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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 computationSun, 03 Dec 2017 20:22:53 +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/2017/Dec/03/t1512329014qlosxqijmvyvf8l.htm/, Retrieved Mon, 13 May 2024 23:29:45 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=308486, Retrieved Mon, 13 May 2024 23:29:45 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact106

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Pearson Correlation] [Pearson Correlati...] [2017-12-03 19:22:53] [dc50920429733eb8e80244e6ce50bf79] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
0
5
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
Dataseries Y:
Download CSV
Histogram 
0
1
0
1
6
9
8
10
28
56
90
124
154
264
281
422
492
782

Tables (Output of Computation)





Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time5 seconds
R ServerBig Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time5 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=308486&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]5 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=308486&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308486&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 Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time5 seconds
R ServerBig Analytics Cloud Computing Center






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean42.5151.555555555556
Biased Variance672.91666666666745460.024691358
Biased Standard Deviation25.9406373604556213.213565917739
Covariance4913.23529411765
Correlation0.838974001820467
Determination0.70387737573065
T-Test6.16698226770863
p-value (2 sided)1.35347842239444e-05
p-value (1 sided)6.7673921119722e-06
95% CI of Correlation[0.61170301700776, 0.938314089933055]
Degrees of Freedom16
Number of Observations18

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 42.5 & 151.555555555556 \tabularnewline
Biased Variance & 672.916666666667 & 45460.024691358 \tabularnewline
Biased Standard Deviation & 25.9406373604556 & 213.213565917739 \tabularnewline
Covariance & 4913.23529411765 \tabularnewline
Correlation & 0.838974001820467 \tabularnewline
Determination & 0.70387737573065 \tabularnewline
T-Test & 6.16698226770863 \tabularnewline
p-value (2 sided) & 1.35347842239444e-05 \tabularnewline
p-value (1 sided) & 6.7673921119722e-06 \tabularnewline
95% CI of Correlation & [0.61170301700776, 0.938314089933055] \tabularnewline
Degrees of Freedom & 16 \tabularnewline
Number of Observations & 18 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=308486&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]42.5[/C][C]151.555555555556[/C][/ROW]
[ROW][C]Biased Variance[/C][C]672.916666666667[/C][C]45460.024691358[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]25.9406373604556[/C][C]213.213565917739[/C][/ROW]
[ROW][C]Covariance[/C][C]4913.23529411765[/C][/ROW]
[ROW][C]Correlation[/C][C]0.838974001820467[/C][/ROW]
[ROW][C]Determination[/C][C]0.70387737573065[/C][/ROW]
[ROW][C]T-Test[/C][C]6.16698226770863[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]1.35347842239444e-05[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]6.7673921119722e-06[/C][/ROW]
[ROW][C]95% CI of Correlation[/C][C][0.61170301700776, 0.938314089933055][/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]16[/C][/ROW]
[ROW][C]Number of Observations[/C][C]18[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=308486&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308486&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
Mean42.5151.555555555556
Biased Variance672.91666666666745460.024691358
Biased Standard Deviation25.9406373604556213.213565917739
Covariance4913.23529411765
Correlation0.838974001820467
Determination0.70387737573065
T-Test6.16698226770863
p-value (2 sided)1.35347842239444e-05
p-value (1 sided)6.7673921119722e-06
95% CI of Correlation[0.61170301700776, 0.938314089933055]
Degrees of Freedom16
Number of Observations18






Normality Tests
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 1.0934, p-value = 0.5789
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 10.629, p-value = 0.00492
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 0.2021, p-value = 0.8564

> ad.y
	Anderson-Darling normality test
data:  y
A = 1.7842, p-value = 8.942e-05


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

> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 1.0934, p-value = 0.5789
alternative hypothesis: greater

 \tabularnewline

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 10.629, p-value = 0.00492
alternative hypothesis: greater

 \tabularnewline

> ad.x
	Anderson-Darling normality test
data:  x
A = 0.2021, p-value = 0.8564

 \tabularnewline

> ad.y
	Anderson-Darling normality test
data:  y
A = 1.7842, p-value = 8.942e-05

 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=308486&T=2

[TABLE]
[ROW][C]Normality Tests[/C][/ROW]
[ROW][C]
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 1.0934, p-value = 0.5789
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 10.629, p-value = 0.00492
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> ad.x
	Anderson-Darling normality test
data:  x
A = 0.2021, p-value = 0.8564

[/C][/ROW]
[ROW][C]
> ad.y
	Anderson-Darling normality test
data:  y
A = 1.7842, p-value = 8.942e-05

[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=308486&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308486&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 = 1.0934, p-value = 0.5789
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 10.629, p-value = 0.00492
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 0.2021, p-value = 0.8564

> ad.y
	Anderson-Darling normality test
data:  y
A = 1.7842, p-value = 8.942e-05


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$estimate)[1,1]
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Pearson Product Moment Correlation - Ungrouped Data',3,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Statistic',1,TRUE)
a<-table.element(a,'Variable X',1,TRUE)
a<-table.element(a,'Variable Y',1,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Mean',header=TRUE)
a<-table.element(a,mean(x))
a<-table.element(a,mean(y))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Biased Variance',header=TRUE)
a<-table.element(a,varx)
a<-table.element(a,vary)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Biased Standard Deviation',header=TRUE)
a<-table.element(a,sqrt(varx))
a<-table.element(a,sqrt(vary))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Covariance',header=TRUE)
a<-table.element(a,cov(x,y),2)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Correlation',header=TRUE)
a<-table.element(a,cxy,2)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Determination',header=TRUE)
a<-table.element(a,cxy*cxy,2)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'T-Test',header=TRUE)
a<-table.element(a,as.matrix(corxy$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')
qqPlot(x,main='QQplot of variable x')
dev.off()
bitmap(file='test3.png')
qqPlot(y,main='QQplot of variable y')
dev.off()