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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, 05 Aug 2020 23:46:38 +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/2020/Aug/05/t15966643777nr0snfgw9c19zo.htm/, Retrieved Fri, 26 Apr 2024 03:44:47 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=319210, Retrieved Fri, 26 Apr 2024 03:44:47 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact91

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
08
10
04
03
02
03
05
07
08
03
Dataseries Y:
Download CSV
Histogram 
90
300
600
340
60
240
500
520
550
540

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
R Framework error message
Warning: there are blank lines in the 'Data X' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.

\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
R Framework error message & 
Warning: there are blank lines in the 'Data X' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.
 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=319210&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] [ROW]R Framework error message[/C][C]
Warning: there are blank lines in the 'Data X' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.
[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=319210&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=319210&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
R Framework error message
Warning: there are blank lines in the 'Data X' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean5.3374
Biased Variance6.8135064
Biased Standard Deviation2.60959767013998187.253838411927
Covariance35.3333333333333
Correlation0.0650762973974341
Determination0.00423492448295929
T-Test0.184454554684186
p-value (2 sided)0.858246929283576
p-value (1 sided)0.429123464641788
95% CI of Correlation[-0.588670020276625, 0.667358421738631]
Degrees of Freedom8
Number of Observations10

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 5.3 & 374 \tabularnewline
Biased Variance & 6.81 & 35064 \tabularnewline
Biased Standard Deviation & 2.60959767013998 & 187.253838411927 \tabularnewline
Covariance & 35.3333333333333 \tabularnewline
Correlation & 0.0650762973974341 \tabularnewline
Determination & 0.00423492448295929 \tabularnewline
T-Test & 0.184454554684186 \tabularnewline
p-value (2 sided) & 0.858246929283576 \tabularnewline
p-value (1 sided) & 0.429123464641788 \tabularnewline
95% CI of Correlation & [-0.588670020276625, 0.667358421738631] \tabularnewline
Degrees of Freedom & 8 \tabularnewline
Number of Observations & 10 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=319210&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]5.3[/C][C]374[/C][/ROW]
[ROW][C]Biased Variance[/C][C]6.81[/C][C]35064[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]2.60959767013998[/C][C]187.253838411927[/C][/ROW]
[ROW][C]Covariance[/C][C]35.3333333333333[/C][/ROW]
[ROW][C]Correlation[/C][C]0.0650762973974341[/C][/ROW]
[ROW][C]Determination[/C][C]0.00423492448295929[/C][/ROW]
[ROW][C]T-Test[/C][C]0.184454554684186[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0.858246929283576[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0.429123464641788[/C][/ROW]
[ROW][C]95% CI of Correlation[/C][C][-0.588670020276625, 0.667358421738631][/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]8[/C][/ROW]
[ROW][C]Number of Observations[/C][C]10[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=319210&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=319210&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
Mean5.3374
Biased Variance6.8135064
Biased Standard Deviation2.60959767013998187.253838411927
Covariance35.3333333333333
Correlation0.0650762973974341
Determination0.00423492448295929
T-Test0.184454554684186
p-value (2 sided)0.858246929283576
p-value (1 sided)0.429123464641788
95% CI of Correlation[-0.588670020276625, 0.667358421738631]
Degrees of Freedom8
Number of Observations10






Normality Tests
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 0.9437, p-value = 0.6238
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 0.99147, p-value = 0.6091
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 0.47254, p-value = 0.1878

> ad.y
	Anderson-Darling normality test
data:  y
A = 0.47077, p-value = 0.1898


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

> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 0.9437, p-value = 0.6238
alternative hypothesis: greater

 \tabularnewline

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 0.99147, p-value = 0.6091
alternative hypothesis: greater

 \tabularnewline

> ad.x
	Anderson-Darling normality test
data:  x
A = 0.47254, p-value = 0.1878

 \tabularnewline

> ad.y
	Anderson-Darling normality test
data:  y
A = 0.47077, p-value = 0.1898

 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=319210&T=2

[TABLE]
[ROW][C]Normality Tests[/C][/ROW]
[ROW][C]
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 0.9437, p-value = 0.6238
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 0.99147, p-value = 0.6091
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> ad.x
	Anderson-Darling normality test
data:  x
A = 0.47254, p-value = 0.1878

[/C][/ROW]
[ROW][C]
> ad.y
	Anderson-Darling normality test
data:  y
A = 0.47077, p-value = 0.1898

[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=319210&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=319210&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 = 0.9437, p-value = 0.6238
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 0.99147, p-value = 0.6091
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 0.47254, p-value = 0.1878

> ad.y
	Anderson-Darling normality test
data:  y
A = 0.47077, p-value = 0.1898


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()