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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, 01 Dec 2015 12:39:37 +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/2015/Dec/01/t1448973658o1q29rp2myaiu3h.htm/, Retrieved Thu, 16 May 2024 04:34:32 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=284706, Retrieved Thu, 16 May 2024 04:34:32 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact64

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [ML Fitting and QQ Plot- Normal Distribution] [Paper - Histogram...] [2015-12-01 12:09:02] [e7b69f276c668efa4454b31fcaf26444]
- RMPD    [Pearson Correlation] [Paper - Pearson C...] [2015-12-01 12:39:37] [024df7c298481a95aca593c6dd9022cb] [Current]
- RMP       [Bivariate Kernel Density Estimation] [Paper - Kernel De...] [2015-12-01 12:55:39] [e7b69f276c668efa4454b31fcaf26444]
-    D      [Pearson Correlation] [Paper - Pearson C...] [2015-12-01 13:34:15] [e7b69f276c668efa4454b31fcaf26444]
-    D      [Pearson Correlation] [Paper - Pearson C...] [2015-12-01 13:47:34] [e7b69f276c668efa4454b31fcaf26444]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
11
19
16
24
15
17
19
19
28
26
15
26
16
24
25
22
15
21
22
27
26
26
22
21
22
20
21
20
22
21
8
22
20
24
17
20
23
20
22
19
15
20
22
17
14
24
17
23
25
16
18
20
18
23
24
23
13
20
20
19
22
22
15
17
19
20
22
21
21
16
20
21
20
23
18
16
17
24
13
19
20
22
19
21
15
21
24
22
20
21
19
14
25
11
17
22
20
22
15
23
20
22
16
25
18
19
25
21
22
21
22
23
20
6
15
18
24
22
21
23
20
20
18
25
16
20
14
22
26
20
17
22
22
20
17
22
17
22
21
25
11
19
24
17
22
17
26
20
19
21
24
21
19
13
24
28
27
22
23
19
18
23
21
22
17
15
21
20
26
19
28
21
19
22
21
20
19
11
17
19
20
17
21
21
12
23
22
22
21
20
18
21
24
22
20
17
19
16
19
23
8
22
23
15
17
21
25
18
20
21
21
24
22
22
23
17
15
22
19
18
21
20
19
19
16
18
23
22
23
20
24
25
25
20
23
21
23
23
11
21
27
19
21
16
21
22
16
18
23
24
20
20
18
4
14
22
17
23
20
18
19
20
15
24
21
19
19
27
23
23
20
17
21
23
22
16
20
16
Dataseries Y:
Download CSV
Histogram 
12.9
12.2
12.8
7.4
6.7
12.6
14.8
13.3
11.1
8.2
11.4
6.4
10.6
12
6.3
11.3
11.9
9.3
9.6
10
6.4
13.8
10.8
13.8
11.7
10.9
16.1
13.4
9.9
11.5
8.3
11.7
9
9.7
10.8
10.3
10.4
12.7
9.3
11.8
5.9
11.4
13
10.8
12.3
11.3
11.8
7.9
12.7
12.3
11.6
6.7
10.9
12.1
13.3
10.1
5.7
14.3
8
13.3
9.3
12.5
7.6
15.9
9.2
9.1
11.1
13
14.5
12.2
12.3
11.4
8.8
14.6
12.6
13
12.6
13.2
9.9
7.7
10.5
13.4
10.9
4.3
10.3
11.8
11.2
11.4
8.6
13.2
12.6
5.6
9.9
8.8
7.7
9
7.3
11.4
13.6
7.9
10.7
10.3
8.3
9.6
14.2
8.5
13.5
4.9
6.4
9.6
11.6
11.1
4.35
12.7
18.1
17.85
16.6
12.6
17.1
19.1
16.1
13.35
18.4
14.7
10.6
12.6
16.2
13.6
18.9
14.1
14.5
16.15
14.75
14.8
12.45
12.65
17.35
8.6
18.4
16.1
11.6
17.75
15.25
17.65
16.35
17.65
13.6
14.35
14.75
18.25
9.9
16
18.25
16.85
14.6
13.85
18.95
15.6
14.85
11.75
18.45
15.9
17.1
16.1
19.9
10.95
18.45
15.1
15
11.35
15.95
18.1
14.6
15.4
15.4
17.6
13.35
19.1
15.35
7.6
13.4
13.9
19.1
15.25
12.9
16.1
17.35
13.15
12.15
12.6
10.35
15.4
9.6
18.2
13.6
14.85
14.75
14.1
14.9
16.25
19.25
13.6
13.6
15.65
12.75
14.6
9.85
12.65
19.2
16.6
11.2
15.25
11.9
13.2
16.35
12.4
15.85
18.15
11.15
15.65
17.75
7.65
12.35
15.6
19.3
15.2
17.1
15.6
18.4
19.05
18.55
19.1
13.1
12.85
9.5
4.5
11.85
13.6
11.7
12.4
13.35
11.4
14.9
19.9
11.2
14.6
17.6
14.05
16.1
13.35
11.85
11.95
14.75
15.15
13.2
16.85
7.85
7.7
12.6
7.85
10.95
12.35
9.95
14.9
16.65
13.4
13.95
15.7
16.85
10.95
15.35
12.2
15.1
17.75
15.2
14.6
16.65
8.1

