FreeStatistics.org

Free Statistics

of Irreproducible Research!

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 computationFri, 16 Dec 2016 15:09:41 +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/2016/Dec/16/t14818974040nfzzbcgmsj9aux.htm/, Retrieved Fri, 01 Nov 2024 03:35:06 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=300288, Retrieved Fri, 01 Nov 2024 03:35:06 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact113

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 correlation] [2016-12-16 14:09:41] [33f2a624cfeb2efbc43d2c77b7c0dad6] [Current]
Feedback Forum

Post a new message

Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
18
19
18
15
19
19
19
NA
18
20
14
15
18
19
16
18
18
NA
17
19
19
17
18
16
20
13
19
15
17
17
16
17
19
18
19
20
16
17
16
16
16
16
14
17
18
16
16
NA
16
15
19
16
17
19
17
17
15
16
16
16
17
18
18
18
19
14
13
18
16
15
18
18
16
19
17
17
19
19
20
19
18
16
16
15
20
16
16
20
20
18
15
14
16
14
18
20
20
18
20
14
20
17
20
14
16
20
19
18
17
17
19
15
18
15
16
16
20
18
20
18
17
19
18
19
17
18
17
16
19
18
17
18
16
20
14
17
13
13
17
18
16
NA
19
NA
17
16
17
17
17
20
14
20
19
16
19
17
19
20
19
19
16
18
16
17
18
16
17
15
18
Dataseries Y:
Download CSV
Histogram 
13
16
17
NA
NA
16
NA
NA
NA
17
17
15
16
14
16
17
NA
NA
NA
NA
16
NA
16
NA
NA
NA
16
15
16
16
13
15
17
NA
13
17
NA
14
14
18
NA
17
13
16
15
15
NA
15
13
NA
17
NA
NA
11
14
13
NA
17
16
NA
17
16
16
16
15
12
17
14
14
16
NA
NA
NA
NA
NA
15
16
14
15
17
NA
10
NA
17
NA
20
17
18
NA
17
14
NA
17
NA
17
NA
16
18
18
16
NA
NA
15
13
NA
NA
NA
NA
NA
16
NA
NA
NA
12
NA
16
16
NA
16
14
15
14
NA
15
NA
15
16
NA
NA
NA
11
NA
18
NA
11
NA
18
NA
15
19
17
NA
14
NA
13
17
14
19
14
NA
NA
16
16
15
12
NA
17
NA
NA
18
15
18
15
NA
NA
NA
16
NA
16

Tables (Output of Computation)





Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time4 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 time4 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300288&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]4 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=300288&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300288&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 time4 seconds
R ServerBig Analytics Cloud Computing Center






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean17.284313725490215.4803921568627
Biased Variance3.046616685890043.50451749327182
Biased Standard Deviation1.745456010872241.87203565491468
Covariance0.466026014366142
Correlation0.141223944718938
Determination0.0199442025619776
T-Test1.42653666091272
p-value (2 sided)0.156828177616684
p-value (1 sided)0.0784140888083422
95% CI of Correlation[-0.0547547650776989, 0.326725485560765]
Degrees of Freedom100
Number of Observations102

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 17.2843137254902 & 15.4803921568627 \tabularnewline
Biased Variance & 3.04661668589004 & 3.50451749327182 \tabularnewline
Biased Standard Deviation & 1.74545601087224 & 1.87203565491468 \tabularnewline
Covariance & 0.466026014366142 \tabularnewline
Correlation & 0.141223944718938 \tabularnewline
Determination & 0.0199442025619776 \tabularnewline
T-Test & 1.42653666091272 \tabularnewline
p-value (2 sided) & 0.156828177616684 \tabularnewline
p-value (1 sided) & 0.0784140888083422 \tabularnewline
95% CI of Correlation & [-0.0547547650776989, 0.326725485560765] \tabularnewline
Degrees of Freedom & 100 \tabularnewline
Number of Observations & 102 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300288&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]17.2843137254902[/C][C]15.4803921568627[/C][/ROW]
[ROW][C]Biased Variance[/C][C]3.04661668589004[/C][C]3.50451749327182[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]1.74545601087224[/C][C]1.87203565491468[/C][/ROW]
[ROW][C]Covariance[/C][C]0.466026014366142[/C][/ROW]
[ROW][C]Correlation[/C][C]0.141223944718938[/C][/ROW]
[ROW][C]Determination[/C][C]0.0199442025619776[/C][/ROW]
[ROW][C]T-Test[/C][C]1.42653666091272[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0.156828177616684[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0.0784140888083422[/C][/ROW]
[ROW][C]95% CI of Correlation[/C][C][-0.0547547650776989, 0.326725485560765][/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]100[/C][/ROW]
[ROW][C]Number of Observations[/C][C]102[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300288&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300288&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
Mean17.284313725490215.4803921568627
Biased Variance3.046616685890043.50451749327182
Biased Standard Deviation1.745456010872241.87203565491468
Covariance0.466026014366142
Correlation0.141223944718938
Determination0.0199442025619776
T-Test1.42653666091272
p-value (2 sided)0.156828177616684
p-value (1 sided)0.0784140888083422
95% CI of Correlation[-0.0547547650776989, 0.326725485560765]
Degrees of Freedom100
Number of Observations102






Normality Tests
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 3.1496, p-value = 0.207
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 4.7984, p-value = 0.09079
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 1.8887, p-value = 7.462e-05

> ad.y
	Anderson-Darling normality test
data:  y
A = 1.9821, p-value = 4.39e-05


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

> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 3.1496, p-value = 0.207
alternative hypothesis: greater

 \tabularnewline

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 4.7984, p-value = 0.09079
alternative hypothesis: greater

 \tabularnewline

> ad.x
	Anderson-Darling normality test
data:  x
A = 1.8887, p-value = 7.462e-05

 \tabularnewline

> ad.y
	Anderson-Darling normality test
data:  y
A = 1.9821, p-value = 4.39e-05

 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300288&T=2

[TABLE]
[ROW][C]Normality Tests[/C][/ROW]
[ROW][C]
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 3.1496, p-value = 0.207
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 4.7984, p-value = 0.09079
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> ad.x
	Anderson-Darling normality test
data:  x
A = 1.8887, p-value = 7.462e-05

[/C][/ROW]
[ROW][C]
> ad.y
	Anderson-Darling normality test
data:  y
A = 1.9821, p-value = 4.39e-05

[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300288&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300288&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 = 3.1496, p-value = 0.207
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 4.7984, p-value = 0.09079
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 1.8887, p-value = 7.462e-05

> ad.y
	Anderson-Darling normality test
data:  y
A = 1.9821, p-value = 4.39e-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()