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 computationThu, 07 Dec 2017 11:24:27 +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/2017/Dec/07/t1512642411uk16vv8nan94zvt.htm/, Retrieved Wed, 15 May 2024 01:00:24 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=308669, Retrieved Wed, 15 May 2024 01:00:24 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact140

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Pearson Correlation] [correlatie tss. p...] [2017-12-07 10:24:27] [cda93ecb4418fdfcddc4dd0935c61e4c] [Current]
Feedback Forum

Post a new message

Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
9
7
8
8
5
10
9
7
6
8
8
9
9
6
8
7
7
8
8
9
9
8
9
7
8
4
8
2
6
5
7
8
6
3
8
9
7
5
8
2
6
4
6
7
1
4
6
7
3
7
2
2
7
6
4
1
2
7
6
3
3
7
5
6
4
0
3
4
4
0
3
1
3
0
4
0
6
3
5
0
1
5
5
4
4
3
Dataseries Y:
Download CSV
Histogram 
7
7
6
6
8
7
8
7
0
7
7
8
9
8
8
7
5
7
5
8
9
4
5
7
5
1
8
0
7
0
8
6
6
0
3
8
6
1
0
1
4
6
1
8
2
8
7
5
4
7
4
6
7
6
6
1
2
3
6
0
0
5
8
2
1
8
6
5
4
0
5
0
5
4
2
1
2
4
2
1
4
3
1
5
3
5

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=308669&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=308669&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308669&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
Mean5.337209302325584.63953488372093
Biased Variance7.014196863169287.53285559762034
Biased Standard Deviation2.648432907054522.74460481629329
Covariance4.01709986320109
Correlation0.546215859947569
Determination0.298351765658262
T-Test5.97646294116047
p-value (2 sided)5.33319310062003e-08
p-value (1 sided)2.66659655031002e-08
95% CI of Correlation[0.378097651347465, 0.679457764781812]
Degrees of Freedom84
Number of Observations86

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 5.33720930232558 & 4.63953488372093 \tabularnewline
Biased Variance & 7.01419686316928 & 7.53285559762034 \tabularnewline
Biased Standard Deviation & 2.64843290705452 & 2.74460481629329 \tabularnewline
Covariance & 4.01709986320109 \tabularnewline
Correlation & 0.546215859947569 \tabularnewline
Determination & 0.298351765658262 \tabularnewline
T-Test & 5.97646294116047 \tabularnewline
p-value (2 sided) & 5.33319310062003e-08 \tabularnewline
p-value (1 sided) & 2.66659655031002e-08 \tabularnewline
95% CI of Correlation & [0.378097651347465, 0.679457764781812] \tabularnewline
Degrees of Freedom & 84 \tabularnewline
Number of Observations & 86 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=308669&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]5.33720930232558[/C][C]4.63953488372093[/C][/ROW]
[ROW][C]Biased Variance[/C][C]7.01419686316928[/C][C]7.53285559762034[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]2.64843290705452[/C][C]2.74460481629329[/C][/ROW]
[ROW][C]Covariance[/C][C]4.01709986320109[/C][/ROW]
[ROW][C]Correlation[/C][C]0.546215859947569[/C][/ROW]
[ROW][C]Determination[/C][C]0.298351765658262[/C][/ROW]
[ROW][C]T-Test[/C][C]5.97646294116047[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]5.33319310062003e-08[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]2.66659655031002e-08[/C][/ROW]
[ROW][C]95% CI of Correlation[/C][C][0.378097651347465, 0.679457764781812][/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]84[/C][/ROW]
[ROW][C]Number of Observations[/C][C]86[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=308669&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308669&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
Mean5.337209302325584.63953488372093
Biased Variance7.014196863169287.53285559762034
Biased Standard Deviation2.648432907054522.74460481629329
Covariance4.01709986320109
Correlation0.546215859947569
Determination0.298351765658262
T-Test5.97646294116047
p-value (2 sided)5.33319310062003e-08
p-value (1 sided)2.66659655031002e-08
95% CI of Correlation[0.378097651347465, 0.679457764781812]
Degrees of Freedom84
Number of Observations86






Normality Tests
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 4.7203, p-value = 0.09441
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 6.6259, p-value = 0.03641
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 1.4886, p-value = 0.0007178

> ad.y
	Anderson-Darling normality test
data:  y
A = 2.3698, p-value = 4.778e-06


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

> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 4.7203, p-value = 0.09441
alternative hypothesis: greater

 \tabularnewline

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 6.6259, p-value = 0.03641
alternative hypothesis: greater

 \tabularnewline

> ad.x
	Anderson-Darling normality test
data:  x
A = 1.4886, p-value = 0.0007178

 \tabularnewline

> ad.y
	Anderson-Darling normality test
data:  y
A = 2.3698, p-value = 4.778e-06

 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=308669&T=2

[TABLE]
[ROW][C]Normality Tests[/C][/ROW]
[ROW][C]
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 4.7203, p-value = 0.09441
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 6.6259, p-value = 0.03641
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> ad.x
	Anderson-Darling normality test
data:  x
A = 1.4886, p-value = 0.0007178

[/C][/ROW]
[ROW][C]
> ad.y
	Anderson-Darling normality test
data:  y
A = 2.3698, p-value = 4.778e-06

[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=308669&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308669&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 = 4.7203, p-value = 0.09441
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 6.6259, p-value = 0.03641
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 1.4886, p-value = 0.0007178

> ad.y
	Anderson-Darling normality test
data:  y
A = 2.3698, p-value = 4.778e-06


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()