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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 computationMon, 15 Dec 2014 15:23:13 +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/2014/Dec/15/t1418657000i62p0ahku6a8s7t.htm/, Retrieved Thu, 16 May 2024 19:10:10 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=268624, Retrieved Thu, 16 May 2024 19:10:10 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact45

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Pearson Correlation] [] [2014-12-15 15:23:13] [d33b7eb92cfcc384850e3711242e8bfe] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
23
16
33
32
37
14
52
75
72
15
29
13
40
19
24
121
93
36
23
85
41
46
18
35
17
4
28
44
10
38
57
23
36
22
40
31
11
38
24
37
37
22
15
2
43
31
29
45
25
4
31
-4
66
61
32
31
39
19
31
36
42
21
21
25
32
26
28
32
41
29
33
17
13
32
30
34
59
13
23
10
5
31
19
32
30
25
48
35
67
15
22
18
33
46
24
14
12
38
12
28
41
12
31
33
34
21
20
44
52
7
29
11
26
24
7
60
13
20
52
28
25
39
9
19
13
60
19
34
14
17
45
66
48
29
-2
51
2
24
40
20
19
16
20
40
27
25
49
39
61
19
67
45
30
8
19
52
22
17
33
34
22
30
25
38
26
Dataseries Y:
Download CSV
Histogram 
51
56
67
69
57
56
55
63
67
65
47
76
64
68
64
65
71
63
60
68
72
70
61
61
62
71
71
51
56
70
73
76
68
48
52
60
59
57
79
60
60
59
62
59
61
71
57
66
63
69
58
59
48
66
73
67
61
68
75
62
69
58
60
74
55
62
63
69
58
58
68
72
62
62
65
69
66
72
62
75
58
66
55
47
72
62
64
64
19
50
68
70
79
69
71
48
73
74
66
71
74
78
75
53
60
70
69
65
78
78
59
72
70
63
63
71
74
67
66
62
80
73
67
61
73
74
32
69
69
84
64
58
59
78
57
60
68
68
73
69
67
60
65
66
74
81
72
55
49
74
53
64
65
57
51
80
67
70
74
75
70
69
65
55
71

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=268624&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=268624&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=268624&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
Mean30.864.7878787878788
Biased Variance324.52363636363679.1004591368228
Biased Standard Deviation18.01453958233848.89384388983879
Covariance-12.1341463414634
Correlation-0.0752759877940898
Determination0.00566647433837596
T-Test-0.963794012706558
p-value (2 sided)0.336576879075425
p-value (1 sided)0.168288439537713
Degrees of Freedom163
Number of Observations165

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 30.8 & 64.7878787878788 \tabularnewline
Biased Variance & 324.523636363636 & 79.1004591368228 \tabularnewline
Biased Standard Deviation & 18.0145395823384 & 8.89384388983879 \tabularnewline
Covariance & -12.1341463414634 \tabularnewline
Correlation & -0.0752759877940898 \tabularnewline
Determination & 0.00566647433837596 \tabularnewline
T-Test & -0.963794012706558 \tabularnewline
p-value (2 sided) & 0.336576879075425 \tabularnewline
p-value (1 sided) & 0.168288439537713 \tabularnewline
Degrees of Freedom & 163 \tabularnewline
Number of Observations & 165 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=268624&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]30.8[/C][C]64.7878787878788[/C][/ROW]
[ROW][C]Biased Variance[/C][C]324.523636363636[/C][C]79.1004591368228[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]18.0145395823384[/C][C]8.89384388983879[/C][/ROW]
[ROW][C]Covariance[/C][C]-12.1341463414634[/C][/ROW]
[ROW][C]Correlation[/C][C]-0.0752759877940898[/C][/ROW]
[ROW][C]Determination[/C][C]0.00566647433837596[/C][/ROW]
[ROW][C]T-Test[/C][C]-0.963794012706558[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0.336576879075425[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0.168288439537713[/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=268624&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=268624&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
Mean30.864.7878787878788
Biased Variance324.52363636363679.1004591368228
Biased Standard Deviation18.01453958233848.89384388983879
Covariance-12.1341463414634
Correlation-0.0752759877940898
Determination0.00566647433837596
T-Test-0.963794012706558
p-value (2 sided)0.336576879075425
p-value (1 sided)0.168288439537713
Degrees of Freedom163
Number of Observations165






Normality Tests
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 151.0034, p-value < 2.2e-16
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 139.8607, p-value < 2.2e-16
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 2.5521, p-value = 1.811e-06

> ad.y
	Anderson-Darling normality test
data:  y
A = 1.1343, p-value = 0.005585


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

> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 151.0034, p-value < 2.2e-16
alternative hypothesis: greater

 \tabularnewline

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 139.8607, p-value < 2.2e-16
alternative hypothesis: greater

 \tabularnewline

> ad.x
	Anderson-Darling normality test
data:  x
A = 2.5521, p-value = 1.811e-06

 \tabularnewline

> ad.y
	Anderson-Darling normality test
data:  y
A = 1.1343, p-value = 0.005585

 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=268624&T=2

[TABLE]
[ROW][C]Normality Tests[/C][/ROW]
[ROW][C]
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 151.0034, p-value < 2.2e-16
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 139.8607, p-value < 2.2e-16
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> ad.x
	Anderson-Darling normality test
data:  x
A = 2.5521, p-value = 1.811e-06

[/C][/ROW]
[ROW][C]
> ad.y
	Anderson-Darling normality test
data:  y
A = 1.1343, p-value = 0.005585

[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=268624&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=268624&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 = 151.0034, p-value < 2.2e-16
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 139.8607, p-value < 2.2e-16
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 2.5521, p-value = 1.811e-06

> ad.y
	Anderson-Darling normality test
data:  y
A = 1.1343, p-value = 0.005585


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):
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()