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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 computationMon, 01 Sep 2014 23:05:41 +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/2014/Sep/01/t14096092065feutlv4r8x9br1.htm/, Retrieved Sat, 11 May 2024 16:12:15 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=235783, Retrieved Sat, 11 May 2024 16:12:15 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact162

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Pearson Correlation] [] [2014-09-01 22:05:41] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
66
63
63
54
54
59
59
56
56
58
58
59
59
60
60
59
59
47
47
47
47
48
48
49
49
47
47
46
46
53
53
59
59
46
46
Dataseries Y:
Download CSV
Histogram 
332
318
312
313
314
314
320
327
329
326
322
315
313
314
317
315
314
313
314
321
329
334
336
338
337
338
333
333
335
335
345
342
336
335
333

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Maurice George Kendall' @ kendall.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 & 2 seconds \tabularnewline
R Server & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235783&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235783&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235783&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 time2 seconds
R Server'Sir Maurice George Kendall' @ kendall.wessa.net






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean53.8857142857143325.771428571429
Biased Variance36.9012244897959103.433469387755
Biased Standard Deviation6.074637807293210.170224647851
Covariance-26.6739495798319
Correlation-0.419418191982078
Determination0.175911619765515
T-Test-2.65410034487658
p-value (2 sided)0.0121399099301223
p-value (1 sided)0.00606995496506114
Degrees of Freedom33
Number of Observations35

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 53.8857142857143 & 325.771428571429 \tabularnewline
Biased Variance & 36.9012244897959 & 103.433469387755 \tabularnewline
Biased Standard Deviation & 6.0746378072932 & 10.170224647851 \tabularnewline
Covariance & -26.6739495798319 \tabularnewline
Correlation & -0.419418191982078 \tabularnewline
Determination & 0.175911619765515 \tabularnewline
T-Test & -2.65410034487658 \tabularnewline
p-value (2 sided) & 0.0121399099301223 \tabularnewline
p-value (1 sided) & 0.00606995496506114 \tabularnewline
Degrees of Freedom & 33 \tabularnewline
Number of Observations & 35 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235783&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]53.8857142857143[/C][C]325.771428571429[/C][/ROW]
[ROW][C]Biased Variance[/C][C]36.9012244897959[/C][C]103.433469387755[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]6.0746378072932[/C][C]10.170224647851[/C][/ROW]
[ROW][C]Covariance[/C][C]-26.6739495798319[/C][/ROW]
[ROW][C]Correlation[/C][C]-0.419418191982078[/C][/ROW]
[ROW][C]Determination[/C][C]0.175911619765515[/C][/ROW]
[ROW][C]T-Test[/C][C]-2.65410034487658[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0.0121399099301223[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0.00606995496506114[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]33[/C][/ROW]
[ROW][C]Number of Observations[/C][C]35[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235783&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235783&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
Mean53.8857142857143325.771428571429
Biased Variance36.9012244897959103.433469387755
Biased Standard Deviation6.074637807293210.170224647851
Covariance-26.6739495798319
Correlation-0.419418191982078
Determination0.175911619765515
T-Test-2.65410034487658
p-value (2 sided)0.0121399099301223
p-value (1 sided)0.00606995496506114
Degrees of Freedom33
Number of Observations35






Normality Tests
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 2.8353, p-value = 0.2423
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 3.1442, p-value = 0.2076
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 1.689, p-value = 0.0001999

> ad.y
	Anderson-Darling normality test
data:  y
A = 1.4731, p-value = 0.0006963


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

> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 2.8353, p-value = 0.2423
alternative hypothesis: greater

 \tabularnewline

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 3.1442, p-value = 0.2076
alternative hypothesis: greater

 \tabularnewline

> ad.x
	Anderson-Darling normality test
data:  x
A = 1.689, p-value = 0.0001999

 \tabularnewline

> ad.y
	Anderson-Darling normality test
data:  y
A = 1.4731, p-value = 0.0006963

 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235783&T=2

[TABLE]
[ROW][C]Normality Tests[/C][/ROW]
[ROW][C]
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 2.8353, p-value = 0.2423
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 3.1442, p-value = 0.2076
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> ad.x
	Anderson-Darling normality test
data:  x
A = 1.689, p-value = 0.0001999

[/C][/ROW]
[ROW][C]
> ad.y
	Anderson-Darling normality test
data:  y
A = 1.4731, p-value = 0.0006963

[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235783&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235783&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 = 2.8353, p-value = 0.2423
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 3.1442, p-value = 0.2076
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 1.689, p-value = 0.0001999

> ad.y
	Anderson-Darling normality test
data:  y
A = 1.4731, p-value = 0.0006963


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
Parameters (R input):
R code (references can be found in the software module):
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,'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()