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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, 02 Dec 2015 20:56:37 +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/Dec/02/t14490914276zk0kcx2kgt4c4j.htm/, Retrieved Sat, 18 May 2024 14:42:21 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=284891, Retrieved Sat, 18 May 2024 14:42:21 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact73

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 Correlati...] [2015-12-02 20:56:37] [e06df5f969f4593868060c9950546ebc] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
455
450
463
457
463
477
473
489
469
489
485
486
496
481
469
459
458
459
442
Dataseries Y:
Download CSV
Histogram 
51
64
80
102
114
122
127
132
129
135
148
152
164
167
169
167
169
167
152

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'George Udny Yule' @ yule.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 & 3 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284891&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284891&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284891&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 time3 seconds
R Server'George Udny Yule' @ yule.wessa.net






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean469.473684210526132.157894736842
Biased Variance216.6703601108031249.92243767313
Biased Standard Deviation14.719726903404335.3542421453654
Covariance188.754385964912
Correlation0.343617023305611
Determination0.118072658705409
T-Test1.50862996166808
p-value (2 sided)0.149753615183687
p-value (1 sided)0.0748768075918436
95% CI of Correlation[-0.131044983471687, 0.690116964885997]
Degrees of Freedom17
Number of Observations19

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 469.473684210526 & 132.157894736842 \tabularnewline
Biased Variance & 216.670360110803 & 1249.92243767313 \tabularnewline
Biased Standard Deviation & 14.7197269034043 & 35.3542421453654 \tabularnewline
Covariance & 188.754385964912 \tabularnewline
Correlation & 0.343617023305611 \tabularnewline
Determination & 0.118072658705409 \tabularnewline
T-Test & 1.50862996166808 \tabularnewline
p-value (2 sided) & 0.149753615183687 \tabularnewline
p-value (1 sided) & 0.0748768075918436 \tabularnewline
95% CI of Correlation & [-0.131044983471687, 0.690116964885997] \tabularnewline
Degrees of Freedom & 17 \tabularnewline
Number of Observations & 19 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284891&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]469.473684210526[/C][C]132.157894736842[/C][/ROW]
[ROW][C]Biased Variance[/C][C]216.670360110803[/C][C]1249.92243767313[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]14.7197269034043[/C][C]35.3542421453654[/C][/ROW]
[ROW][C]Covariance[/C][C]188.754385964912[/C][/ROW]
[ROW][C]Correlation[/C][C]0.343617023305611[/C][/ROW]
[ROW][C]Determination[/C][C]0.118072658705409[/C][/ROW]
[ROW][C]T-Test[/C][C]1.50862996166808[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0.149753615183687[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0.0748768075918436[/C][/ROW]
[ROW][C]95% CI of Correlation[/C][C][-0.131044983471687, 0.690116964885997][/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]17[/C][/ROW]
[ROW][C]Number of Observations[/C][C]19[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284891&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284891&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
Mean469.473684210526132.157894736842
Biased Variance216.6703601108031249.92243767313
Biased Standard Deviation14.719726903404335.3542421453654
Covariance188.754385964912
Correlation0.343617023305611
Determination0.118072658705409
T-Test1.50862996166808
p-value (2 sided)0.149753615183687
p-value (1 sided)0.0748768075918436
95% CI of Correlation[-0.131044983471687, 0.690116964885997]
Degrees of Freedom17
Number of Observations19






Normality Tests
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 0.85858, p-value = 0.651
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 2.5542, p-value = 0.2788
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 0.33128, p-value = 0.4818

> ad.y
	Anderson-Darling normality test
data:  y
A = 0.75231, p-value = 0.04133


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

> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 0.85858, p-value = 0.651
alternative hypothesis: greater

 \tabularnewline

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 2.5542, p-value = 0.2788
alternative hypothesis: greater

 \tabularnewline

> ad.x
	Anderson-Darling normality test
data:  x
A = 0.33128, p-value = 0.4818

 \tabularnewline

> ad.y
	Anderson-Darling normality test
data:  y
A = 0.75231, p-value = 0.04133

 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284891&T=2

[TABLE]
[ROW][C]Normality Tests[/C][/ROW]
[ROW][C]
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 0.85858, p-value = 0.651
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 2.5542, p-value = 0.2788
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> ad.x
	Anderson-Darling normality test
data:  x
A = 0.33128, p-value = 0.4818

[/C][/ROW]
[ROW][C]
> ad.y
	Anderson-Darling normality test
data:  y
A = 0.75231, p-value = 0.04133

[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284891&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284891&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 = 0.85858, p-value = 0.651
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 2.5542, p-value = 0.2788
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 0.33128, p-value = 0.4818

> ad.y
	Anderson-Darling normality test
data:  y
A = 0.75231, p-value = 0.04133


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()