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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 computationSat, 07 Nov 2015 10:30:04 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/Nov/07/t1446892229zjwe4suedzph35j.htm/, Retrieved Tue, 14 May 2024 15:42:25 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=283207, Retrieved Tue, 14 May 2024 15:42:25 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact92

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Pearson Correlation] [Task 9 - Chapter 4] [2015-11-07 10:30:04] [39661ea0cc1af7d66f31b3ef3719ea7a] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
1
1
1
0
1
1
1
1
1
1
0
1
1
1
0
1
1
1
1
0
1
1
0
0
1
0
1
0
0
1
0
1
0
0
0
1
1
1
1
1
1
1
1
1
0
1
1
1
1
0
1
1
1
0
1
1
1
1
0
0
1
1
1
0
0
1
1
0
1
1
1
1
1
1
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
1
1
1
1
1
1
1
0
0
1
0
0
0
1
Dataseries Y:
Download CSV
Histogram 
4
0
4
0
0
0
0
0
4
1
4
0
2
0
0
0
1
0
0
2
2
1
2
0
3
0
0
0
1
0
0
4
0
1
0
0
4
1
0
4
0
4
0
0
0
4
0
0
4
4
0
1
0
4
0
2
0
4
4
0
0
4
0
0
2
0
0
0
4
4
2
0
0
4
0
0
1
2
0
2
0
4
4
0
0
4
0
4
2
2
0
0
4
0
0
0
4
4
0
0
2
1
0
2
1

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time5 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 5 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=283207&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]5 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=283207&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=283207&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 Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time5 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.wessa.net






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean0.6380952380952381.32380952380952
Biased Variance0.230929705215422.73324263038549
Biased Standard Deviation0.4805514594873471.65325213757173
Covariance0.0606227106227106
Correlation0.0755788705982466
Determination0.00571216568090651
T-Test0.769241927409323
p-value (2 sided)0.44351013512986
p-value (1 sided)0.22175506756493
95% CI of Correlation[-0.117792703279659, 0.263428139232766]
Degrees of Freedom103
Number of Observations105

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 0.638095238095238 & 1.32380952380952 \tabularnewline
Biased Variance & 0.23092970521542 & 2.73324263038549 \tabularnewline
Biased Standard Deviation & 0.480551459487347 & 1.65325213757173 \tabularnewline
Covariance & 0.0606227106227106 \tabularnewline
Correlation & 0.0755788705982466 \tabularnewline
Determination & 0.00571216568090651 \tabularnewline
T-Test & 0.769241927409323 \tabularnewline
p-value (2 sided) & 0.44351013512986 \tabularnewline
p-value (1 sided) & 0.22175506756493 \tabularnewline
95% CI of Correlation & [-0.117792703279659, 0.263428139232766] \tabularnewline
Degrees of Freedom & 103 \tabularnewline
Number of Observations & 105 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=283207&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]0.638095238095238[/C][C]1.32380952380952[/C][/ROW]
[ROW][C]Biased Variance[/C][C]0.23092970521542[/C][C]2.73324263038549[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]0.480551459487347[/C][C]1.65325213757173[/C][/ROW]
[ROW][C]Covariance[/C][C]0.0606227106227106[/C][/ROW]
[ROW][C]Correlation[/C][C]0.0755788705982466[/C][/ROW]
[ROW][C]Determination[/C][C]0.00571216568090651[/C][/ROW]
[ROW][C]T-Test[/C][C]0.769241927409323[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0.44351013512986[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0.22175506756493[/C][/ROW]
[ROW][C]95% CI of Correlation[/C][C][-0.117792703279659, 0.263428139232766][/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]103[/C][/ROW]
[ROW][C]Number of Observations[/C][C]105[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=283207&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=283207&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
Mean0.6380952380952381.32380952380952
Biased Variance0.230929705215422.73324263038549
Biased Standard Deviation0.4805514594873471.65325213757173
Covariance0.0606227106227106
Correlation0.0755788705982466
Determination0.00571216568090651
T-Test0.769241927409323
p-value (2 sided)0.44351013512986
p-value (1 sided)0.22175506756493
95% CI of Correlation[-0.117792703279659, 0.263428139232766]
Degrees of Freedom103
Number of Observations105






Normality Tests
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 17.977, p-value = 0.0001248
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 15.552, p-value = 0.0004196
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 20.63, p-value < 2.2e-16

> ad.y
	Anderson-Darling normality test
data:  y
A = 12.631, p-value < 2.2e-16


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

> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 17.977, p-value = 0.0001248
alternative hypothesis: greater

 \tabularnewline

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 15.552, p-value = 0.0004196
alternative hypothesis: greater

 \tabularnewline

> ad.x
	Anderson-Darling normality test
data:  x
A = 20.63, p-value < 2.2e-16

 \tabularnewline

> ad.y
	Anderson-Darling normality test
data:  y
A = 12.631, p-value < 2.2e-16

 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=283207&T=2

[TABLE]
[ROW][C]Normality Tests[/C][/ROW]
[ROW][C]
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 17.977, p-value = 0.0001248
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 15.552, p-value = 0.0004196
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> ad.x
	Anderson-Darling normality test
data:  x
A = 20.63, p-value < 2.2e-16

[/C][/ROW]
[ROW][C]
> ad.y
	Anderson-Darling normality test
data:  y
A = 12.631, p-value < 2.2e-16

[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=283207&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=283207&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 = 17.977, p-value = 0.0001248
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 15.552, p-value = 0.0004196
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 20.63, p-value < 2.2e-16

> ad.y
	Anderson-Darling normality test
data:  y
A = 12.631, p-value < 2.2e-16


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$estimate)[1,1]
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Pearson Product Moment Correlation - Ungrouped Data',3,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Statistic',1,TRUE)
a<-table.element(a,'Variable X',1,TRUE)
a<-table.element(a,'Variable Y',1,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('arithmetic_mean.htm','Mean',''),header=TRUE)
a<-table.element(a,mean(x))
a<-table.element(a,mean(y))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('biased.htm','Biased Variance',''),header=TRUE)
a<-table.element(a,varx)
a<-table.element(a,vary)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('biased1.htm','Biased Standard Deviation',''),header=TRUE)
a<-table.element(a,sqrt(varx))
a<-table.element(a,sqrt(vary))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('covariance.htm','Covariance',''),header=TRUE)
a<-table.element(a,cov(x,y),2)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('pearson_correlation.htm','Correlation',''),header=TRUE)
a<-table.element(a,cxy,2)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('coeff_of_determination.htm','Determination',''),header=TRUE)
a<-table.element(a,cxy*cxy,2)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('ttest_statistic.htm','T-Test',''),header=TRUE)
a<-table.element(a,as.matrix(corxy$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')
qq.plot(x,main='QQplot of variable x')
dev.off()
bitmap(file='test3.png')
qq.plot(y,main='QQplot of variable y')
dev.off()