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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 computationWed, 06 Aug 2014 16:34:22 +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/Aug/06/t1407339303k894svu7nsur8kp.htm/, Retrieved Thu, 16 May 2024 17:17:30 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=235414, Retrieved Thu, 16 May 2024 17:17:30 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact144

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Pearson Correlation] [Republcans and wages] [2014-08-06 15:34:22] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
37
37
46
46
41
41
44
44
42
42
41
41
40
40
41
41
53
53
52
52
52
52
51
51
53
53
54
54
47
47
41
41
54
54
52
Dataseries Y:
Download CSV
Histogram 
241
262
284
302
313
326
344
359
374
385
399
412
426
440
459
467
479
490
503
523
549
576
596
608
620
638
651
671
695
722
739
747
756
768
776

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'Herman Ole Andreas Wold' @ wold.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 & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235414&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235414&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235414&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'Herman Ole Andreas Wold' @ wold.wessa.net






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean46.5714285714286511.428571428571
Biased Variance32.759183673469425941.8448979592
Biased Standard Deviation5.72356389616377161.064722698545
Covariance578.012605042017
Correlation0.609089646636635
Determination0.370990197639941
T-Test4.41173563838634
p-value (2 sided)0.000103159395962837
p-value (1 sided)5.15796979814187e-05
Degrees of Freedom33
Number of Observations35

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 46.5714285714286 & 511.428571428571 \tabularnewline
Biased Variance & 32.7591836734694 & 25941.8448979592 \tabularnewline
Biased Standard Deviation & 5.72356389616377 & 161.064722698545 \tabularnewline
Covariance & 578.012605042017 \tabularnewline
Correlation & 0.609089646636635 \tabularnewline
Determination & 0.370990197639941 \tabularnewline
T-Test & 4.41173563838634 \tabularnewline
p-value (2 sided) & 0.000103159395962837 \tabularnewline
p-value (1 sided) & 5.15796979814187e-05 \tabularnewline
Degrees of Freedom & 33 \tabularnewline
Number of Observations & 35 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235414&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]46.5714285714286[/C][C]511.428571428571[/C][/ROW]
[ROW][C]Biased Variance[/C][C]32.7591836734694[/C][C]25941.8448979592[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]5.72356389616377[/C][C]161.064722698545[/C][/ROW]
[ROW][C]Covariance[/C][C]578.012605042017[/C][/ROW]
[ROW][C]Correlation[/C][C]0.609089646636635[/C][/ROW]
[ROW][C]Determination[/C][C]0.370990197639941[/C][/ROW]
[ROW][C]T-Test[/C][C]4.41173563838634[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0.000103159395962837[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]5.15796979814187e-05[/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=235414&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235414&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
Mean46.5714285714286511.428571428571
Biased Variance32.759183673469425941.8448979592
Biased Standard Deviation5.72356389616377161.064722698545
Covariance578.012605042017
Correlation0.609089646636635
Determination0.370990197639941
T-Test4.41173563838634
p-value (2 sided)0.000103159395962837
p-value (1 sided)5.15796979814187e-05
Degrees of Freedom33
Number of Observations35






Normality Tests
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 3.6527, p-value = 0.161
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 2.2101, p-value = 0.3312
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 1.9223, p-value = 5.202e-05

> ad.y
	Anderson-Darling normality test
data:  y
A = 0.4621, p-value = 0.2431


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

> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 3.6527, p-value = 0.161
alternative hypothesis: greater

 \tabularnewline

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 2.2101, p-value = 0.3312
alternative hypothesis: greater

 \tabularnewline

> ad.x
	Anderson-Darling normality test
data:  x
A = 1.9223, p-value = 5.202e-05

 \tabularnewline

> ad.y
	Anderson-Darling normality test
data:  y
A = 0.4621, p-value = 0.2431

 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235414&T=2

[TABLE]
[ROW][C]Normality Tests[/C][/ROW]
[ROW][C]
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 3.6527, p-value = 0.161
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 2.2101, p-value = 0.3312
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> ad.x
	Anderson-Darling normality test
data:  x
A = 1.9223, p-value = 5.202e-05

[/C][/ROW]
[ROW][C]
> ad.y
	Anderson-Darling normality test
data:  y
A = 0.4621, p-value = 0.2431

[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235414&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235414&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 = 3.6527, p-value = 0.161
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 2.2101, p-value = 0.3312
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 1.9223, p-value = 5.202e-05

> ad.y
	Anderson-Darling normality test
data:  y
A = 0.4621, p-value = 0.2431


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()