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 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 & 4 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284706&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]4 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=284706&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284706&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 time4 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean20.046762589928112.975
Biased Variance13.749611821334311.4802293165468
Biased Standard Deviation3.70804690117783.3882487093699
Covariance0.330776173285198
Correlation0.0262330442297796
Determination0.000688172609561574
T-Test0.435966098172947
p-value (2 sided)0.663202120342332
p-value (1 sided)0.331601060171166
95% CI of Correlation[-0.0916929344476061, 0.143433391540727]
Degrees of Freedom276
Number of Observations278

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 20.0467625899281 & 12.975 \tabularnewline
Biased Variance & 13.7496118213343 & 11.4802293165468 \tabularnewline
Biased Standard Deviation & 3.7080469011778 & 3.3882487093699 \tabularnewline
Covariance & 0.330776173285198 \tabularnewline
Correlation & 0.0262330442297796 \tabularnewline
Determination & 0.000688172609561574 \tabularnewline
T-Test & 0.435966098172947 \tabularnewline
p-value (2 sided) & 0.663202120342332 \tabularnewline
p-value (1 sided) & 0.331601060171166 \tabularnewline
95% CI of Correlation & [-0.0916929344476061, 0.143433391540727] \tabularnewline
Degrees of Freedom & 276 \tabularnewline
Number of Observations & 278 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284706&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]20.0467625899281[/C][C]12.975[/C][/ROW]
[ROW][C]Biased Variance[/C][C]13.7496118213343[/C][C]11.4802293165468[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]3.7080469011778[/C][C]3.3882487093699[/C][/ROW]
[ROW][C]Covariance[/C][C]0.330776173285198[/C][/ROW]
[ROW][C]Correlation[/C][C]0.0262330442297796[/C][/ROW]
[ROW][C]Determination[/C][C]0.000688172609561574[/C][/ROW]
[ROW][C]T-Test[/C][C]0.435966098172947[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0.663202120342332[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0.331601060171166[/C][/ROW]
[ROW][C]95% CI of Correlation[/C][C][-0.0916929344476061, 0.143433391540727][/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]276[/C][/ROW]
[ROW][C]Number of Observations[/C][C]278[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284706&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284706&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
Mean20.046762589928112.975
Biased Variance13.749611821334311.4802293165468
Biased Standard Deviation3.70804690117783.3882487093699
Covariance0.330776173285198
Correlation0.0262330442297796
Determination0.000688172609561574
T-Test0.435966098172947
p-value (2 sided)0.663202120342332
p-value (1 sided)0.331601060171166
95% CI of Correlation[-0.0916929344476061, 0.143433391540727]
Degrees of Freedom276
Number of Observations278






Normality Tests
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 72.914, p-value < 2.2e-16
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 3.2947, p-value = 0.1926
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 3.1274, p-value = 7.347e-08

> ad.y
	Anderson-Darling normality test
data:  y
A = 0.42625, p-value = 0.3124


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

> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 72.914, p-value < 2.2e-16
alternative hypothesis: greater

 \tabularnewline

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 3.2947, p-value = 0.1926
alternative hypothesis: greater

 \tabularnewline

> ad.x
	Anderson-Darling normality test
data:  x
A = 3.1274, p-value = 7.347e-08

 \tabularnewline

> ad.y
	Anderson-Darling normality test
data:  y
A = 0.42625, p-value = 0.3124

 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284706&T=2

[TABLE]
[ROW][C]Normality Tests[/C][/ROW]
[ROW][C]
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 72.914, p-value < 2.2e-16
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 3.2947, p-value = 0.1926
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> ad.x
	Anderson-Darling normality test
data:  x
A = 3.1274, p-value = 7.347e-08

[/C][/ROW]
[ROW][C]
> ad.y
	Anderson-Darling normality test
data:  y
A = 0.42625, p-value = 0.3124

[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284706&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284706&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 = 72.914, p-value < 2.2e-16
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 3.2947, p-value = 0.1926
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 3.1274, p-value = 7.347e-08

> ad.y
	Anderson-Darling normality test
data:  y
A = 0.42625, p-value = 0.3124


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$estimate)[1,1]
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Pearson Product Moment Correlation - Ungrouped Data',3,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Statistic',1,TRUE)
a<-table.element(a,'Variable X',1,TRUE)
a<-table.element(a,'Variable Y',1,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('arithmetic_mean.htm','Mean',''),header=TRUE)
a<-table.element(a,mean(x))
a<-table.element(a,mean(y))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('biased.htm','Biased Variance',''),header=TRUE)
a<-table.element(a,varx)
a<-table.element(a,vary)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('biased1.htm','Biased Standard Deviation',''),header=TRUE)
a<-table.element(a,sqrt(varx))
a<-table.element(a,sqrt(vary))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('covariance.htm','Covariance',''),header=TRUE)
a<-table.element(a,cov(x,y),2)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('pearson_correlation.htm','Correlation',''),header=TRUE)
a<-table.element(a,cxy,2)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('coeff_of_determination.htm','Determination',''),header=TRUE)
a<-table.element(a,cxy*cxy,2)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('ttest_statistic.htm','T-Test',''),header=TRUE)
a<-table.element(a,as.matrix(corxy$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,'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')
qq.plot(x,main='QQplot of variable x')
dev.off()
bitmap(file='test3.png')
qq.plot(y,main='QQplot of variable y')
dev.off()