FreeStatistics.org

Free Statistics

of Irreproducible Research!

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 computationWed, 14 Dec 2016 19:18:27 +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/2016/Dec/14/t1481739563qpvjm0xttls7g3z.htm/, Retrieved Fri, 01 Nov 2024 03:32:39 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=299679, Retrieved Fri, 01 Nov 2024 03:32:39 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact100

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] [2016-12-14 18:18:27] [764c82b5188e0f78ebd58145511e4f2b] [Current]
Feedback Forum

Post a new message

Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
10
13
14
NA
NA
13
NA
NA
NA
14
14
12
12
11
12
14
NA
NA
NA
NA
13
NA
13
NA
NA
NA
12
12
13
13
10
12
13
NA
10
14
NA
10
10
14
NA
14
10
13
12
12
NA
12
10
NA
14
NA
NA
8
11
10
NA
14
12
NA
14
13
13
13
12
10
14
11
10
13
NA
NA
NA
NA
NA
12
13
11
10
14
NA
7
NA
13
NA
15
13
14
NA
13
11
NA
14
NA
14
NA
12
13
14
13
NA
NA
12
10
NA
NA
NA
NA
NA
12
NA
NA
NA
9
NA
12
13
NA
13
11
12
11
NA
12
NA
12
13
NA
NA
NA
8
NA
13
NA
8
NA
13
NA
12
15
14
NA
11
NA
10
14
10
15
11
NA
NA
12
13
12
9
NA
14
NA
NA
14
12
15
11
NA
NA
NA
12
NA
11
Dataseries Y:
Download CSV
Histogram 
18
21
21
18
21
21
17
19
23
23
21
20
20
19
19
20
20
NA
21
21
19
22
21
20
21
19
20
20
20
21
19
23
22
NA
18
21
19
19
19
20
21
23
18
23
20
20
20
18
21
NA
21
23
22
21
19
20
17
18
20
21
24
20
22
17
22
18
19
20
20
20
19
23
NA
20
22
19
21
20
19
19
21
18
21
22
22
21
23
22
20
NA
17
19
21
21
21
20
21
22
23
23
20
22
21
22
NA
24
NA
18
20
20
19
20
20
19
19
19
19
20
23
19
19
19
20
21
21
19
19
21
18
18
15
20
21
17
18
19
23
NA
21
24
23
20
20
20
20
22
22
21
19
20
17
20
19
21
20
21
22
19
17
21
20
19
22
21
20
20
21
21
19

Tables (Output of Computation)





Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time5 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 time5 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299679&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]5 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=299679&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299679&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 time5 seconds
R ServerBig Analytics Cloud Computing Center






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean12.127450980392220.3235294117647
Biased Variance2.895520953479432.70905420991926
Biased Standard Deviation1.701623035069591.64592047496811
Covariance1.39400116482236
Correlation0.492847019881576
Determination0.24289818500615
T-Test5.6641531979683
p-value (2 sided)1.42382353885832e-07
p-value (1 sided)7.11911769429158e-08
95% CI of Correlation[0.330001577392972, 0.627206452903519]
Degrees of Freedom100
Number of Observations102

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 12.1274509803922 & 20.3235294117647 \tabularnewline
Biased Variance & 2.89552095347943 & 2.70905420991926 \tabularnewline
Biased Standard Deviation & 1.70162303506959 & 1.64592047496811 \tabularnewline
Covariance & 1.39400116482236 \tabularnewline
Correlation & 0.492847019881576 \tabularnewline
Determination & 0.24289818500615 \tabularnewline
T-Test & 5.6641531979683 \tabularnewline
p-value (2 sided) & 1.42382353885832e-07 \tabularnewline
p-value (1 sided) & 7.11911769429158e-08 \tabularnewline
95% CI of Correlation & [0.330001577392972, 0.627206452903519] \tabularnewline
Degrees of Freedom & 100 \tabularnewline
Number of Observations & 102 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299679&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]12.1274509803922[/C][C]20.3235294117647[/C][/ROW]
[ROW][C]Biased Variance[/C][C]2.89552095347943[/C][C]2.70905420991926[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]1.70162303506959[/C][C]1.64592047496811[/C][/ROW]
[ROW][C]Covariance[/C][C]1.39400116482236[/C][/ROW]
[ROW][C]Correlation[/C][C]0.492847019881576[/C][/ROW]
[ROW][C]Determination[/C][C]0.24289818500615[/C][/ROW]
[ROW][C]T-Test[/C][C]5.6641531979683[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]1.42382353885832e-07[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]7.11911769429158e-08[/C][/ROW]
[ROW][C]95% CI of Correlation[/C][C][0.330001577392972, 0.627206452903519][/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]100[/C][/ROW]
[ROW][C]Number of Observations[/C][C]102[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299679&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299679&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
Mean12.127450980392220.3235294117647
Biased Variance2.895520953479432.70905420991926
Biased Standard Deviation1.701623035069591.64592047496811
Covariance1.39400116482236
Correlation0.492847019881576
Determination0.24289818500615
T-Test5.6641531979683
p-value (2 sided)1.42382353885832e-07
p-value (1 sided)7.11911769429158e-08
95% CI of Correlation[0.330001577392972, 0.627206452903519]
Degrees of Freedom100
Number of Observations102






Normality Tests
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 6.7302, p-value = 0.03456
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 0.11092, p-value = 0.9461
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 2.4197, p-value = 3.674e-06

> ad.y
	Anderson-Darling normality test
data:  y
A = 1.7926, p-value = 0.0001288


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

> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 6.7302, p-value = 0.03456
alternative hypothesis: greater

 \tabularnewline

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 0.11092, p-value = 0.9461
alternative hypothesis: greater

 \tabularnewline

> ad.x
	Anderson-Darling normality test
data:  x
A = 2.4197, p-value = 3.674e-06

 \tabularnewline

> ad.y
	Anderson-Darling normality test
data:  y
A = 1.7926, p-value = 0.0001288

 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299679&T=2

[TABLE]
[ROW][C]Normality Tests[/C][/ROW]
[ROW][C]
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 6.7302, p-value = 0.03456
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 0.11092, p-value = 0.9461
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> ad.x
	Anderson-Darling normality test
data:  x
A = 2.4197, p-value = 3.674e-06

[/C][/ROW]
[ROW][C]
> ad.y
	Anderson-Darling normality test
data:  y
A = 1.7926, p-value = 0.0001288

[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299679&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299679&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 = 6.7302, p-value = 0.03456
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 0.11092, p-value = 0.9461
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 2.4197, p-value = 3.674e-06

> ad.y
	Anderson-Darling normality test
data:  y
A = 1.7926, p-value = 0.0001288


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()