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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 computationMon, 29 Apr 2019 17:06:28 +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/Apr/29/t1556550678zwdy4yfpfry0ihs.htm/, Retrieved Sun, 12 May 2024 11:27:43 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Sun, 12 May 2024 11:27:43 +0200
QR Codes:

Original text written by user:These are the data for April
IsPrivate?This computation is private
User-defined keywordsHubpages Impressions and CPM
Estimated Impact0

Tree of Dependent Computations

Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
229
377
2372
382
399
301
238
241
263
362
376
319
373
237
211
313
383
380
385
388
217
218
307
339
339
335
368
Dataseries Y:
Download CSV
Histogram 
7.10
5.06
1.16
5.10
4.78
5.39
6.87
5.84
6.99
5.40
6.77
6.21
5.59
7.07
5.63
5.94
4.69
4.92
5.12
4.64
7.28
5.88
5.00
5.57
4.77
5.10
5.06

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=&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=&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
Mean394.5185185185195.51592592592593
Biased Variance154308.9903978051.39357969821674
Biased Standard Deviation392.8218303478121.18049976629254
Covariance-381.268190883191
Correlation-0.791732799741002
Determination0.626840826185726
T-Test-6.48039651926834
p-value (2 sided)8.7015116620502e-07
p-value (1 sided)4.3507558310251e-07
95% CI of Correlation[-0.900741193920238, -0.588901279990885]
Degrees of Freedom25
Number of Observations27

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 394.518518518519 & 5.51592592592593 \tabularnewline
Biased Variance & 154308.990397805 & 1.39357969821674 \tabularnewline
Biased Standard Deviation & 392.821830347812 & 1.18049976629254 \tabularnewline
Covariance & -381.268190883191 \tabularnewline
Correlation & -0.791732799741002 \tabularnewline
Determination & 0.626840826185726 \tabularnewline
T-Test & -6.48039651926834 \tabularnewline
p-value (2 sided) & 8.7015116620502e-07 \tabularnewline
p-value (1 sided) & 4.3507558310251e-07 \tabularnewline
95% CI of Correlation & [-0.900741193920238, -0.588901279990885] \tabularnewline
Degrees of Freedom & 25 \tabularnewline
Number of Observations & 27 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]394.518518518519[/C][C]5.51592592592593[/C][/ROW]
[ROW][C]Biased Variance[/C][C]154308.990397805[/C][C]1.39357969821674[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]392.821830347812[/C][C]1.18049976629254[/C][/ROW]
[ROW][C]Covariance[/C][C]-381.268190883191[/C][/ROW]
[ROW][C]Correlation[/C][C]-0.791732799741002[/C][/ROW]
[ROW][C]Determination[/C][C]0.626840826185726[/C][/ROW]
[ROW][C]T-Test[/C][C]-6.48039651926834[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]8.7015116620502e-07[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]4.3507558310251e-07[/C][/ROW]
[ROW][C]95% CI of Correlation[/C][C][-0.900741193920238, -0.588901279990885][/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]25[/C][/ROW]
[ROW][C]Number of Observations[/C][C]27[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
Mean394.5185185185195.51592592592593
Biased Variance154308.9903978051.39357969821674
Biased Standard Deviation392.8218303478121.18049976629254
Covariance-381.268190883191
Correlation-0.791732799741002
Determination0.626840826185726
T-Test-6.48039651926834
p-value (2 sided)8.7015116620502e-07
p-value (1 sided)4.3507558310251e-07
95% CI of Correlation[-0.900741193920238, -0.588901279990885]
Degrees of Freedom25
Number of Observations27






Normality Tests
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 585.93, p-value < 2.2e-16
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 32.424, p-value = 9.104e-08
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 6.7301, p-value < 2.2e-16

> ad.y
	Anderson-Darling normality test
data:  y
A = 1.108, p-value = 0.005501


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

> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 585.93, p-value < 2.2e-16
alternative hypothesis: greater

 \tabularnewline

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 32.424, p-value = 9.104e-08
alternative hypothesis: greater

 \tabularnewline

> ad.x
	Anderson-Darling normality test
data:  x
A = 6.7301, p-value < 2.2e-16

 \tabularnewline

> ad.y
	Anderson-Darling normality test
data:  y
A = 1.108, p-value = 0.005501

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

[TABLE]
[ROW][C]Normality Tests[/C][/ROW]
[ROW][C]
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 585.93, p-value < 2.2e-16
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 32.424, p-value = 9.104e-08
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> ad.x
	Anderson-Darling normality test
data:  x
A = 6.7301, p-value < 2.2e-16

[/C][/ROW]
[ROW][C]
> ad.y
	Anderson-Darling normality test
data:  y
A = 1.108, p-value = 0.005501

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

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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 = 585.93, p-value < 2.2e-16
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 32.424, p-value = 9.104e-08
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 6.7301, p-value < 2.2e-16

> ad.y
	Anderson-Darling normality test
data:  y
A = 1.108, p-value = 0.005501


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()