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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 14:28:54 +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/t1418653869bu6an44vi0vgoza.htm/, Retrieved Thu, 16 May 2024 13:16:26 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=268500, Retrieved Thu, 16 May 2024 13:16:26 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact48

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 14:28:54] [fe6a3e2d5def86ae31dbd813f23b564f] [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
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

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=268500&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=268500&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=268500&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
Mean53.23030303030330.8
Biased Variance100.359081726354324.523636363636
Biased Standard Deviation10.017937997729618.0145395823384
Covariance25.119512195122
Correlation0.138346953131899
Determination0.0191398794408798
T-Test1.78344558232117
p-value (2 sided)0.0763745651695378
p-value (1 sided)0.0381872825847689
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 & 30.8 \tabularnewline
Biased Variance & 100.359081726354 & 324.523636363636 \tabularnewline
Biased Standard Deviation & 10.0179379977296 & 18.0145395823384 \tabularnewline
Covariance & 25.119512195122 \tabularnewline
Correlation & 0.138346953131899 \tabularnewline
Determination & 0.0191398794408798 \tabularnewline
T-Test & 1.78344558232117 \tabularnewline
p-value (2 sided) & 0.0763745651695378 \tabularnewline
p-value (1 sided) & 0.0381872825847689 \tabularnewline
Degrees of Freedom & 163 \tabularnewline
Number of Observations & 165 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=268500&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]30.8[/C][/ROW]
[ROW][C]Biased Variance[/C][C]100.359081726354[/C][C]324.523636363636[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]10.0179379977296[/C][C]18.0145395823384[/C][/ROW]
[ROW][C]Covariance[/C][C]25.119512195122[/C][/ROW]
[ROW][C]Correlation[/C][C]0.138346953131899[/C][/ROW]
[ROW][C]Determination[/C][C]0.0191398794408798[/C][/ROW]
[ROW][C]T-Test[/C][C]1.78344558232117[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0.0763745651695378[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0.0381872825847689[/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=268500&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=268500&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
Mean53.23030303030330.8
Biased Variance100.359081726354324.523636363636
Biased Standard Deviation10.017937997729618.0145395823384
Covariance25.119512195122
Correlation0.138346953131899
Determination0.0191398794408798
T-Test1.78344558232117
p-value (2 sided)0.0763745651695378
p-value (1 sided)0.0381872825847689
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 = 151.0034, 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 = 2.5521, p-value = 1.811e-06


\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 = 151.0034, 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 = 2.5521, p-value = 1.811e-06

 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=268500&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 = 151.0034, 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 = 2.5521, p-value = 1.811e-06

[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=268500&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=268500&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 = 151.0034, 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 = 2.5521, p-value = 1.811e-06


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()