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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 computationTue, 08 Dec 2015 11:32:55 +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/08/t14495744291v9k5rh1x9dop5z.htm/, Retrieved Thu, 16 May 2024 14:00:03 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=285474, Retrieved Thu, 16 May 2024 14:00:03 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact99

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
8945
7764
8704
7546
7694
10499
7614
8248
8158
8174
8097
9154
10287
7972
7518
9492
8317
8158
9174
8262
10533
10434
8047
7831
8062
8834
8957
8753
7663
8290
8435
10802
9391
10280
8461
9152
8380
8171
8386
8212
9103
8461
8443
9253
8220
10435
8627
8196
9431
7917
8186
Dataseries Y:
Download CSV
Histogram 
0.36
0.39
0.34
0.51
0.52
0.25
0.58
0.53
0.6
0.55
0.59
0.41
0.34
0.51
0.56
0.53
0.56
0.59
0.39
0.47
0.23
0.24
0.42
0.42
0.55
0.36
0.46
0.43
0.56
0.63
0.48
0.34
0.48
0.25
0.59
0.5
0.51
0.56
0.54
0.57
0.61
0.72
0.66
0.51
0.57
0.21
0.31
0.4
0.23
0.39
0.25

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 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 & 4 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=285474&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]4 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=285474&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=285474&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 time4 seconds
R Server'George Udny Yule' @ yule.wessa.net






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean8688.68627450980.461960784313726
Biased Variance748921.6270665130.015996155324875
Biased Standard Deviation865.4025809220310.126475908080848
Covariance-69.5351725490196
Correlation-0.622842691225451
Determination0.387933018012962
T-Test-5.57284464769681
p-value (2 sided)1.05745455017227e-06
p-value (1 sided)5.28727275086134e-07
95% CI of Correlation[-0.76680748107663, -0.419215355219432]
Degrees of Freedom49
Number of Observations51

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 8688.6862745098 & 0.461960784313726 \tabularnewline
Biased Variance & 748921.627066513 & 0.015996155324875 \tabularnewline
Biased Standard Deviation & 865.402580922031 & 0.126475908080848 \tabularnewline
Covariance & -69.5351725490196 \tabularnewline
Correlation & -0.622842691225451 \tabularnewline
Determination & 0.387933018012962 \tabularnewline
T-Test & -5.57284464769681 \tabularnewline
p-value (2 sided) & 1.05745455017227e-06 \tabularnewline
p-value (1 sided) & 5.28727275086134e-07 \tabularnewline
95% CI of Correlation & [-0.76680748107663, -0.419215355219432] \tabularnewline
Degrees of Freedom & 49 \tabularnewline
Number of Observations & 51 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=285474&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]8688.6862745098[/C][C]0.461960784313726[/C][/ROW]
[ROW][C]Biased Variance[/C][C]748921.627066513[/C][C]0.015996155324875[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]865.402580922031[/C][C]0.126475908080848[/C][/ROW]
[ROW][C]Covariance[/C][C]-69.5351725490196[/C][/ROW]
[ROW][C]Correlation[/C][C]-0.622842691225451[/C][/ROW]
[ROW][C]Determination[/C][C]0.387933018012962[/C][/ROW]
[ROW][C]T-Test[/C][C]-5.57284464769681[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]1.05745455017227e-06[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]5.28727275086134e-07[/C][/ROW]
[ROW][C]95% CI of Correlation[/C][C][-0.76680748107663, -0.419215355219432][/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]49[/C][/ROW]
[ROW][C]Number of Observations[/C][C]51[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=285474&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=285474&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
Mean8688.68627450980.461960784313726
Biased Variance748921.6270665130.015996155324875
Biased Standard Deviation865.4025809220310.126475908080848
Covariance-69.5351725490196
Correlation-0.622842691225451
Determination0.387933018012962
T-Test-5.57284464769681
p-value (2 sided)1.05745455017227e-06
p-value (1 sided)5.28727275086134e-07
95% CI of Correlation[-0.76680748107663, -0.419215355219432]
Degrees of Freedom49
Number of Observations51






Normality Tests
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 7.7154, p-value = 0.02112
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 2.4989, p-value = 0.2867
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 2.0082, p-value = 3.458e-05

> ad.y
	Anderson-Darling normality test
data:  y
A = 0.93454, p-value = 0.01644


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

> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 7.7154, p-value = 0.02112
alternative hypothesis: greater

 \tabularnewline

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 2.4989, p-value = 0.2867
alternative hypothesis: greater

 \tabularnewline

> ad.x
	Anderson-Darling normality test
data:  x
A = 2.0082, p-value = 3.458e-05

 \tabularnewline

> ad.y
	Anderson-Darling normality test
data:  y
A = 0.93454, p-value = 0.01644

 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=285474&T=2

[TABLE]
[ROW][C]Normality Tests[/C][/ROW]
[ROW][C]
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 7.7154, p-value = 0.02112
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 2.4989, p-value = 0.2867
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> ad.x
	Anderson-Darling normality test
data:  x
A = 2.0082, p-value = 3.458e-05

[/C][/ROW]
[ROW][C]
> ad.y
	Anderson-Darling normality test
data:  y
A = 0.93454, p-value = 0.01644

[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=285474&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=285474&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 = 7.7154, p-value = 0.02112
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 2.4989, p-value = 0.2867
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 2.0082, p-value = 3.458e-05

> ad.y
	Anderson-Darling normality test
data:  y
A = 0.93454, p-value = 0.01644


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()