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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, 09 Dec 2015 11:54:10 +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/09/t1449662060kwiq80rf42w1owo.htm/, Retrieved Thu, 16 May 2024 06:49:33 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=285633, Retrieved Thu, 16 May 2024 06:49:33 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact83

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Pearson Correlation] [] [2015-12-09 11:54:10] [5264f2fb10908d9927130993ef716e6e] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
934
130
115
207
264
325
473
368
402
294
244
153
192
159
135
Dataseries Y:
Download CSV
Histogram 
2.72
2.87
2.90
2.91
2.93
2.93
2.77
2.69
2.56
2.87
2.47
2.43
2.38
2.46
2.68

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'Gwilym Jenkins' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=285633&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=285633&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=285633&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'Gwilym Jenkins' @ jenkins.wessa.net






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean2932.70466666666667
Biased Variance40228.26666666670.0372382222222222
Biased Standard Deviation200.5698548303470.192972076275875
Covariance3.25785714285715
Correlation0.0785613039809925
Determination0.00617187848319391
T-Test0.284134990189837
p-value (2 sided)0.780782167986392
p-value (1 sided)0.390391083993196
95% CI of Correlation[-0.451887309556359, 0.567966868251745]
Degrees of Freedom13
Number of Observations15

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 293 & 2.70466666666667 \tabularnewline
Biased Variance & 40228.2666666667 & 0.0372382222222222 \tabularnewline
Biased Standard Deviation & 200.569854830347 & 0.192972076275875 \tabularnewline
Covariance & 3.25785714285715 \tabularnewline
Correlation & 0.0785613039809925 \tabularnewline
Determination & 0.00617187848319391 \tabularnewline
T-Test & 0.284134990189837 \tabularnewline
p-value (2 sided) & 0.780782167986392 \tabularnewline
p-value (1 sided) & 0.390391083993196 \tabularnewline
95% CI of Correlation & [-0.451887309556359, 0.567966868251745] \tabularnewline
Degrees of Freedom & 13 \tabularnewline
Number of Observations & 15 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=285633&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]293[/C][C]2.70466666666667[/C][/ROW]
[ROW][C]Biased Variance[/C][C]40228.2666666667[/C][C]0.0372382222222222[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]200.569854830347[/C][C]0.192972076275875[/C][/ROW]
[ROW][C]Covariance[/C][C]3.25785714285715[/C][/ROW]
[ROW][C]Correlation[/C][C]0.0785613039809925[/C][/ROW]
[ROW][C]Determination[/C][C]0.00617187848319391[/C][/ROW]
[ROW][C]T-Test[/C][C]0.284134990189837[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0.780782167986392[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0.390391083993196[/C][/ROW]
[ROW][C]95% CI of Correlation[/C][C][-0.451887309556359, 0.567966868251745][/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]13[/C][/ROW]
[ROW][C]Number of Observations[/C][C]15[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=285633&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=285633&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
Mean2932.70466666666667
Biased Variance40228.26666666670.0372382222222222
Biased Standard Deviation200.5698548303470.192972076275875
Covariance3.25785714285715
Correlation0.0785613039809925
Determination0.00617187848319391
T-Test0.284134990189837
p-value (2 sided)0.780782167986392
p-value (1 sided)0.390391083993196
95% CI of Correlation[-0.451887309556359, 0.567966868251745]
Degrees of Freedom13
Number of Observations15






Normality Tests
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 21.372, p-value = 2.287e-05
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 1.4835, p-value = 0.4763
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 1.1167, p-value = 0.004348

> ad.y
	Anderson-Darling normality test
data:  y
A = 0.61714, p-value = 0.08777


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

> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 21.372, p-value = 2.287e-05
alternative hypothesis: greater

 \tabularnewline

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 1.4835, p-value = 0.4763
alternative hypothesis: greater

 \tabularnewline

> ad.x
	Anderson-Darling normality test
data:  x
A = 1.1167, p-value = 0.004348

 \tabularnewline

> ad.y
	Anderson-Darling normality test
data:  y
A = 0.61714, p-value = 0.08777

 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=285633&T=2

[TABLE]
[ROW][C]Normality Tests[/C][/ROW]
[ROW][C]
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 21.372, p-value = 2.287e-05
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 1.4835, p-value = 0.4763
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> ad.x
	Anderson-Darling normality test
data:  x
A = 1.1167, p-value = 0.004348

[/C][/ROW]
[ROW][C]
> ad.y
	Anderson-Darling normality test
data:  y
A = 0.61714, p-value = 0.08777

[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=285633&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=285633&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 = 21.372, p-value = 2.287e-05
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 1.4835, p-value = 0.4763
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 1.1167, p-value = 0.004348

> ad.y
	Anderson-Darling normality test
data:  y
A = 0.61714, p-value = 0.08777


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par3 = TRUE ;
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()