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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 computationThu, 14 Dec 2017 17:28:52 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2017/Dec/14/t1513270797w2tt24p5glcu2sa.htm/, Retrieved Tue, 14 May 2024 10:47:05 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=309562, Retrieved Tue, 14 May 2024 10:47:05 +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] [pearson correlation] [2017-12-14 16:28:52] [7c64beff23d1126809c420b7c106481b] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
2
7
16
16
11
13
10
12
22
1
12
12
24
2
19
10
7
9
21
7
19
8
23
12
6
15
5
5
9
21
15
5
1
18
19
4
7
20
19
11
3
15
20
3
19
6
6
18
14
21
12
14
8
6
20
1
6
22
17
21
3
19
2
22
10
15
15
22
10
15
24
22
13
21
14
16
11
11
12
22
22
15
20
1
5
22
3
21
21
2
17
3
16
16
9
9
13
21
15
1
17
9
11
13
2
14
24
18
20
10
14
22
19
19
Dataseries Y:
Download CSV
Histogram 
19
28
83
82
70
30
32
40
84
31
72
39
72
28
57
68
40
22
23
50
18
68
41
48
48
27
19
19
30
32
19
32
21
63
76
39
62
42
21
70
21
31
37
27
5
26
24
49
40
62
76
49
27
22
30
31
63
23
80
46
36
47
42
43
44
59
52
43
77
34
32
27
59
55
57
31
54
59
53
26
32
77
34
55
24
26
34
57
26
33
87
28
7
29
82
82
45
71
45
34
77
63
73
40
43
49
40
43
20
42
75
67
47
69

Tables (Output of Computation)





Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R ServerBig Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time4 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=309562&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]4 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=309562&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=309562&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 Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R ServerBig Analytics Cloud Computing Center






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean13.070175438596544.9122807017544
Biased Variance45.5564789165897388.062480763312
Biased Standard Deviation6.7495539790855619.6993015298338
Covariance20.9973606582829
Correlation0.156535338700068
Determination0.0245033122619451
T-Test1.67729135691959
p-value (2 sided)0.0962742986029634
p-value (1 sided)0.0481371493014817
95% CI of Correlation[-0.0281910610151997, 0.330923140097364]
Degrees of Freedom112
Number of Observations114

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 13.0701754385965 & 44.9122807017544 \tabularnewline
Biased Variance & 45.5564789165897 & 388.062480763312 \tabularnewline
Biased Standard Deviation & 6.74955397908556 & 19.6993015298338 \tabularnewline
Covariance & 20.9973606582829 \tabularnewline
Correlation & 0.156535338700068 \tabularnewline
Determination & 0.0245033122619451 \tabularnewline
T-Test & 1.67729135691959 \tabularnewline
p-value (2 sided) & 0.0962742986029634 \tabularnewline
p-value (1 sided) & 0.0481371493014817 \tabularnewline
95% CI of Correlation & [-0.0281910610151997, 0.330923140097364] \tabularnewline
Degrees of Freedom & 112 \tabularnewline
Number of Observations & 114 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=309562&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]13.0701754385965[/C][C]44.9122807017544[/C][/ROW]
[ROW][C]Biased Variance[/C][C]45.5564789165897[/C][C]388.062480763312[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]6.74955397908556[/C][C]19.6993015298338[/C][/ROW]
[ROW][C]Covariance[/C][C]20.9973606582829[/C][/ROW]
[ROW][C]Correlation[/C][C]0.156535338700068[/C][/ROW]
[ROW][C]Determination[/C][C]0.0245033122619451[/C][/ROW]
[ROW][C]T-Test[/C][C]1.67729135691959[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0.0962742986029634[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0.0481371493014817[/C][/ROW]
[ROW][C]95% CI of Correlation[/C][C][-0.0281910610151997, 0.330923140097364][/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]112[/C][/ROW]
[ROW][C]Number of Observations[/C][C]114[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=309562&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=309562&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
Mean13.070175438596544.9122807017544
Biased Variance45.5564789165897388.062480763312
Biased Standard Deviation6.7495539790855619.6993015298338
Covariance20.9973606582829
Correlation0.156535338700068
Determination0.0245033122619451
T-Test1.67729135691959
p-value (2 sided)0.0962742986029634
p-value (1 sided)0.0481371493014817
95% CI of Correlation[-0.0281910610151997, 0.330923140097364]
Degrees of Freedom112
Number of Observations114






Normality Tests
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 6.9255, p-value = 0.03134
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 6.3629, p-value = 0.04153
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 1.5734, p-value = 0.0004516

> ad.y
	Anderson-Darling normality test
data:  y
A = 1.8103, p-value = 0.0001175


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

> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 6.9255, p-value = 0.03134
alternative hypothesis: greater

 \tabularnewline

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 6.3629, p-value = 0.04153
alternative hypothesis: greater

 \tabularnewline

> ad.x
	Anderson-Darling normality test
data:  x
A = 1.5734, p-value = 0.0004516

 \tabularnewline

> ad.y
	Anderson-Darling normality test
data:  y
A = 1.8103, p-value = 0.0001175

 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=309562&T=2

[TABLE]
[ROW][C]Normality Tests[/C][/ROW]
[ROW][C]
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 6.9255, p-value = 0.03134
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 6.3629, p-value = 0.04153
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> ad.x
	Anderson-Darling normality test
data:  x
A = 1.5734, p-value = 0.0004516

[/C][/ROW]
[ROW][C]
> ad.y
	Anderson-Darling normality test
data:  y
A = 1.8103, p-value = 0.0001175

[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=309562&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=309562&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 = 6.9255, p-value = 0.03134
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 6.3629, p-value = 0.04153
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 1.5734, p-value = 0.0004516

> ad.y
	Anderson-Darling normality test
data:  y
A = 1.8103, p-value = 0.0001175


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
Parameters (R input):
R code (references can be found in the software module):
library(psychometric)
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$estimate)[1,1]
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Pearson Product Moment Correlation - Ungrouped Data',3,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Statistic',1,TRUE)
a<-table.element(a,'Variable X',1,TRUE)
a<-table.element(a,'Variable Y',1,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Mean',header=TRUE)
a<-table.element(a,mean(x))
a<-table.element(a,mean(y))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Biased Variance',header=TRUE)
a<-table.element(a,varx)
a<-table.element(a,vary)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Biased Standard Deviation',header=TRUE)
a<-table.element(a,sqrt(varx))
a<-table.element(a,sqrt(vary))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Covariance',header=TRUE)
a<-table.element(a,cov(x,y),2)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Correlation',header=TRUE)
a<-table.element(a,cxy,2)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Determination',header=TRUE)
a<-table.element(a,cxy*cxy,2)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'T-Test',header=TRUE)
a<-table.element(a,as.matrix(corxy$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,'95% CI of Correlation',header=TRUE)
a<-table.element(a,paste('[',CIr(r=cxy, n = lx, level = .95)[1],', ', CIr(r=cxy, n = lx, level = .95)[2],']',sep=''),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')
qqPlot(x,main='QQplot of variable x')
dev.off()
bitmap(file='test3.png')
qqPlot(y,main='QQplot of variable y')
dev.off()