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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 computationWed, 27 Jun 2018 03:11:21 +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/2018/Jun/27/t1530062012soayyn43rudqfss.htm/, Retrieved Thu, 09 May 2024 01:44:30 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=315080, Retrieved Thu, 09 May 2024 01:44:30 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact132

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Pearson Correlation] [] [2018-06-27 01:11:21] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
35
38
40
27
24
36
28
35
35
25
28
39
38
25
36
34
28
39
29
34
38
31
40
27
27
38
36
Dataseries Y:
Download CSV
Histogram 
88.00
84.75
89.20
90.00
91.20
89.00
88.00
89.60
89.60
83.75
89.80
90.00
89.40
92.20
90.40
92.00
91.00
90.60
91.50
91.80
89.60
87.60
89.20
90.00
88.00
89.80
88.25

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=315080&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=315080&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=315080&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
Mean32.96296296296389.4166666666667
Biased Variance26.77640603566533.65740740740741
Biased Standard Deviation5.174592354540141.9124349420065
Covariance-0.418589743589745
Correlation-0.0407319642721479
Determination0.00165909291346754
T-Test-0.203828977156941
p-value (2 sided)0.840137267229248
p-value (1 sided)0.420068633614624
95% CI of Correlation[-0.414332593869995, 0.344616217895029]
Degrees of Freedom25
Number of Observations27

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 32.962962962963 & 89.4166666666667 \tabularnewline
Biased Variance & 26.7764060356653 & 3.65740740740741 \tabularnewline
Biased Standard Deviation & 5.17459235454014 & 1.9124349420065 \tabularnewline
Covariance & -0.418589743589745 \tabularnewline
Correlation & -0.0407319642721479 \tabularnewline
Determination & 0.00165909291346754 \tabularnewline
T-Test & -0.203828977156941 \tabularnewline
p-value (2 sided) & 0.840137267229248 \tabularnewline
p-value (1 sided) & 0.420068633614624 \tabularnewline
95% CI of Correlation & [-0.414332593869995, 0.344616217895029] \tabularnewline
Degrees of Freedom & 25 \tabularnewline
Number of Observations & 27 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=315080&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]32.962962962963[/C][C]89.4166666666667[/C][/ROW]
[ROW][C]Biased Variance[/C][C]26.7764060356653[/C][C]3.65740740740741[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]5.17459235454014[/C][C]1.9124349420065[/C][/ROW]
[ROW][C]Covariance[/C][C]-0.418589743589745[/C][/ROW]
[ROW][C]Correlation[/C][C]-0.0407319642721479[/C][/ROW]
[ROW][C]Determination[/C][C]0.00165909291346754[/C][/ROW]
[ROW][C]T-Test[/C][C]-0.203828977156941[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0.840137267229248[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0.420068633614624[/C][/ROW]
[ROW][C]95% CI of Correlation[/C][C][-0.414332593869995, 0.344616217895029][/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=315080&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=315080&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
Mean32.96296296296389.4166666666667
Biased Variance26.77640603566533.65740740740741
Biased Standard Deviation5.174592354540141.9124349420065
Covariance-0.418589743589745
Correlation-0.0407319642721479
Determination0.00165909291346754
T-Test-0.203828977156941
p-value (2 sided)0.840137267229248
p-value (1 sided)0.420068633614624
95% CI of Correlation[-0.414332593869995, 0.344616217895029]
Degrees of Freedom25
Number of Observations27






Normality Tests
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 2.5805, p-value = 0.2752
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 9.7502, p-value = 0.007634
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 1.057, p-value = 0.007412

> ad.y
	Anderson-Darling normality test
data:  y
A = 0.83414, p-value = 0.02728


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

> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 2.5805, p-value = 0.2752
alternative hypothesis: greater

 \tabularnewline

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 9.7502, p-value = 0.007634
alternative hypothesis: greater

 \tabularnewline

> ad.x
	Anderson-Darling normality test
data:  x
A = 1.057, p-value = 0.007412

 \tabularnewline

> ad.y
	Anderson-Darling normality test
data:  y
A = 0.83414, p-value = 0.02728

 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=315080&T=2

[TABLE]
[ROW][C]Normality Tests[/C][/ROW]
[ROW][C]
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 2.5805, p-value = 0.2752
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 9.7502, p-value = 0.007634
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> ad.x
	Anderson-Darling normality test
data:  x
A = 1.057, p-value = 0.007412

[/C][/ROW]
[ROW][C]
> ad.y
	Anderson-Darling normality test
data:  y
A = 0.83414, p-value = 0.02728

[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=315080&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=315080&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 = 2.5805, p-value = 0.2752
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 9.7502, p-value = 0.007634
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 1.057, p-value = 0.007412

> ad.y
	Anderson-Darling normality test
data:  y
A = 0.83414, p-value = 0.02728


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()