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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 computationFri, 20 Nov 2015 21:52:57 +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/Nov/20/t14480565358lzai99cmr2sj11.htm/, Retrieved Tue, 14 May 2024 13:21:01 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=283736, Retrieved Tue, 14 May 2024 13:21:01 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact123

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Pearson Correlation] [Approval Rating] [2015-11-20 21:52:57] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
0
6
12
18
24
30
36
42
48
54
60
66
72
78
Dataseries Y:
Download CSV
Histogram 
67
54
51
45
48
43
46
45
53
45
41
42
46
47

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gertrude Mary Cox' @ cox.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 & 3 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=283736&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=283736&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=283736&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 time3 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean3948.0714285714286
Biased Variance58541.2091836734694
Biased Standard Deviation24.18677324489566.41943795619752
Covariance-102.230769230769
Correlation-0.611395174178666
Determination0.373804059008962
T-Test-2.67643995997682
p-value (2 sided)0.0201692390836084
p-value (1 sided)0.0100846195418042
95% CI of Correlation[-0.862262207876601, -0.119619484498161]
Degrees of Freedom12
Number of Observations14

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 39 & 48.0714285714286 \tabularnewline
Biased Variance & 585 & 41.2091836734694 \tabularnewline
Biased Standard Deviation & 24.1867732448956 & 6.41943795619752 \tabularnewline
Covariance & -102.230769230769 \tabularnewline
Correlation & -0.611395174178666 \tabularnewline
Determination & 0.373804059008962 \tabularnewline
T-Test & -2.67643995997682 \tabularnewline
p-value (2 sided) & 0.0201692390836084 \tabularnewline
p-value (1 sided) & 0.0100846195418042 \tabularnewline
95% CI of Correlation & [-0.862262207876601, -0.119619484498161] \tabularnewline
Degrees of Freedom & 12 \tabularnewline
Number of Observations & 14 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=283736&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]39[/C][C]48.0714285714286[/C][/ROW]
[ROW][C]Biased Variance[/C][C]585[/C][C]41.2091836734694[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]24.1867732448956[/C][C]6.41943795619752[/C][/ROW]
[ROW][C]Covariance[/C][C]-102.230769230769[/C][/ROW]
[ROW][C]Correlation[/C][C]-0.611395174178666[/C][/ROW]
[ROW][C]Determination[/C][C]0.373804059008962[/C][/ROW]
[ROW][C]T-Test[/C][C]-2.67643995997682[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0.0201692390836084[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0.0100846195418042[/C][/ROW]
[ROW][C]95% CI of Correlation[/C][C][-0.862262207876601, -0.119619484498161][/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]12[/C][/ROW]
[ROW][C]Number of Observations[/C][C]14[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=283736&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=283736&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
Mean3948.0714285714286
Biased Variance58541.2091836734694
Biased Standard Deviation24.18677324489566.41943795619752
Covariance-102.230769230769
Correlation-0.611395174178666
Determination0.373804059008962
T-Test-2.67643995997682
p-value (2 sided)0.0201692390836084
p-value (1 sided)0.0100846195418042
95% CI of Correlation[-0.862262207876601, -0.119619484498161]
Degrees of Freedom12
Number of Observations14






Normality Tests
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 0.85732, p-value = 0.6514
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 10.995, p-value = 0.004097
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 0.16777, p-value = 0.9185

> ad.y
	Anderson-Darling normality test
data:  y
A = 0.90349, p-value = 0.01526


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

> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 0.85732, p-value = 0.6514
alternative hypothesis: greater

 \tabularnewline

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 10.995, p-value = 0.004097
alternative hypothesis: greater

 \tabularnewline

> ad.x
	Anderson-Darling normality test
data:  x
A = 0.16777, p-value = 0.9185

 \tabularnewline

> ad.y
	Anderson-Darling normality test
data:  y
A = 0.90349, p-value = 0.01526

 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=283736&T=2

[TABLE]
[ROW][C]Normality Tests[/C][/ROW]
[ROW][C]
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 0.85732, p-value = 0.6514
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 10.995, p-value = 0.004097
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> ad.x
	Anderson-Darling normality test
data:  x
A = 0.16777, p-value = 0.9185

[/C][/ROW]
[ROW][C]
> ad.y
	Anderson-Darling normality test
data:  y
A = 0.90349, p-value = 0.01526

[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=283736&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=283736&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 = 0.85732, p-value = 0.6514
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 10.995, p-value = 0.004097
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 0.16777, p-value = 0.9185

> ad.y
	Anderson-Darling normality test
data:  y
A = 0.90349, p-value = 0.01526


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()