6
15.9
9.2
9.1
11.1
13
14.5
12.2
12.3
11.4
8.8
14.6
12.6
13
12.6
13.2
9.9
7.7
10.5
13.4
10.9
4.3
10.3
11.8
11.2
11.4
8.6
13.2
12.6
5.6
9.9
8.8
7.7
9
7.3
11.4
13.6
7.9
10.7
10.3
8.3
9.6
14.2
8.5
13.5
4.9
6.4
9.6
11.6
11.1
4.35
12.7
18.1
17.85
16.6
12.6
17.1
19.1
16.1
13.35
18.4
14.7
10.6
12.6
16.2
13.6
18.9
14.1
14.5
16.15
14.75
14.8
12.45
12.65
17.35
8.6
18.4
16.1
11.6
17.75
15.25
17.65
16.35
17.65
13.6
14.35
14.75
18.25
9.9
16
18.25
16.85
14.6
13.85
18.95
15.6
14.85
11.75
18.45
15.9
17.1
16.1
19.9
10.95
18.45
15.1
15
11.35
15.95
18.1
14.6
15.4
15.4
17.6
13.35
19.1
15.35
7.6
13.4
13.9
19.1
15.25
12.9
16.1
17.35
13.15
12.15
12.6
10.35
15.4
9.6
18.2
13.6
14.85
14.75
14.1
14.9
16.25
19.25
13.6
13.6
15.65
12.75
14.6
9.85
12.65
19.2
16.6
11.2
15.25
11.9
13.2
16.35
12.4
15.85
18.15
11.15
15.65
17.75
7.65
12.35
15.6
19.3
15.2
17.1
15.6
18.4
19.05
18.55
19.1
13.1
12.85
9.5
4.5
11.85
13.6
11.7
12.4
13.35
11.4
14.9
19.9
11.2
14.6
17.6
14.05
16.1
13.35
11.85
11.95
14.75
15.15
13.2
16.85
7.85
7.7
12.6
7.85
10.95
12.35
9.95
14.9
16.65
13.4
13.95
15.7
16.85
10.95
15.35
12.2
15.1
17.75
15.2
14.6
16.65
8.1

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'Gwilym Jenkins' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284731&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284731&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284731&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'Gwilym Jenkins' @ jenkins.wessa.net






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean22.982014388489212.975
Biased Variance9.5284534961958511.4802293165468
Biased Standard Deviation3.086819317063423.3882487093699
Covariance-0.739440433212996
Correlation-0.0704452438298977
Determination0.00496253237825374
T-Test-1.17323902579854
p-value (2 sided)0.241711474413485
p-value (1 sided)0.120855737206742
95% CI of Correlation[-0.186542297058155, 0.0475921730552498]
Degrees of Freedom276
Number of Observations278

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 22.9820143884892 & 12.975 \tabularnewline
Biased Variance & 9.52845349619585 & 11.4802293165468 \tabularnewline
Biased Standard Deviation & 3.08681931706342 & 3.3882487093699 \tabularnewline
Covariance & -0.739440433212996 \tabularnewline
Correlation & -0.0704452438298977 \tabularnewline
Determination & 0.00496253237825374 \tabularnewline
T-Test & -1.17323902579854 \tabularnewline
p-value (2 sided) & 0.241711474413485 \tabularnewline
p-value (1 sided) & 0.120855737206742 \tabularnewline
95% CI of Correlation & [-0.186542297058155, 0.0475921730552498] \tabularnewline
Degrees of Freedom & 276 \tabularnewline
Number of Observations & 278 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284731&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]22.9820143884892[/C][C]12.975[/C][/ROW]
[ROW][C]Biased Variance[/C][C]9.52845349619585[/C][C]11.4802293165468[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]3.08681931706342[/C][C]3.3882487093699[/C][/ROW]
[ROW][C]Covariance[/C][C]-0.739440433212996[/C][/ROW]
[ROW][C]Correlation[/C][C]-0.0704452438298977[/C][/ROW]
[ROW][C]Determination[/C][C]0.00496253237825374[/C][/ROW]
[ROW][C]T-Test[/C][C]-1.17323902579854[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0.241711474413485[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0.120855737206742[/C][/ROW]
[ROW][C]95% CI of Correlation[/C][C][-0.186542297058155, 0.0475921730552498][/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]276[/C][/ROW]
[ROW][C]Number of Observations[/C][C]278[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284731&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284731&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
Mean22.982014388489212.975
Biased Variance9.5284534961958511.4802293165468
Biased Standard Deviation3.086819317063423.3882487093699
Covariance-0.739440433212996
Correlation-0.0704452438298977
Determination0.00496253237825374
T-Test-1.17323902579854
p-value (2 sided)0.241711474413485
p-value (1 sided)0.120855737206742
95% CI of Correlation[-0.186542297058155, 0.0475921730552498]
Degrees of Freedom276
Number of Observations278






Normality Tests
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 171.76, p-value < 2.2e-16
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 3.2947, p-value = 0.1926
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 2.5809, p-value = 1.583e-06

> ad.y
	Anderson-Darling normality test
data:  y
A = 0.42625, p-value = 0.3124


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

> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 171.76, p-value < 2.2e-16
alternative hypothesis: greater

 \tabularnewline

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 3.2947, p-value = 0.1926
alternative hypothesis: greater

 \tabularnewline

> ad.x
	Anderson-Darling normality test
data:  x
A = 2.5809, p-value = 1.583e-06

 \tabularnewline

> ad.y
	Anderson-Darling normality test
data:  y
A = 0.42625, p-value = 0.3124

 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284731&T=2

[TABLE]
[ROW][C]Normality Tests[/C][/ROW]
[ROW][C]
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 171.76, p-value < 2.2e-16
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 3.2947, p-value = 0.1926
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> ad.x
	Anderson-Darling normality test
data:  x
A = 2.5809, p-value = 1.583e-06

[/C][/ROW]
[ROW][C]
> ad.y
	Anderson-Darling normality test
data:  y
A = 0.42625, p-value = 0.3124

[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284731&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284731&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 = 171.76, p-value < 2.2e-16
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 3.2947, p-value = 0.1926
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 2.5809, p-value = 1.583e-06

> ad.y
	Anderson-Darling normality test
data:  y
A = 0.42625, p-value = 0.3124


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()