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 computationMon, 11 Jan 2016 10:47:10 +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/2016/Jan/11/t1452509242lld3e6x6f5za757.htm/, Retrieved Tue, 07 May 2024 07:04:26 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=289609, Retrieved Tue, 07 May 2024 07:04:26 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact57

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Pearson Correlation] [Vraag 2] [2016-01-11 10:47:10] [5c12abf8e1d909674bdd524d224ad2b3] [Current]
Feedback Forum

Post a new message

Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
6
7
2
11
13
3
17
10
4
12
7
11
3
5
1
12
18
8
6
1
Dataseries Y:
Download CSV
Histogram 
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
1
0

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'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 & 4 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=289609&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=289609&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=289609&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'Gertrude Mary Cox' @ cox.wessa.net






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean7.850.3
Biased Variance23.92750.21
Biased Standard Deviation4.891574388681010.458257569495584
Covariance-0.794736842105263
Correlation-0.336812841913255
Determination0.113442890477683
T-Test-1.51764968440214
p-value (2 sided)0.146470224220227
p-value (1 sided)0.0732351121101135
95% CI of Correlation[-0.678243657206379, 0.124222960334379]
Degrees of Freedom18
Number of Observations20

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 7.85 & 0.3 \tabularnewline
Biased Variance & 23.9275 & 0.21 \tabularnewline
Biased Standard Deviation & 4.89157438868101 & 0.458257569495584 \tabularnewline
Covariance & -0.794736842105263 \tabularnewline
Correlation & -0.336812841913255 \tabularnewline
Determination & 0.113442890477683 \tabularnewline
T-Test & -1.51764968440214 \tabularnewline
p-value (2 sided) & 0.146470224220227 \tabularnewline
p-value (1 sided) & 0.0732351121101135 \tabularnewline
95% CI of Correlation & [-0.678243657206379, 0.124222960334379] \tabularnewline
Degrees of Freedom & 18 \tabularnewline
Number of Observations & 20 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=289609&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]7.85[/C][C]0.3[/C][/ROW]
[ROW][C]Biased Variance[/C][C]23.9275[/C][C]0.21[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]4.89157438868101[/C][C]0.458257569495584[/C][/ROW]
[ROW][C]Covariance[/C][C]-0.794736842105263[/C][/ROW]
[ROW][C]Correlation[/C][C]-0.336812841913255[/C][/ROW]
[ROW][C]Determination[/C][C]0.113442890477683[/C][/ROW]
[ROW][C]T-Test[/C][C]-1.51764968440214[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0.146470224220227[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0.0732351121101135[/C][/ROW]
[ROW][C]95% CI of Correlation[/C][C][-0.678243657206379, 0.124222960334379][/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]18[/C][/ROW]
[ROW][C]Number of Observations[/C][C]20[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=289609&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=289609&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
Mean7.850.3
Biased Variance23.92750.21
Biased Standard Deviation4.891574388681010.458257569495584
Covariance-0.794736842105263
Correlation-0.336812841913255
Determination0.113442890477683
T-Test-1.51764968440214
p-value (2 sided)0.146470224220227
p-value (1 sided)0.0732351121101135
95% CI of Correlation[-0.678243657206379, 0.124222960334379]
Degrees of Freedom18
Number of Observations20






Normality Tests
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 1.0361, p-value = 0.5957
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 3.8171, p-value = 0.1483
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 0.31387, p-value = 0.5188

> ad.y
	Anderson-Darling normality test
data:  y
A = 4.2123, p-value = 6.658e-11


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

> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 1.0361, p-value = 0.5957
alternative hypothesis: greater

 \tabularnewline

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 3.8171, p-value = 0.1483
alternative hypothesis: greater

 \tabularnewline

> ad.x
	Anderson-Darling normality test
data:  x
A = 0.31387, p-value = 0.5188

 \tabularnewline

> ad.y
	Anderson-Darling normality test
data:  y
A = 4.2123, p-value = 6.658e-11

 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=289609&T=2

[TABLE]
[ROW][C]Normality Tests[/C][/ROW]
[ROW][C]
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 1.0361, p-value = 0.5957
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 3.8171, p-value = 0.1483
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> ad.x
	Anderson-Darling normality test
data:  x
A = 0.31387, p-value = 0.5188

[/C][/ROW]
[ROW][C]
> ad.y
	Anderson-Darling normality test
data:  y
A = 4.2123, p-value = 6.658e-11

[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=289609&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=289609&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 = 1.0361, p-value = 0.5957
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 3.8171, p-value = 0.1483
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 0.31387, p-value = 0.5188

> ad.y
	Anderson-Darling normality test
data:  y
A = 4.2123, p-value = 6.658e-11


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()