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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, 16 Dec 2014 08:31:15 +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/2014/Dec/16/t1418718680acvuv007f6eolbz.htm/, Retrieved Thu, 16 May 2024 08:30:27 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=269166, Retrieved Thu, 16 May 2024 08:30:27 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact78

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Pearson Correlation] [] [2014-12-16 08:31:15] [d33b7eb92cfcc384850e3711242e8bfe] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
52
16
46
56
52
55
50
59
60
52
44
67
52
55
37
54
72
51
48
60
50
63
33
67
46
54
59
61
33
47
69
52
55
41
73
52
50
51
60
56
56
29
66
66
73
55
64
40
46
58
43
61
51
50
52
54
66
61
80
51
56
56
56
53
47
25
47
46
50
39
51
58
35
58
60
62
63
53
46
67
59
64
38
50
48
48
47
66
47
63
58
44
51
43
55
38
45
50
54
57
60
55
56
49
37
59
46
51
58
64
53
48
51
47
59
62
62
51
64
52
67
50
54
58
56
63
31
65
71
50
57
47
47
57
43
41
63
63
56
51
50
22
41
59
56
66
53
42
52
54
44
62
53
50
36
76
66
62
59
47
55
58
60
44
57
Dataseries Y:
Download CSV
Histogram 
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
23
20
15
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
0
18
25
23
12
18
24
11
18
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
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

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'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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=269166&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=269166&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=269166&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'Gwilym Jenkins' @ jenkins.wessa.net






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean53.23030303030320.2848484848485
Biased Variance100.35908172635430.6885583103765
Biased Standard Deviation10.01793799772965.53972547247393
Covariance4.97668144863267
Correlation0.0891318999367393
Determination0.0079444955863329
T-Test1.1425072921828
p-value (2 sided)0.254918634455126
p-value (1 sided)0.127459317227563
Degrees of Freedom163
Number of Observations165

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 53.230303030303 & 20.2848484848485 \tabularnewline
Biased Variance & 100.359081726354 & 30.6885583103765 \tabularnewline
Biased Standard Deviation & 10.0179379977296 & 5.53972547247393 \tabularnewline
Covariance & 4.97668144863267 \tabularnewline
Correlation & 0.0891318999367393 \tabularnewline
Determination & 0.0079444955863329 \tabularnewline
T-Test & 1.1425072921828 \tabularnewline
p-value (2 sided) & 0.254918634455126 \tabularnewline
p-value (1 sided) & 0.127459317227563 \tabularnewline
Degrees of Freedom & 163 \tabularnewline
Number of Observations & 165 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=269166&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]53.230303030303[/C][C]20.2848484848485[/C][/ROW]
[ROW][C]Biased Variance[/C][C]100.359081726354[/C][C]30.6885583103765[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]10.0179379977296[/C][C]5.53972547247393[/C][/ROW]
[ROW][C]Covariance[/C][C]4.97668144863267[/C][/ROW]
[ROW][C]Correlation[/C][C]0.0891318999367393[/C][/ROW]
[ROW][C]Determination[/C][C]0.0079444955863329[/C][/ROW]
[ROW][C]T-Test[/C][C]1.1425072921828[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0.254918634455126[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0.127459317227563[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]163[/C][/ROW]
[ROW][C]Number of Observations[/C][C]165[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=269166&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=269166&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
Mean53.23030303030320.2848484848485
Biased Variance100.35908172635430.6885583103765
Biased Standard Deviation10.01793799772965.53972547247393
Covariance4.97668144863267
Correlation0.0891318999367393
Determination0.0079444955863329
T-Test1.1425072921828
p-value (2 sided)0.254918634455126
p-value (1 sided)0.127459317227563
Degrees of Freedom163
Number of Observations165






Normality Tests
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 18.3644, p-value = 0.0001029
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 81.5075, p-value < 2.2e-16
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 0.8748, p-value = 0.0245

> ad.y
	Anderson-Darling normality test
data:  y
A = 3.5566, p-value = 6.395e-09


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

> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 18.3644, p-value = 0.0001029
alternative hypothesis: greater

 \tabularnewline

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 81.5075, p-value < 2.2e-16
alternative hypothesis: greater

 \tabularnewline

> ad.x
	Anderson-Darling normality test
data:  x
A = 0.8748, p-value = 0.0245

 \tabularnewline

> ad.y
	Anderson-Darling normality test
data:  y
A = 3.5566, p-value = 6.395e-09

 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=269166&T=2

[TABLE]
[ROW][C]Normality Tests[/C][/ROW]
[ROW][C]
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 18.3644, p-value = 0.0001029
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 81.5075, p-value < 2.2e-16
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> ad.x
	Anderson-Darling normality test
data:  x
A = 0.8748, p-value = 0.0245

[/C][/ROW]
[ROW][C]
> ad.y
	Anderson-Darling normality test
data:  y
A = 3.5566, p-value = 6.395e-09

[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=269166&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=269166&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 = 18.3644, p-value = 0.0001029
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 81.5075, p-value < 2.2e-16
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 0.8748, p-value = 0.0245

> ad.y
	Anderson-Darling normality test
data:  y
A = 3.5566, p-value = 6.395e-09


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()