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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 computationWed, 14 Dec 2016 15:25:13 +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/t1481725917rpsb8b6uj4g0r7u.htm/, Retrieved Fri, 03 May 2024 23:34:12 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=299500, Retrieved Fri, 03 May 2024 23:34:12 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact65

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 14:25:13] [8263efc94e08b372ab727a2b95bd56b1] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
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Dataseries Y:
Download CSV
Histogram 
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Tables (Output of Computation)





Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time4 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 time4 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299500&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]4 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=299500&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299500&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 time4 seconds
R ServerBig Analytics Cloud Computing Center






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean8.6506024096385512.9518072289157
Biased Variance5.034547829873712.58803890259835
Biased Standard Deviation2.24377980868751.60873829524828
Covariance0.298211025921869
Correlation0.0821171593021049
Determination0.00674322785184727
T-Test1.05517641136957
p-value (2 sided)0.292896630133385
p-value (1 sided)0.146448315066692
95% CI of Correlation[-0.0710935986337644, 0.231542481821248]
Degrees of Freedom164
Number of Observations166

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 8.65060240963855 & 12.9518072289157 \tabularnewline
Biased Variance & 5.03454782987371 & 2.58803890259835 \tabularnewline
Biased Standard Deviation & 2.2437798086875 & 1.60873829524828 \tabularnewline
Covariance & 0.298211025921869 \tabularnewline
Correlation & 0.0821171593021049 \tabularnewline
Determination & 0.00674322785184727 \tabularnewline
T-Test & 1.05517641136957 \tabularnewline
p-value (2 sided) & 0.292896630133385 \tabularnewline
p-value (1 sided) & 0.146448315066692 \tabularnewline
95% CI of Correlation & [-0.0710935986337644, 0.231542481821248] \tabularnewline
Degrees of Freedom & 164 \tabularnewline
Number of Observations & 166 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299500&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]8.65060240963855[/C][C]12.9518072289157[/C][/ROW]
[ROW][C]Biased Variance[/C][C]5.03454782987371[/C][C]2.58803890259835[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]2.2437798086875[/C][C]1.60873829524828[/C][/ROW]
[ROW][C]Covariance[/C][C]0.298211025921869[/C][/ROW]
[ROW][C]Correlation[/C][C]0.0821171593021049[/C][/ROW]
[ROW][C]Determination[/C][C]0.00674322785184727[/C][/ROW]
[ROW][C]T-Test[/C][C]1.05517641136957[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0.292896630133385[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0.146448315066692[/C][/ROW]
[ROW][C]95% CI of Correlation[/C][C][-0.0710935986337644, 0.231542481821248][/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]164[/C][/ROW]
[ROW][C]Number of Observations[/C][C]166[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299500&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299500&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
Mean8.6506024096385512.9518072289157
Biased Variance5.034547829873712.58803890259835
Biased Standard Deviation2.24377980868751.60873829524828
Covariance0.298211025921869
Correlation0.0821171593021049
Determination0.00674322785184727
T-Test1.05517641136957
p-value (2 sided)0.292896630133385
p-value (1 sided)0.146448315066692
95% CI of Correlation[-0.0710935986337644, 0.231542481821248]
Degrees of Freedom164
Number of Observations166






Normality Tests
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 0.95249, p-value = 0.6211
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 0.25278, p-value = 0.8813
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 1.5039, p-value = 0.0006829

> ad.y
	Anderson-Darling normality test
data:  y
A = 4.2289, p-value = 1.494e-10


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

> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 0.95249, p-value = 0.6211
alternative hypothesis: greater

 \tabularnewline

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 0.25278, p-value = 0.8813
alternative hypothesis: greater

 \tabularnewline

> ad.x
	Anderson-Darling normality test
data:  x
A = 1.5039, p-value = 0.0006829

 \tabularnewline

> ad.y
	Anderson-Darling normality test
data:  y
A = 4.2289, p-value = 1.494e-10

 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299500&T=2

[TABLE]
[ROW][C]Normality Tests[/C][/ROW]
[ROW][C]
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 0.95249, p-value = 0.6211
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 0.25278, p-value = 0.8813
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> ad.x
	Anderson-Darling normality test
data:  x
A = 1.5039, p-value = 0.0006829

[/C][/ROW]
[ROW][C]
> ad.y
	Anderson-Darling normality test
data:  y
A = 4.2289, p-value = 1.494e-10

[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299500&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299500&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 = 0.95249, p-value = 0.6211
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 0.25278, p-value = 0.8813
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 1.5039, p-value = 0.0006829

> ad.y
	Anderson-Darling normality test
data:  y
A = 4.2289, p-value = 1.494e-10


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()