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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, 28 Nov 2017 19:24:35 +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/Nov/28/t15118937944p9ftn2ztoipnyb.htm/, Retrieved Sat, 18 May 2024 17:38:11 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=308263, Retrieved Sat, 18 May 2024 17:38:11 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact145

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Pearson Correlation] [] [2017-11-28 18:24:35] [d45155ea4037f62d47a0a82219388c6c] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
36
32
33
39
34
39
36
33
30
39
37
37
35
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41
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43
30
33
28
30
28
39
34
34
29
32
33
27
35
38
40
34
34
26
39
34
39
26
30
34
34
29
41
43
31
33
34
30
23
29
35
40
27
30
27
29
33
32
33
36
34
45
30
22
24
25
26
27
27
35
36
32
35
35
36
37
33
25
35
37
36
35
29
35
31
30
37
36
35
32
34
37
36
39
37
31
40
38
35
38
32
41
28
40
25
28
37
37
40
26
30
32
31
28
34
39
33
43
37
31
31
34
32
27
34
28
32
39
28
39
32
36
31
39
23
25
32
32
36
39
31
32
28
34
28
38
35
32
26
32
28
31
33
38
38
36
31
36
43
37
28
35
34
40
31
41
35
38
37
31
Dataseries Y:
Download CSV
Histogram 
21
22
17
21
19
23
21
22
11
20
18
16
18
13
17
20
20
15
18
15
19
19
19
20
20
16
18
17
18
13
20
21
17
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20
15
15
19
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22
20
18
14
15
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18
8
13
13
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12
16
21
20
18
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21
16
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22
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12
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15
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21
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18
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21
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24
12
15
18
19
22
19
16
19
18
18
19
21
19
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23
17
18
19
15
14
18
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21
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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=308263&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=308263&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308263&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
Mean33.541899441340817.9441340782123
Biased Variance21.00802097312827.49408570269342
Biased Standard Deviation4.583450771321562.73753277655144
Covariance7.90684828322139
Correlation0.626640526023747
Determination0.392678348855319
T-Test10.6978309120219
p-value (2 sided)6.44475732956223e-21
p-value (1 sided)3.22237866478112e-21
95% CI of Correlation[0.52854746278, 0.708219765081087]
Degrees of Freedom177
Number of Observations179

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 33.5418994413408 & 17.9441340782123 \tabularnewline
Biased Variance & 21.0080209731282 & 7.49408570269342 \tabularnewline
Biased Standard Deviation & 4.58345077132156 & 2.73753277655144 \tabularnewline
Covariance & 7.90684828322139 \tabularnewline
Correlation & 0.626640526023747 \tabularnewline
Determination & 0.392678348855319 \tabularnewline
T-Test & 10.6978309120219 \tabularnewline
p-value (2 sided) & 6.44475732956223e-21 \tabularnewline
p-value (1 sided) & 3.22237866478112e-21 \tabularnewline
95% CI of Correlation & [0.52854746278, 0.708219765081087] \tabularnewline
Degrees of Freedom & 177 \tabularnewline
Number of Observations & 179 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=308263&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]33.5418994413408[/C][C]17.9441340782123[/C][/ROW]
[ROW][C]Biased Variance[/C][C]21.0080209731282[/C][C]7.49408570269342[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]4.58345077132156[/C][C]2.73753277655144[/C][/ROW]
[ROW][C]Covariance[/C][C]7.90684828322139[/C][/ROW]
[ROW][C]Correlation[/C][C]0.626640526023747[/C][/ROW]
[ROW][C]Determination[/C][C]0.392678348855319[/C][/ROW]
[ROW][C]T-Test[/C][C]10.6978309120219[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]6.44475732956223e-21[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]3.22237866478112e-21[/C][/ROW]
[ROW][C]95% CI of Correlation[/C][C][0.52854746278, 0.708219765081087][/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]177[/C][/ROW]
[ROW][C]Number of Observations[/C][C]179[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=308263&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308263&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
Mean33.541899441340817.9441340782123
Biased Variance21.00802097312827.49408570269342
Biased Standard Deviation4.583450771321562.73753277655144
Covariance7.90684828322139
Correlation0.626640526023747
Determination0.392678348855319
T-Test10.6978309120219
p-value (2 sided)6.44475732956223e-21
p-value (1 sided)3.22237866478112e-21
95% CI of Correlation[0.52854746278, 0.708219765081087]
Degrees of Freedom177
Number of Observations179






Normality Tests
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 1.9488, p-value = 0.3774
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 5.6189, p-value = 0.06024
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 0.67485, p-value = 0.07677

> ad.y
	Anderson-Darling normality test
data:  y
A = 1.4345, p-value = 0.001016


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

> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 1.9488, p-value = 0.3774
alternative hypothesis: greater

 \tabularnewline

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 5.6189, p-value = 0.06024
alternative hypothesis: greater

 \tabularnewline

> ad.x
	Anderson-Darling normality test
data:  x
A = 0.67485, p-value = 0.07677

 \tabularnewline

> ad.y
	Anderson-Darling normality test
data:  y
A = 1.4345, p-value = 0.001016

 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=308263&T=2

[TABLE]
[ROW][C]Normality Tests[/C][/ROW]
[ROW][C]
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 1.9488, p-value = 0.3774
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 5.6189, p-value = 0.06024
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> ad.x
	Anderson-Darling normality test
data:  x
A = 0.67485, p-value = 0.07677

[/C][/ROW]
[ROW][C]
> ad.y
	Anderson-Darling normality test
data:  y
A = 1.4345, p-value = 0.001016

[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=308263&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308263&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 = 1.9488, p-value = 0.3774
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 5.6189, p-value = 0.06024
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 0.67485, p-value = 0.07677

> ad.y
	Anderson-Darling normality test
data:  y
A = 1.4345, p-value = 0.001016


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par2 = grey ; par3 = FALSE ; par4 = Unknown ;
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()