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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 computationSat, 13 Dec 2014 15:36:00 +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/13/t1418485019huqsvnazji8nw2m.htm/, Retrieved Thu, 16 May 2024 17:35:06 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=267163, Retrieved Thu, 16 May 2024 17:35:06 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact102

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          [Pearson Correlation] [WS3: question 4 (...] [2014-10-16 20:35:26] [1764622206627ac897c737076a0cb4c8]
-    D              [Pearson Correlation] [] [2014-12-13 15:36:00] [6260c34aa94cecca073345f42e0d4b5d] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
24
47
36
47
55
66
57
52
67
54
46
49
28
50
52
45
64
63
39
42
54
36
49
60
33
46
48
52
35
40
63
32
45
51
48
38
59
53
50
30
61
61
47
51
44
54
53
58
49
53
48
40
55
55
52
50
37
47
51
45
57
28
53
60
38
44
40
48
48
62
58
47
24
41
47
37
54
53
55
57
58
58
35
43
44
45
61
53
41
38
41
55
51
54
39
48
54
59
47
44
55
48
59
48
51
65
46
44
38
58
50
19
54
60
50
50
48
32
69
55
52
53
41
53
56
55
13
52
46
56
27
53
45
52
31
38
41
44
49
51
40
49
51
43
56
38
42
55
55
44
49
51
42
57
43
48
59
55
50
30
54
49
48
59
43
49
56
49
50
49
29
44
57
57
49
54
60
58
62
43
54
49
64
55
54
64
45
59
50
57
65
60
55
46
61
43
55
47
38
59
48
51
55
71
54
60
42
49
52
61
52
52
54
38
64
46
59
Dataseries Y:
Download CSV
Histogram 
52
62
40
48
40
77
61
44
66
49
40
53
59
58
53
58
49
51
58
48
53
39
47
51
52
57
37
46
48
33
28
45
56
45
53
47
39
62
59
55
50
45
59
39
41
53
44
61
41
54
36
47
54
54
57
47
32
66
41
54
54
40
60
53
25
58
50
56
48
15
43
52
49
46
56
62
48
50
35
50
67
48
42
48
58
31
60
43
50
57
30
44
65
49
70
48
54
52
61
61
66
53
56
44
50
73
52
53
53
48
45
44
50
31
50
43
64
56
46
41
58
46
52
37
50
46
51
54
47
35
57
44
49
45
57
58
63
46
52
53
57
27
59
52
51
45
53
38
60
51
45
39
52
39
48
38
57
47
62
57
45
55
43
53
51
28
41
49
50
42
40
41
42
46
49
52
54
50
61
52
49
39
61
41
63
62
46
47
65
44
37
66
73
38
49
64
56
42
36
45
45
47
59
48
53
50
49
65
47
60
46
50
55
48
43
66
65
52
38
44
61
41
38
64
59
54
36
34
48
55
44
46
53
20
49
35
62
41
36
54
59
54
54
52
39
50
59
53
43
55
56
45
42
42
53
51
38
51
61
57
55
62
23
52
48
55
43
44
70
31
45
49
66
49
46
50
48
58
62
55
49

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=267163&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=267163&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=267163&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
Mean49.336405529953949.9493087557604
Biased Variance86.923697678863487.5780755590478
Biased Standard Deviation9.323287922126169.35831585057096
Covariance5.04027991124765
Correlation0.0575018579800967
Determination0.00330646367116321
T-Test0.844540122173011
p-value (2 sided)0.39930641885498
p-value (1 sided)0.19965320942749
Degrees of Freedom215
Number of Observations217

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 49.3364055299539 & 49.9493087557604 \tabularnewline
Biased Variance & 86.9236976788634 & 87.5780755590478 \tabularnewline
Biased Standard Deviation & 9.32328792212616 & 9.35831585057096 \tabularnewline
Covariance & 5.04027991124765 \tabularnewline
Correlation & 0.0575018579800967 \tabularnewline
Determination & 0.00330646367116321 \tabularnewline
T-Test & 0.844540122173011 \tabularnewline
p-value (2 sided) & 0.39930641885498 \tabularnewline
p-value (1 sided) & 0.19965320942749 \tabularnewline
Degrees of Freedom & 215 \tabularnewline
Number of Observations & 217 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=267163&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]49.3364055299539[/C][C]49.9493087557604[/C][/ROW]
[ROW][C]Biased Variance[/C][C]86.9236976788634[/C][C]87.5780755590478[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]9.32328792212616[/C][C]9.35831585057096[/C][/ROW]
[ROW][C]Covariance[/C][C]5.04027991124765[/C][/ROW]
[ROW][C]Correlation[/C][C]0.0575018579800967[/C][/ROW]
[ROW][C]Determination[/C][C]0.00330646367116321[/C][/ROW]
[ROW][C]T-Test[/C][C]0.844540122173011[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0.39930641885498[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0.19965320942749[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]215[/C][/ROW]
[ROW][C]Number of Observations[/C][C]217[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=267163&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=267163&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
Mean49.336405529953949.9493087557604
Biased Variance86.923697678863487.5780755590478
Biased Standard Deviation9.323287922126169.35831585057096
Covariance5.04027991124765
Correlation0.0575018579800967
Determination0.00330646367116321
T-Test0.844540122173011
p-value (2 sided)0.39930641885498
p-value (1 sided)0.19965320942749
Degrees of Freedom215
Number of Observations217






Normality Tests
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 29.4768, p-value = 3.974e-07
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 5.7274, p-value = 0.05706
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 1.6233, p-value = 0.0003503

> ad.y
	Anderson-Darling normality test
data:  y
A = 0.4495, p-value = 0.2743


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

> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 29.4768, p-value = 3.974e-07
alternative hypothesis: greater

 \tabularnewline

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 5.7274, p-value = 0.05706
alternative hypothesis: greater

 \tabularnewline

> ad.x
	Anderson-Darling normality test
data:  x
A = 1.6233, p-value = 0.0003503

 \tabularnewline

> ad.y
	Anderson-Darling normality test
data:  y
A = 0.4495, p-value = 0.2743

 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=267163&T=2

[TABLE]
[ROW][C]Normality Tests[/C][/ROW]
[ROW][C]
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 29.4768, p-value = 3.974e-07
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 5.7274, p-value = 0.05706
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> ad.x
	Anderson-Darling normality test
data:  x
A = 1.6233, p-value = 0.0003503

[/C][/ROW]
[ROW][C]
> ad.y
	Anderson-Darling normality test
data:  y
A = 0.4495, p-value = 0.2743

[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=267163&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=267163&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 = 29.4768, p-value = 3.974e-07
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 5.7274, p-value = 0.05706
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 1.6233, p-value = 0.0003503

> ad.y
	Anderson-Darling normality test
data:  y
A = 0.4495, p-value = 0.2743


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()