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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 computationThu, 16 Oct 2014 21:35:26 +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/Oct/16/t1413491745mid8vmp6oj0o85t.htm/, Retrieved Sun, 12 May 2024 18:39:15 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=243057, Retrieved Sun, 12 May 2024 18:39:15 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact81

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Percentiles] [Intrinsic Motivat...] [2010-10-12 12:10:58] [b98453cac15ba1066b407e146608df68]
- RMPD  [Kernel Density Estimation] [] [2011-10-18 22:42:23] [b98453cac15ba1066b407e146608df68]
- RMPD    [Percentiles] [] [2011-10-18 22:46:45] [b98453cac15ba1066b407e146608df68]
- RMPD      [Notched Boxplots] [] [2011-10-18 22:58:56] [b98453cac15ba1066b407e146608df68]
- RM D        [Back to Back Histogram] [] [2011-10-18 23:05:48] [b98453cac15ba1066b407e146608df68]
- RMPD            [Pearson Correlation] [WS3: question 4 (...] [2014-10-16 20:35:26] [baa7d013c3374cabca6c222951a47a9f] [Current]
-    D              [Pearson Correlation] [] [2014-12-13 15:36:00] [ea990983fba95a758c0bb6d29c9aee24]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
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Dataseries Y:
Download CSV
Histogram 
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22
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Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 & 1 seconds \tabularnewline
R Server & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=243057&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]1 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=243057&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=243057&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 time1 seconds
R Server'Sir Maurice George Kendall' @ kendall.wessa.net






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean22.691358024691423.037037037037
Biased Variance9.6701722298430110.0109739368999
Biased Standard Deviation3.109690053661783.16401231617386
Covariance9.17920404876927
Correlation0.927172657403478
Determination0.859649136636627
T-Test31.3049534791383
p-value (2 sided)0
p-value (1 sided)0
Degrees of Freedom160
Number of Observations162

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 22.6913580246914 & 23.037037037037 \tabularnewline
Biased Variance & 9.67017222984301 & 10.0109739368999 \tabularnewline
Biased Standard Deviation & 3.10969005366178 & 3.16401231617386 \tabularnewline
Covariance & 9.17920404876927 \tabularnewline
Correlation & 0.927172657403478 \tabularnewline
Determination & 0.859649136636627 \tabularnewline
T-Test & 31.3049534791383 \tabularnewline
p-value (2 sided) & 0 \tabularnewline
p-value (1 sided) & 0 \tabularnewline
Degrees of Freedom & 160 \tabularnewline
Number of Observations & 162 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=243057&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]22.6913580246914[/C][C]23.037037037037[/C][/ROW]
[ROW][C]Biased Variance[/C][C]9.67017222984301[/C][C]10.0109739368999[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]3.10969005366178[/C][C]3.16401231617386[/C][/ROW]
[ROW][C]Covariance[/C][C]9.17920404876927[/C][/ROW]
[ROW][C]Correlation[/C][C]0.927172657403478[/C][/ROW]
[ROW][C]Determination[/C][C]0.859649136636627[/C][/ROW]
[ROW][C]T-Test[/C][C]31.3049534791383[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]160[/C][/ROW]
[ROW][C]Number of Observations[/C][C]162[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=243057&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=243057&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
Mean22.691358024691423.037037037037
Biased Variance9.6701722298430110.0109739368999
Biased Standard Deviation3.109690053661783.16401231617386
Covariance9.17920404876927
Correlation0.927172657403478
Determination0.859649136636627
T-Test31.3049534791383
p-value (2 sided)0
p-value (1 sided)0
Degrees of Freedom160
Number of Observations162






Normality Tests
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 5.1271, p-value = 0.07703
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 28.3924, p-value = 6.834e-07
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 1.1648, p-value = 0.004691

> ad.y
	Anderson-Darling normality test
data:  y
A = 1.4847, p-value = 0.0007611


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

> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 5.1271, p-value = 0.07703
alternative hypothesis: greater

 \tabularnewline

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 28.3924, p-value = 6.834e-07
alternative hypothesis: greater

 \tabularnewline

> ad.x
	Anderson-Darling normality test
data:  x
A = 1.1648, p-value = 0.004691

 \tabularnewline

> ad.y
	Anderson-Darling normality test
data:  y
A = 1.4847, p-value = 0.0007611

 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=243057&T=2

[TABLE]
[ROW][C]Normality Tests[/C][/ROW]
[ROW][C]
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 5.1271, p-value = 0.07703
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 28.3924, p-value = 6.834e-07
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> ad.x
	Anderson-Darling normality test
data:  x
A = 1.1648, p-value = 0.004691

[/C][/ROW]
[ROW][C]
> ad.y
	Anderson-Darling normality test
data:  y
A = 1.4847, p-value = 0.0007611

[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=243057&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=243057&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 = 5.1271, p-value = 0.07703
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 28.3924, p-value = 6.834e-07
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 1.1648, p-value = 0.004691

> ad.y
	Anderson-Darling normality test
data:  y
A = 1.4847, p-value = 0.0007611


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()