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 computationSun, 18 Dec 2016 16:21:40 +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/18/t1482075422qxkqji026ef9pn0.htm/, Retrieved Fri, 01 Nov 2024 03:43:02 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=301141, Retrieved Fri, 01 Nov 2024 03:43:02 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact82

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Pearson Correlation] [] [2016-12-18 15:21:40] [c6ea875f0603e0876d03f43aca979571] [Current]
Feedback Forum

Post a new message

Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
9
8
10
10
9
10
9
13
11
10
8
9
10
10
10
11
9
7
11
11
10
10
10
9
9
9
10
11
10
8
10
4
8
13
10
9
11
10
9
10
10
11
12
10
10
8
10
9
11
12
7
9
11
8
9
9
9
7
9
9
9
11
7
11
7
12
8
9
9
11
9
8
9
10
13
11
9
9
10
9
11
11
8
8
7
9
11
8
11
10
9
Dataseries Y:
Download CSV
Histogram 
10
13
14
13
14
14
12
12
11
12
14
13
13
12
12
13
10
12
13
10
14
10
10
14
14
10
13
12
12
10
14
8
10
14
12
14
13
13
13
14
11
10
13
12
13
11
10
14
13
15
13
14
13
11
14
14
12
13
13
10
12
9
12
13
13
11
12
11
12
12
13
8
13
8
13
15
14
11
14
10
15
12
13
12
9
14
14
12
15
12
11

Tables (Output of Computation)





Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time3 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 time3 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301141&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]3 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=301141&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301141&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 time3 seconds
R ServerBig Analytics Cloud Computing Center






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean9.5494505494505512.2527472527473
Biased Variance2.181620577224972.76029465040454
Biased Standard Deviation1.477031000766391.66141344956773
Covariance0.648473748473749
Correlation0.261352214470255
Determination0.068304980008506
T-Test2.55437291480595
p-value (2 sided)0.0123378454193214
p-value (1 sided)0.00616892270966069
95% CI of Correlation[0.0585592686649189, 0.443429832351301]
Degrees of Freedom89
Number of Observations91

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 9.54945054945055 & 12.2527472527473 \tabularnewline
Biased Variance & 2.18162057722497 & 2.76029465040454 \tabularnewline
Biased Standard Deviation & 1.47703100076639 & 1.66141344956773 \tabularnewline
Covariance & 0.648473748473749 \tabularnewline
Correlation & 0.261352214470255 \tabularnewline
Determination & 0.068304980008506 \tabularnewline
T-Test & 2.55437291480595 \tabularnewline
p-value (2 sided) & 0.0123378454193214 \tabularnewline
p-value (1 sided) & 0.00616892270966069 \tabularnewline
95% CI of Correlation & [0.0585592686649189, 0.443429832351301] \tabularnewline
Degrees of Freedom & 89 \tabularnewline
Number of Observations & 91 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301141&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]9.54945054945055[/C][C]12.2527472527473[/C][/ROW]
[ROW][C]Biased Variance[/C][C]2.18162057722497[/C][C]2.76029465040454[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]1.47703100076639[/C][C]1.66141344956773[/C][/ROW]
[ROW][C]Covariance[/C][C]0.648473748473749[/C][/ROW]
[ROW][C]Correlation[/C][C]0.261352214470255[/C][/ROW]
[ROW][C]Determination[/C][C]0.068304980008506[/C][/ROW]
[ROW][C]T-Test[/C][C]2.55437291480595[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0.0123378454193214[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0.00616892270966069[/C][/ROW]
[ROW][C]95% CI of Correlation[/C][C][0.0585592686649189, 0.443429832351301][/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]89[/C][/ROW]
[ROW][C]Number of Observations[/C][C]91[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301141&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301141&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
Mean9.5494505494505512.2527472527473
Biased Variance2.181620577224972.76029465040454
Biased Standard Deviation1.477031000766391.66141344956773
Covariance0.648473748473749
Correlation0.261352214470255
Determination0.068304980008506
T-Test2.55437291480595
p-value (2 sided)0.0123378454193214
p-value (1 sided)0.00616892270966069
95% CI of Correlation[0.0585592686649189, 0.443429832351301]
Degrees of Freedom89
Number of Observations91






Normality Tests
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 8.325, p-value = 0.01557
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 5.98, p-value = 0.05029
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 2.0607, p-value = 2.78e-05

> ad.y
	Anderson-Darling normality test
data:  y
A = 2.5064, p-value = 2.22e-06


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

> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 8.325, p-value = 0.01557
alternative hypothesis: greater

 \tabularnewline

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 5.98, p-value = 0.05029
alternative hypothesis: greater

 \tabularnewline

> ad.x
	Anderson-Darling normality test
data:  x
A = 2.0607, p-value = 2.78e-05

 \tabularnewline

> ad.y
	Anderson-Darling normality test
data:  y
A = 2.5064, p-value = 2.22e-06

 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301141&T=2

[TABLE]
[ROW][C]Normality Tests[/C][/ROW]
[ROW][C]
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 8.325, p-value = 0.01557
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 5.98, p-value = 0.05029
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> ad.x
	Anderson-Darling normality test
data:  x
A = 2.0607, p-value = 2.78e-05

[/C][/ROW]
[ROW][C]
> ad.y
	Anderson-Darling normality test
data:  y
A = 2.5064, p-value = 2.22e-06

[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301141&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301141&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 = 8.325, p-value = 0.01557
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 5.98, p-value = 0.05029
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 2.0607, p-value = 2.78e-05

> ad.y
	Anderson-Darling normality test
data:  y
A = 2.5064, p-value = 2.22e-06


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par2 = grey ; par3 = FALSE ; par4 = 5-point Likert ;
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()