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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, 05 Dec 2017 15:06:12 +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/05/t1512483926zqt6j7nhz5yxdt9.htm/, Retrieved Tue, 14 May 2024 04:50:31 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=308553, Retrieved Tue, 14 May 2024 04:50:31 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact107

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
10
15
14
14
8
19
17
18
10
15
16
12
13
10
14
15
20
9
12
13
16
12
14
15
19
16
16
14
14
14
13
18
15
15
15
13
14
15
14
19
16
16
12
10
11
13
14
11
11
16
9
16
19
13
15
14
15
11
14
15
17
16
13
15
14
15
14
12
12
15
17
13
5
7
10
15
9
9
15
14
11
18
20
20
16
15
14
13
18
14
12
9
19
13
12
14
6
14
11
11
14
12
19
13
14
17
12
16
15
15
15
16
15
12
13
14
17
14
14
14
15
11
11
16
12
12
19
18
16
16
13
11
10
14
14
14
16
10
16
7
16
15
17
11
11
10
13
14
13
13
12
10
15
6
15
15
11
14
14
16
12
15
20
12
9
13
15
19
11
11
17
15
14
15
11
12
15
16
16
Dataseries Y:
Download CSV
Histogram 
36
32
33
39
34
39
36
33
30
39
37
37
35
32
36
36
41
36
37
29
39
37
32
36
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

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=308553&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=308553&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308553&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
Mean13.821229050279333.5418994413408
Biased Variance8.1691582659717221.0080209731282
Biased Standard Deviation2.858173939068744.58345077132156
Covariance5.94573473102756
Correlation0.451326957471739
Determination0.203696022540697
T-Test6.72881309440174
p-value (2 sided)2.28722756502875e-10
p-value (1 sided)1.14361378251438e-10
95% CI of Correlation[0.326251604390336, 0.560871163410057]
Degrees of Freedom177
Number of Observations179

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 13.8212290502793 & 33.5418994413408 \tabularnewline
Biased Variance & 8.16915826597172 & 21.0080209731282 \tabularnewline
Biased Standard Deviation & 2.85817393906874 & 4.58345077132156 \tabularnewline
Covariance & 5.94573473102756 \tabularnewline
Correlation & 0.451326957471739 \tabularnewline
Determination & 0.203696022540697 \tabularnewline
T-Test & 6.72881309440174 \tabularnewline
p-value (2 sided) & 2.28722756502875e-10 \tabularnewline
p-value (1 sided) & 1.14361378251438e-10 \tabularnewline
95% CI of Correlation & [0.326251604390336, 0.560871163410057] \tabularnewline
Degrees of Freedom & 177 \tabularnewline
Number of Observations & 179 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=308553&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]13.8212290502793[/C][C]33.5418994413408[/C][/ROW]
[ROW][C]Biased Variance[/C][C]8.16915826597172[/C][C]21.0080209731282[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]2.85817393906874[/C][C]4.58345077132156[/C][/ROW]
[ROW][C]Covariance[/C][C]5.94573473102756[/C][/ROW]
[ROW][C]Correlation[/C][C]0.451326957471739[/C][/ROW]
[ROW][C]Determination[/C][C]0.203696022540697[/C][/ROW]
[ROW][C]T-Test[/C][C]6.72881309440174[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]2.28722756502875e-10[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]1.14361378251438e-10[/C][/ROW]
[ROW][C]95% CI of Correlation[/C][C][0.326251604390336, 0.560871163410057][/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=308553&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308553&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
Mean13.821229050279333.5418994413408
Biased Variance8.1691582659717221.0080209731282
Biased Standard Deviation2.858173939068744.58345077132156
Covariance5.94573473102756
Correlation0.451326957471739
Determination0.203696022540697
T-Test6.72881309440174
p-value (2 sided)2.28722756502875e-10
p-value (1 sided)1.14361378251438e-10
95% CI of Correlation[0.326251604390336, 0.560871163410057]
Degrees of Freedom177
Number of Observations179






Normality Tests
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 3.2929, p-value = 0.1927
alternative hypothesis: greater

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

> ad.x
	Anderson-Darling normality test
data:  x
A = 1.6909, p-value = 0.0002371

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


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

> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 3.2929, p-value = 0.1927
alternative hypothesis: greater

 \tabularnewline

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

 \tabularnewline

> ad.x
	Anderson-Darling normality test
data:  x
A = 1.6909, p-value = 0.0002371

 \tabularnewline

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

 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=308553&T=2

[TABLE]
[ROW][C]Normality Tests[/C][/ROW]
[ROW][C]
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 3.2929, p-value = 0.1927
alternative hypothesis: greater

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

[/C][/ROW]
[ROW][C]
> ad.x
	Anderson-Darling normality test
data:  x
A = 1.6909, p-value = 0.0002371

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

[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=308553&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308553&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 = 3.2929, p-value = 0.1927
alternative hypothesis: greater

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

> ad.x
	Anderson-Darling normality test
data:  x
A = 1.6909, p-value = 0.0002371

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


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()