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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, 09 Dec 2014 18:37:35 +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/2014/Dec/09/t1418150718qak85923x5szqh8.htm/, Retrieved Thu, 16 May 2024 20:34:57 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=264799, Retrieved Thu, 16 May 2024 20:34:57 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact93

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Percentiles] [Intrinsic Motivat...] [2010-10-12 12:10:58] [b98453cac15ba1066b407e146608df68]
- RMPD  [Kernel Density Estimation] [] [2011-10-18 22:42:23] [b98453cac15ba1066b407e146608df68]
- RMPD    [Percentiles] [] [2011-10-18 22:46:45] [b98453cac15ba1066b407e146608df68]
- RMPD      [Notched Boxplots] [] [2011-10-18 22:58:56] [b98453cac15ba1066b407e146608df68]
- RM D        [Back to Back Histogram] [] [2011-10-18 23:05:48] [b98453cac15ba1066b407e146608df68]
- RMPD          [Back to Back Histogram] [] [2014-12-09 17:55:01] [ea990983fba95a758c0bb6d29c9aee24]
- RMPD              [Pearson Correlation] [] [2014-12-09 18:37:35] [6260c34aa94cecca073345f42e0d4b5d] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
21
26
22
22
18
23
12
20
22
21
19
22
15
20
19
18
15
20
21
21
15
16
23
21
18
25
9
30
20
23
16
16
19
25
25
18
23
21
10
14
22
26
23
23
24
24
18
23
15
19
16
25
23
17
19
21
18
27
21
13
8
29
28
23
21
19
19
20
18
19
17
19
25
19
22
23
26
14
28
16
24
20
12
24
22
12
22
20
10
23
17
22
24
18
21
20
20
22
19
20
26
23
24
21
21
19
8
17
20
11
8
15
18
18
19
19
23
22
21
25
30
17
27
23
23
18
18
23
19
15
20
16
24
25
25
19
19
16
19
19
23
21
22
19
20
20
3
23
14
23
20
15
13
16
7
24
17
24
24
19
25
20
28
23
27
18
28
21
19
23
27
22
28
25
21
22
28
20
29
25
25
20
20
16
20
20
23
18
25
18
19
25
25
25
24
19
26
10
17
13
17
30
25
4
16
21
23
22
17
20
20
22
16
23
16
0
18
25
23
12
18
24
11
18
14
23
24
29
18
15
29
16
19
22
16
23
23
19
4
20
24
20
4
24
22
16
3
15
24
17
20
27
23
26
23
17
20
22
19
24
19
23
15
27
26
22
22
18
15
22
27
10
20
17
23
19
13
27
23
16
25
2
26
20
23
22
24
Dataseries Y:
Download CSV
Histogram 
12.9
7.4
12.2
12.8
7.4
6.7
12.6
14.8
13.3
11.1
8.2
11.4
6.4
10.6
12.0
6.3
11.3
11.9
9.3
9.6
10.0
6.4
13.8
10.8
13.8
11.7
10.9
16.1
13.4
9.9
11.5
8.3
11.7
6.1
9.0
9.7
10.8
10.3
10.4
12.7
9.3
11.8
5.9
11.4
13.0
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
8.0
13.3
9.3
12.5
7.6
15.9
9.2
9.1
11.1
13.0
14.5
12.2
12.3
11.4
8.8
14.6
7.3
12.6
NA
13.0
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
9.0
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
15.6
16.35
17.65
13.6
11.7
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
11.9
19.2
16.6
11.2
15.25
11.9
13.2
16.35
12.4
15.85
14.35
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
17.75
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 time2 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 & 2 seconds \tabularnewline
R Server & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=264799&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]2 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=264799&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=264799&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 time2 seconds
R Server'Sir Maurice George Kendall' @ kendall.wessa.net






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean19.98601398601412.9340909090909
Biased Variance26.22358061518911.6641262714558
Biased Standard Deviation5.120896465970493.41527835929311
Covariance1.72574162679426
Correlation0.098329198721557
Determination0.00966863132122345
T-Test1.66514248774723
p-value (2 sided)0.0969870516540763
p-value (1 sided)0.0484935258270381
Degrees of Freedom284
Number of Observations286

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 19.986013986014 & 12.9340909090909 \tabularnewline
Biased Variance & 26.223580615189 & 11.6641262714558 \tabularnewline
Biased Standard Deviation & 5.12089646597049 & 3.41527835929311 \tabularnewline
Covariance & 1.72574162679426 \tabularnewline
Correlation & 0.098329198721557 \tabularnewline
Determination & 0.00966863132122345 \tabularnewline
T-Test & 1.66514248774723 \tabularnewline
p-value (2 sided) & 0.0969870516540763 \tabularnewline
p-value (1 sided) & 0.0484935258270381 \tabularnewline
Degrees of Freedom & 284 \tabularnewline
Number of Observations & 286 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=264799&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]19.986013986014[/C][C]12.9340909090909[/C][/ROW]
[ROW][C]Biased Variance[/C][C]26.223580615189[/C][C]11.6641262714558[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]5.12089646597049[/C][C]3.41527835929311[/C][/ROW]
[ROW][C]Covariance[/C][C]1.72574162679426[/C][/ROW]
[ROW][C]Correlation[/C][C]0.098329198721557[/C][/ROW]
[ROW][C]Determination[/C][C]0.00966863132122345[/C][/ROW]
[ROW][C]T-Test[/C][C]1.66514248774723[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0.0969870516540763[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0.0484935258270381[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]284[/C][/ROW]
[ROW][C]Number of Observations[/C][C]286[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=264799&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=264799&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
Mean19.98601398601412.9340909090909
Biased Variance26.22358061518911.6641262714558
Biased Standard Deviation5.120896465970493.41527835929311
Covariance1.72574162679426
Correlation0.098329198721557
Determination0.00966863132122345
T-Test1.66514248774723
p-value (2 sided)0.0969870516540763
p-value (1 sided)0.0484935258270381
Degrees of Freedom284
Number of Observations286






Normality Tests
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 91.0602, p-value < 2.2e-16
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 3.831, p-value = 0.1473
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 3.9472, p-value = 7.513e-10

> ad.y
	Anderson-Darling normality test
data:  y
A = 0.4893, p-value = 0.2201


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

> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 91.0602, p-value < 2.2e-16
alternative hypothesis: greater

 \tabularnewline

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 3.831, p-value = 0.1473
alternative hypothesis: greater

 \tabularnewline

> ad.x
	Anderson-Darling normality test
data:  x
A = 3.9472, p-value = 7.513e-10

 \tabularnewline

> ad.y
	Anderson-Darling normality test
data:  y
A = 0.4893, p-value = 0.2201

 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=264799&T=2

[TABLE]
[ROW][C]Normality Tests[/C][/ROW]
[ROW][C]
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 91.0602, p-value < 2.2e-16
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 3.831, p-value = 0.1473
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> ad.x
	Anderson-Darling normality test
data:  x
A = 3.9472, p-value = 7.513e-10

[/C][/ROW]
[ROW][C]
> ad.y
	Anderson-Darling normality test
data:  y
A = 0.4893, p-value = 0.2201

[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=264799&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=264799&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 = 91.0602, p-value < 2.2e-16
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 3.831, p-value = 0.1473
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 3.9472, p-value = 7.513e-10

> ad.y
	Anderson-Darling normality test
data:  y
A = 0.4893, p-value = 0.2201


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
Parameters (R input):
R code (references can be found in the software module):
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,'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()