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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_correlation.wasp
Title produced by softwarePearson Correlation
Date of computationTue, 22 Oct 2019 09:45:03 +0200
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2019/Oct/22/t1571730530sxaake7e78xg6fa.htm/, Retrieved Tue, 07 May 2024 14:06:14 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=318929, Retrieved Tue, 07 May 2024 14:06:14 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact76

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Pearson Correlation] [Dates:A1c] [2019-10-22 07:45:03] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
7.00
28.00
2.00
10.00
7.00
17.00
4.00
18.00
10.00
17.00
6.00
30.00
40.00
11.00
24.00
6.00
1.00
18.00
25.00
10.00
14.00
2.00
8.00
7.00
48.00
6.00
22.00
2.00
14.00
4.00
10.00
5.00
5.00
22.00
23.00
0.00
10.00
36.00
12.00
2.00
10.00
75.00
7.00
6.00
3.00
6.00
1.00
14.00
5.00
3.00
14.00
2.00
7.00
22.00
6.00
3.00
32.00
1.00
18.00
3.00
5.00
2.00
1.00
25.00
7.00
0.42
15.00
12.00
2.00
2.00
3.42
9.00
30.00
20.00
12.00
16.00
8.00
0.00
15.00
35.00
14.00
22.00
6.00
3.00
12.00
5.00
20.00
24.00
34.00
12.00
3.00
32.00
18.00
20.00
12.00
14.00
0.00
6.00
3.00
6.00
20.00
3.00
30.00
16.00
3.00
3.00
14.00
26.00
22.00
10.00
5.00
6.00
20.00
5.00
2.00
6.00
14.00
5.00
20.00
7.00
14.00
0.00
4.00
3.00
13.00
7.00
14.00
26.00
36.00
5.00
5.00
3.00
0.00
36.00
12.00
3.00
6.00
28.00
14.00
40.00
24.00
30.00
28.00
10.00
10.00
25.00
27.00
3.00
3.00
14.00
24.00
11.00
28.00
7.00
12.00
6.00
36.00
15.00
6.00
10.00
6.00
7.00
3.00
7.00
14.00
8.00
6.00
10.00
9.00
8.00
3.00
7.00
7.00
1.00
42.00
14.00
42.00
1.00
9.00
20.00
0.42
26.00
9.00
2.00
24.00
14.00
8.00
26.00
14.00
14.00
2.00
16.00
25.00
0.24
0.00
15.00
18.00
18.00
24.00
22.00
14.00
18.00
10.00
24.00
20.00
2.00
18.00
0.00
12.00
28.00
24.00
10.00
14.00
6.00
10.00
1.00
6.00
10.00
20.00
10.00
3.00
40.00
22.00
40.00
2.00
20.00
6.00
3.00
3.00
14.00
48.00
5.00
20.00
3.14
10.00
18.00
12.00
6.00
9.00
22.00
12.00
6.00
4.00
7.00
14.00
9.00
0.56
0.00
42.00
14.00
5.00
10.00
22.00
13.00
36.00
8.00
10.00
5.00
3.00
8.00
7.00
1.00
7.00
10.00
30.00
15.00
20.00
16.00
10.00
6.00
20.00
18.00
11.00
4.00
7.00
30.00
9.00
14.00
8.00
5.00
36.00
14.00
14.00
20.00
24.00
20.00
2.00
35.00
11.00
20.00
10.00
6.00
6.00
26.00
5.00
7.00
16.00
2.00
10.00
8.00
16.00
21.00
30.00
30.00
6.00
16.00
10.00
26.00
14.00
10.00
14.00
23.00
28.00
10.00
24.00
14.00
4.00
14.00
0.00
11.00
30.00
36.00
18.00
6.00
4.00
34.00
11.00
24.00
30.00
36.00
36.00
3.00
34.00
10.00
10.00
7.00
14.00
50.00
34.00
16.00
23.00
0.00
18.00
1.00
10.00
4.00
16.00
5.00
5.00
50.00
13.00
6.00
32.00
10.00
0.00
36.00
5.00
10.00
20.00
10.00
17.00
8.00
0.00
8.00
6.00
20.00
30.00
8.00
26.00
17.00
16.00
0.42
18.00
4.00
14.00
40.00
30.00
30.00
15.00
6.00
2.00
26.00
11.00
30.00
3.00
11.00
18.00
14.00
4.00
6.00
10.00
12.00
22.00
9.00
22.00
5.00
12.00
10.00
20.00
28.00
46.00
12.00
6.00
4.00
Dataseries Y:
Download CSV
Histogram 
6.80
7.20
8.30
9.60
8.40
7.10
10.10
6.00
10.20
7.70
9.40
7.00
11.30
8.30
11.10
7.00
6.90
9.00
8.20
8.60
8.00
8.10
7.40
8.40
8.20
9.70
6.20
7.70
9.70
8.60
7.40
9.50
8.30
8.70
7.00
10.50
8.50
8.50
8.40
7.50
7.90
6.90
5.30
10.60
8.70
6.60
9.00
7.20
9.80
7.40
8.40
7.50
7.40
9.40
4.90
10.30
7.50
6.40
9.30
13.70
8.50
8.60
10.80
7.40
8.40
6.70
8.70
5.50
10.30
7.90
6.90
9.90
6.80
7.40
10.50
7.70
7.50
8.80
7.40
8.20
8.20
7.00
11.90
10.50
9.30
7.80
8.70
8.10
9.50
8.70
12.20
8.30
8.40
7.80
10.60
7.60
7.50
8.20
7.80
7.80
12.10
7.80
7.10
8.40
7.30
8.10
9.00
6.90
8.10
9.20
8.40
9.80
7.00
7.40
7.40
8.30
9.50
11.20
6.60
7.10
7.30
9.10
9.60
8.40
8.80
9.60
10.30
7.20
7.30
7.60
7.30
12.10
7.80
7.70
8.70
6.40
8.30
9.10
9.20
9.80
9.80
8.40
7.50
7.00
7.60
6.20
7.40
8.30
10.50
7.10
9.50
9.60
7.80
7.50
9.60
7.40
6.30
7.40
8.00
8.00
6.30
9.10
10.50
8.30
7.20
8.10
7.20
7.10
9.20
8.90
5.90
11.30
8.10
10.00
7.20
9.70
7.00
8.80
6.80
5.80
8.80
7.50
6.50
14.00
7.40
12.10
8.10
9.20
6.50
6.40
10.20
7.00
8.60
7.30
8.50
6.90
7.20
6.90
6.50
7.90
7.80
9.20
7.50
7.30
5.90
6.70
12.40
8.60
7.40
9.50
12.10
7.40
6.80
6.30
10.00
6.80
10.60
10.40
8.80
9.40
8.90
5.70
6.20
10.60
9.30
7.80
9.60
7.80
7.60
6.80
6.20
9.30
7.60
8.00
8.20
9.00
8.80
7.60
7.30
7.20
7.30
7.80
8.50
8.80
7.60
9.00
9.30
7.90
6.20
7.20
9.40
9.20
11.40
7.60
7.70
10.30
7.50
10.30
10.00
9.90
7.30
6.30
5.90
8.40
8.00
9.50
7.60
10.90
7.90
10.30
12.80
7.30
6.30
5.00
9.50
6.90
12.20
7.80
7.20
7.30
8.30
7.40
6.10
10.20
8.40
6.60
6.50
10.50
9.10
8.40
6.60
7.60
9.90
6.70
9.90
6.90
7.10
9.70
10.10
8.00
7.90
8.20
7.60
7.40
7.10
6.00
8.60
6.10
8.00
7.90
7.50
8.00
7.70
6.70
8.00
6.80
10.00
8.60
11.00
7.40
6.80
8.00
6.10
7.90
8.10
8.20
6.70
8.90
9.40
8.10
8.00
6.30
6.10
9.40
7.00
8.90
8.80
8.60
7.30
10.00
7.40
8.80
11.10
7.30
6.80
10.10
6.40
7.20
6.70
5.80
9.10
6.90
7.30
6.50
8.50
6.60
8.40
10.10
6.90
6.80
6.80
7.60
11.70
7.40
7.30
8.30
9.30
5.90
6.70
7.20
12.20
12.70
5.90
12.20
8.40
7.00
7.50
7.40
6.60
8.80
9.10
8.40
8.00
9.60
8.00
9.40
10.30
9.00
7.40
9.00
7.30
7.00
8.60
9.40
9.20
8.40
9.20
8.90
4.70
6.60
9.00
6.40
6.90
8.30

Tables (Output of Computation)





Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 time1 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=318929&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]1 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=318929&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=318929&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 time1 seconds
R ServerBig Analytics Cloud Computing Center






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean13.9347029702978.24306930693069
Biased Variance124.9860739216742.30631335163219
Biased Standard Deviation11.17971707699591.51865511279954
Covariance-2.83678866422622
Correlation-0.166671250621487
Determination0.0277793057837307
T-Test-3.38915389840056
p-value (2 sided)0.000770376483747265
p-value (1 sided)0.000385188241873633
95% CI of Correlation[-0.260007792095931, -0.0702490013980796]
Degrees of Freedom402
Number of Observations404

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 13.934702970297 & 8.24306930693069 \tabularnewline
Biased Variance & 124.986073921674 & 2.30631335163219 \tabularnewline
Biased Standard Deviation & 11.1797170769959 & 1.51865511279954 \tabularnewline
Covariance & -2.83678866422622 \tabularnewline
Correlation & -0.166671250621487 \tabularnewline
Determination & 0.0277793057837307 \tabularnewline
T-Test & -3.38915389840056 \tabularnewline
p-value (2 sided) & 0.000770376483747265 \tabularnewline
p-value (1 sided) & 0.000385188241873633 \tabularnewline
95% CI of Correlation & [-0.260007792095931, -0.0702490013980796] \tabularnewline
Degrees of Freedom & 402 \tabularnewline
Number of Observations & 404 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=318929&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]13.934702970297[/C][C]8.24306930693069[/C][/ROW]
[ROW][C]Biased Variance[/C][C]124.986073921674[/C][C]2.30631335163219[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]11.1797170769959[/C][C]1.51865511279954[/C][/ROW]
[ROW][C]Covariance[/C][C]-2.83678866422622[/C][/ROW]
[ROW][C]Correlation[/C][C]-0.166671250621487[/C][/ROW]
[ROW][C]Determination[/C][C]0.0277793057837307[/C][/ROW]
[ROW][C]T-Test[/C][C]-3.38915389840056[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0.000770376483747265[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0.000385188241873633[/C][/ROW]
[ROW][C]95% CI of Correlation[/C][C][-0.260007792095931, -0.0702490013980796][/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]402[/C][/ROW]
[ROW][C]Number of Observations[/C][C]404[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=318929&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=318929&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
Mean13.9347029702978.24306930693069
Biased Variance124.9860739216742.30631335163219
Biased Standard Deviation11.17971707699591.51865511279954
Covariance-2.83678866422622
Correlation-0.166671250621487
Determination0.0277793057837307
T-Test-3.38915389840056
p-value (2 sided)0.000770376483747265
p-value (1 sided)0.000385188241873633
95% CI of Correlation[-0.260007792095931, -0.0702490013980796]
Degrees of Freedom402
Number of Observations404






Normality Tests
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 186.19, p-value < 2.2e-16
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 50.589, p-value = 1.034e-11
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 10.532, p-value < 2.2e-16

> ad.y
	Anderson-Darling normality test
data:  y
A = 3.8839, p-value = 1.087e-09


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

> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 186.19, p-value < 2.2e-16
alternative hypothesis: greater

 \tabularnewline

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 50.589, p-value = 1.034e-11
alternative hypothesis: greater

 \tabularnewline

> ad.x
	Anderson-Darling normality test
data:  x
A = 10.532, p-value < 2.2e-16

 \tabularnewline

> ad.y
	Anderson-Darling normality test
data:  y
A = 3.8839, p-value = 1.087e-09

 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=318929&T=2

[TABLE]
[ROW][C]Normality Tests[/C][/ROW]
[ROW][C]
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 186.19, p-value < 2.2e-16
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 50.589, p-value = 1.034e-11
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> ad.x
	Anderson-Darling normality test
data:  x
A = 10.532, p-value < 2.2e-16

[/C][/ROW]
[ROW][C]
> ad.y
	Anderson-Darling normality test
data:  y
A = 3.8839, p-value = 1.087e-09

[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=318929&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=318929&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 = 186.19, p-value < 2.2e-16
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 50.589, p-value = 1.034e-11
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 10.532, p-value < 2.2e-16

> ad.y
	Anderson-Darling normality test
data:  y
A = 3.8839, p-value = 1.087e-09


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()